Operation Management-ICAI-Inter-Production Planning and Productivity Management-Time Study, Work Study, Method Study & Job Evaluation
analysis is the study of the entire process to determine whether operations can be eliminated,
combined or the sequence changed. Operation analysis aims to determine the one best way and can be
applied to method, materials, tools equipment layout, working conditions and human requirements of
each operation.
Job standardisation consists in determining the one best way of performing a job under the means at
command of recording the exact method along with the time for each element of operation and establishing
means to maintain the standard conditions.
Another term connected with time and motion study is the job analysis. Job analysis is the determination
of essential factors in a specific kind of work and of the qualifications of a worker necessary for its
performance.
Time study aims at determining the best manner of doing a job and timing the performance of the job
when done in the best manner.
In motion study the work is divided into fundamental motions and in time study work is divided into
elements of operations. In both cases attempts are made to remove useless motions and improve combination
and sequences of motions and operations. In motion study the best way of doing a work is determined by
motion analysis and operators are trained to follow the method so determined but in time study the best
method is determined by analysis of the methods and equipment, used and motions only roughly considered
and that too indirectly. In time study, setting of production standards, standards for cost purposes and
wage incentives are emphasised. The measurement of human effort is a difficult job which can only be
solved by using scientific method and industrial experience combined with knowledge of psychology.
The use of scientific method involves experiment measurement and elimination of variables connected
with a job.
The variables connected with a job are the method of manufacture, tools and equipments, material, working
conditions, worker concerned and time required to perform the job. In order to measure the last variable
time, the other variables must be eliminated by standardising. In going to proceed for time study, it is first
necessary to standardise the method and conditions of work and to define what an average worker is.
Time study has two sides, mechanical and human.
Before commencing the time study, the time study man should ensure and ascertain the following:
• That motion studies have been carried out so that planning of work, work places and appliances are
satisfactory.
• That the operations can be performed in the correct; sequence without interruption.
• That the human effort involved is minimum.
• That the worker in question has average skill and diligence necessary for the work.
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Work Study:
It is a general term for the techniques: methods study and work measurement which are used in the
examination; of human work in all its contexts and systematically investigate all factors leading to
improvement of efficiency.
Work study aims at finding the best and most efficient way of using the available resources—men, materials,
money and machinery. Once the method study has developed an improved procedure for doing a work
the work measurement or time study will study the time to complete a job.
Method Study:
It is the systematic investigation of the existing method of doing a job in order to develop and install an
easy, rapid, efficient, effective and less fatiguing procedure for doing the same job and at minimum cost.
This is achieved by eliminating unnecessary motions involved in a certain operation or by changing the
sequence of operation or the process itself.
Methods study can be made by the help of both motion study and time study.
The methods study programme must include the following features:–
(a) Uniform application,
(b) Established standard practice,
(c) Continuous review,
(d) Credit distribution.
A new and improved method developed in one department should be spread out to the entire plant
preferably with further improvements.
A new method must not be forgotten between orders as it happens sometimes in batch production. Methods
department should always aim at improved and better ways of doing jobs.
For successful control of methods study, the enthusiastic cooperation of every employee is required. To
gain employee cooperation, distribution of credit is essential. It has been correctly said that a good methods
department rarely takes credit for an original idea. Its success lies in getting new ways and methods adopted
promptly, universally, continuously and cooperatively towards the improvement of productivity.
Job Evaluation:
Job evaluation is the ranking grading, and weighing of essential work characteristics of all jobs in order to
find out or rate the worth of jobs. It is a systematic approach to ascertain the labour worth of each job and
is a very important concern of all employers.
Job evaluation aims at fairness and consistency so far as all wages and salaries are concerned within an
organisation and when systematic and impartial, it stimulates, confidence of the employees. There are
three steps for evaluations of all jobs :–
(i) Preparation of preliminary description of each existing job.
(ii) Analysing each job to arrive at final job descriptions and specifications.
(iii) Analysing each job according to its approved description in order to determine its worth or value.
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Production Planning and Productivity Management
Job Description and Specifications: The understanding of the job content or job description is the primary
requirement.
Job specifications are derived from the job descriptions which have already been approved. The specification
help determining the qualification required of the individual desired for the position. This in turn guides
the personnel department in the selection of employees and also guides shop executives in the placement
of workmen.
Systems of Valuation: There are several systems of job evaluation.
The fundamental criteria in valuation of a job into account are to make a specific list of factors which affect
job values. The many factors are:
(i) Qualifications required of the worker,
(ii) Job difficulties,
(iii) Job responsibilities,
(iv) Working conditions.
All these factors are to be analysed in detail in order to complete the job description. The list of factors, the
manner in which they are apprised and the method of finding out relative worth and money values
distinguishes the various systems of valuation.
The systems of valuations which are commonly adopted are given below:
1. The ranking or grading method,
2. The factor comparison method,
3. Point rating method.
Ranking or Grading Method: Under this system the titles of all jobs are written on cards and the grading is
done by several competent judges. The hourly rates to be paid for different jobs are suggested by the
judges without any consideration to the existing wage. The ranks or grades assigned to each job by all the
judges are averaged and this average is considered the “score” for that job. Hourly rates are then fixed for
jobs according to their ranking.
Factor Comparison Method: The factor comparison method analyses the job into much greater detail than
the grading method. It ranks each job with respect to each factor that characterise the job and the factors
are taken one at a time.
All jobs are compared and ranked first with respect to mental requirements, then skill, then physical
requirements and after that responsibility and lastly working conditions. The total worth of the job is
obtained by adding together money values which are assigned separately to the various levels of rank in
each factor. Factor comparison method is more accurate than the simple ranking systems, since the separate
factors are analysed comparatively. This method is flexible.
Point Rating Method: There are three methods of analytical evaluation of a job. They are:
1. Straight point method.
2. Weighted point method.
3. Valuation of jobs directly in money method, not specifying any maximum weight.
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Straight Point Method: This method assigns equal weights for each characteristic. When evaluating a job
under this system, it is assumed that all the characteristics have ranges of values between same maximum
and minimum points.
Weighted Point Method: In this method different points are assigned to the different characteristics of
doing jobs.
Direct to Money Methods: After selecting the job characteristics, ten key jobs whose rates are believed to
be correct, are taken and the present wage rates of these jobs are distributed to the job characteristics by
each analyst. The jobs are then ranked by the analysts for each characteristic in order of the degree to which
that characteristic is present. This serves as a check to show up any errors made in the original distribution
of the wages rate to the various characteristics.
Problems and Solutions
Problem: 1
Continuous stopwatch study observations for a job are given. Compute the standard time for the job, if the
total allowances are 15%.
Ele. Description Cycle time (min) P.R.
No. 1 2 3 4 5 6 7 8 9 10
A Loosen vice 0.09 0.49 0.89 1.31 1.70 2.09 2.50 2.88 3.29 3.71 90
B Set bar length 0.16 0.56 1.38 1.38 1.76 2.16 2.57 2.95 3.36 3.78 110
C Switch m/c 0.28 0.67 1.49 1.49 1.88 2.28 2.68 3.07 3.40 3.90 120
D Unlock arm & 0.41 0.80 1.61 1.61 2.00 2.41 2.80 3.20 3.62 4.03 100
set saw
Solution:
The individual element cycle timing is computed from the cumulative cycle times as shown in table
below:
Ele. Cycle time (min) Avg. Normal
No. 1 2 3 4 5 6 7 8 9 10 time time
A 0.09 0.08 0.09 0.10 0.09 0.09 0.09 0.08 0.09 0.09 0.089 0.080
B 0.07 0.07 0.06 0.07 0.06 0.07 0.07 0.07 0.07 0.07 0.068 0.075
C 0.12 0.11 0.12 0.11 0.12 0.12 0.11 0.12 0.13 0.12 0.118 0.142
D 0.13 0.13 0.14 0.12 0.12 0.13 0.12 0.13 0.13 0.13 0.128 0.128
Total 0.425
Standard time =
0.425
1 − 0.15 = 0.500 minutes.
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Production Planning and Productivity Management
Problem: 2
The work - study engineer carries out the work sampling study. The following observations were made for
a machine shop.
Total number of observations 7000
No. Working activities 1200
Ratio between manual to machine elements 2:1
Average rating factor 120%
Total number of jobs produced during study 800 units
Rest and personal allowances 17%
Compute the standard time for the job.
Solution:
(i) Overall time per unit (To) =
Duration of study
Number of jobs produced during study =
120 60
800
×
= 9 min.
(ii) Effective time per piece (Te) = To ×
Productive observations
Total observations
= 9 ×
5800
7000
= 7.46 min.
The effective time is to be segregated into manual time and machine element time.
Machine controlled time per piece (Tm) = 7.46 × 1/3 = 2.49 min
Hand controlled time per piece (Th) = 7.46 × 2/3 = 4.97 min
Normal time per piece = Tm + Th × performance rating = 2.49 + 4.97 × 1.2 = 8.46 min.
Standard time per piece = 8.46 (1 + 0.17) = 9.9 minutes.
Problem: 3
The time study of a machinery operation recorded cycle times of 8.0, 7.0, 8.0 and 9.0 minutes. The analyst
rated the observed worker as 90%. The firm uses a 0.15 allowance fraction. Compute the standard time.
Solution:
Average cycle time =
8.0 7.0 8.0 9.0
4
+ + +
= 8.0 minutes.
Normal time = 8.0 × 0.9 = 7.2 minutes.
Standard time =
7.2
(1-0.15) = 8.47 minutes.
The standard time for this machinery operation would be set at 8.47 minutes, which is greater than
the average cycle time observed. The average cycle time was adjusted for the rating factor (90%) and
the allowance fraction (0.15).
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Problem: 4
An analyst wants to obtain a cycle time estimate that is within ± 5% of the true value. A preliminary run of
20 cycles took 40 minutes to complete and had a calculated standard deviation of 0.3 minutes. What is the
coefficient of variation to be used for computing the sample size for the forthcoming time study?
Solution:
Standard deviation of sample(s) = 0.3 min/cycle.
Mean of sample = x =
40 min
20 cycle = 2 min./cycle;
V =
s
x
=
0.3
2
= 0.15
Problem: 5
A job has been time standard for 20 observations. The mean actual time was 5.83 minutes and the standard
deviation of the time is estimated to be 2.04 minutes. How many total observations should be taken for
95% confidence that the mean actual time has been determined within 10%?
Solution:
n =
2 Zs
Ax
⎛ ⎞
⎜ ⎟
⎝ ⎠ =
( )
( )
2 1.96 2.04
0.10 5.83
⎡ ⎤
⎢ ⎥
⎣ ⎦
= 47
Therefore, a total of 47 observations should be made. Since 20 observations have already been made,
only 27 more are necessary.
Problem: 6
An analyst has observed a job long enough to become familiar with it and has divided it into five elements.
The element times for the first four cycles and a performance rating for each element are given in the
following table,
Element Cycle Cycle Cycle Cycle Performance
1 2 3 4 Rating (%)
1 1.246 1.328 1.298 1.306 90
2 0.972 0.895 0.798 0.919 100
3 0.914 1.875 1.964 1.972 100
4 2.121 2.198 2.146 2.421 110
5 1.253 1.175 1.413 2.218 100
(a) Do any of the times look like outliners, i.e. probable errors in reading or recording data that
should not be included in the analysis?
(b) Compute an estimated normal time for the job based on the data available at this stage of the study.
(c) On the basis of the data available, what sample size should be taken to estimate the time for
element 2 within 5% of the true mean time with 95% confidence?
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Production Planning and Productivity Management
Solution:
(a) The times for element 3 in cycle 1 and for element 5 in cycle 4 are suspect and should be
disregarded.
(b) The following estimates are made on the basis of the remaining times
Element Mean actual time Performance Rating (%) Normal time
1 1.295 90 1.116
2 0.896 100 0.896
3 1.937 100 1.937
4 2.222 110 2.444
5 1.28 100 1.28
Normal time for total job = 7.723
(c) For element 2:
x = 0.896
S =
( )2
2
1
x
x
n
n
−
′
′ −
Σ
Σ =
( )2 3.227174 – 3.584
4
3
= 0.0728
n =
2 Zs
Ax
⎛ ⎞
⎜ ⎟
⎝ ⎠ =
( )
( )
2 1.96 0.0728
0.05 0.896
⎡ ⎤
⎢ ⎥
⎣ ⎦
= 10.14
The analyst probably would want to use more than 10 observation, so that workers would have more
confidence in the standard. A Company might make it a general practice to use at least say 15 or more
observations.
Problem: 7
Stopwatch time study figure for a job which is continuous in nature are given below. Calculate the Standard
Time for the job assuming that the sample size is adequate, and total allowances are 15 percent.
Ele. Description Cycle time (min) P.R.
No. per cycle 1 2 3 4 5 6 7 8 9 10
1 A 0.10 0.50 0.90 1.32 1.71 2.10 2.51 2.89 3.30 3.72 90
2 B 0.17 0.57 0.96 1.39 1.77 2.17 2.58 2.96 3.37 3.79 110
3 C 0.29 0.68 1.08 1.50 1.89 2.29 2.69 3.08 3.41 3.91 120
4 B 0.15 0.81 1.22 1.62 2.01 2.42 2.81 3.21 3.63 4.04 100
Solution:
From the continuous study figure the individual time figures are derived.
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Cycle time (min) Normal
Ele. Description 1 2 3 4 5 6 7 8 9 10 Arithmetic time of
No. per cycle Average element
(min)
1 A 0.10 0.08 0.09 0.10 0.09 0.09 0.09 0.08 0.09 0.09 0.090 0.081
2 B 0.07 0.07 0.06 0.07 0.06 0.07 0.07 0.07 0.07 0.07 0.068 0.075
3 C 0.12 0.11 0.12 0.11 0.12 0.12 0.11 0.12 0.13 0.12 0.118 0.142
4 D 0.13 0.13 0.14 0.12 0.12 0.13 0.12 0.13 0.13 0.13 0.128 0.128
Total time = 0.426 min
Standard time = 0.426 ÷ (1 - 0.15) = 0.501 min
2.1 Production Planning and Control Introduction
Production planning control can be viewed as the nervous system of a production operation. The primary
concern of production planning and control is the delivery of products to customers or to inventory stocks
according to some predetermined schedule. All the activities in the manufacturing or production cycle
must be planned, coordinated, organised, and controlled to achieve this objective. From a long-term point
of view (usually from seven to ten years or more) production planning largely deals with plant construction
and location and with product-line, design and development. Short-range planning (from several months
to a year) focuses on such areas as inventory goals and wage budgets. In plans projected over a two-to-five
year period, capital-equipment budgeting and plant capacity and layout are the major concern. Production
planning and control normally reflects the short range activities and focuses on the issues and problems
that arise in the planned utilisation of the labour force, materials, and physical facilities that are required
for manufacturing the products in accordance with the primary objectives of the firm.
Production systems are usually designed to produce a variety of products and are, therefore, complex. In
such complex systems, anything can happen and usually it is so. Therefore, it is vital to exercise some kind
of control over the production activities. Control is possible only when everything is planned. Production
planning and control is thus a very important aspect of production management.
Objectives of production planning and control
The ultimate objective of production planning and control is to contribute to the profits of the enterprise.
This is accomplished by keeping the customers satisfied through the meeting of delivery schedules. Further,
the specific objectives of production planning and control are to establish the routes and schedules for
work that will ensure the optimum utilisation of raw materials, labourers, and machines to provide the
means for ensuring the operation of the plant in accordance with these plans. Production planning and
control is essentially concerned with the control of work-in-process. To control work-in-process effectively
it becomes necessary to control not only the flow of material but also the utilisation of people and machines.
Production planning and control fulfils these objectives by focusing on the following points:
Analysing the orders to determine the raw materials and parts that will be required for their completion,
Answering questions from customers and salesmen concerning the status of their orders,
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Production Planning and Productivity Management
Assisting the costing department in making cost estimates of orders,
Assisting the human resource departments in the manpower planning and assignment of men to
particular jobs,
Controlling the stock of finished parts and products,
Determining the necessary tools required for manufacturing,
Direction and control of the movement of materials through production process,
Initiating changes in orders as requested by customers while orders are in process,
Issuing requisitions for the purchase of necessary materials,
Issuing requisitions for the purchase or manufacture of necessary tools and parts,
Keeping the up-to-date records scheduled and in process,
Maintaining stocks of materials and parts,
Notifying sales and accounting of the acceptance of orders in terms of production feasibility,
Preparing the route sheets and schedules showing the sequence of operation required to produce
particular products,
Production of work orders to initiate production activities,
Receiving and evaluating reports of progress on particular orders and initiating corrective action, if
necessary,
Receiving orders from customers,
Revising plans when production activities cannot conform to original plans and when revisions in
scheduled production are necessary because of rush orders.
Production control involves the following functions:
Planning the production operations in detail,
Routing, i.e., laying down the path for the work to follow and the order in which the various operations
will be carried out,
Scheduling, i.e., establishing the quantity of work to be done, and fixing the time table for performing
the operations,
Dispatching, i.e., issuing the necessary orders, and taking necessary steps to ensure that the time
targets set in the schedules are effectively achieved,
Follow-up, taking necessary steps to check up whether work proceeds according to predetermined
plans and how far there are variances from the standards set earlier,
Inspection, i.e., conducting occasional check-ups of the products manufactured or assembled to ensure
high quality of the production.
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Figure : Techniques of Production Control
Basic types of production control:
Production control can be of six types:
• Block control
This type of control is most prominent in textiles and book and magazine printing. In these industries
it is necessary to keep things separated and this is the fundamental reason why industries resort to
block control.
• Flow control
This type of control is commonly applied in industries like chemicals, petroleum, glass, and some
areas of food manufacturing and processing. Once the production system is thoroughly designed, the
production planning and control department controls the rate of flow of work into the system and
checks it as it comes out of the system. But, under this method, routing and scheduling are done when
the plant is laid out. That is to say, the production line which is established is well balanced and
sequenced before production operations begin; this type of control is more prevalent in continuous
production systems.
• Load control
Load control is typically found wherever a particular bottleneck machine exists in the process of
manufacturing.
• Order control
The most, common type of production control is called order control. This type of control is commonly
employed in companies with intermittent production systems, the so-called job-lot shops. Under this
method, orders come into the shop for different quantities for different products. Therefore, production
planning and control must be based, on the individual orders.
• Special project control
Special production control is necessary in certain projects like the construction of bridges, office
buildings, schools, colleges, universities, hospitals and any other construction industries. Under this
type of control, instead of having sets of elaborate forms for tooling and scheduling, a man or a group
of men keeps in close contact with the work.
• Batch control
Batch control is another important, type of production control which is frequently found in the food
processing industries. Thus, production control in batch-system of control operates with a set of
ingredients that are proportionally related and handled one batch at a time.
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Production Planning and Productivity Management
Production planning and control in continuous-production systems.
Production systems may be continuous or intermittent. The continuous production systems are characterised by:
Fixed-path material handling equipment,
High volume of production,
Product layouts,
Production of standardised products,
Production to stock or long-range orders,
The use of special-purpose machines or automation.
Production planning and control in continuous-production systems involve two activities:
Assuring that supply of raw materials and supplies are on hand to keep the production system supplied
and assuring that finished products are moved from the production-system,
Maintaining a constant rate of flow of the production, so that the system can operate near capacity in
some case or can meet the quantity requirements of the production.
Production planning in intermittent production systems:
The intermittent production systems are characterized by the following:
General purpose production machines are normally utilised and process layout is favoured.
Materials handling equipment is typically of the varied path type such as hand trucks and forklift
trucks.
Relatively high cost, skilled labour is needed to turn out the various quantities and types of products.
The company generally manufactures a wide variety of products; for the majority of items, sales
volumes and consequently production order sizes are small in relation to the total production.
Problems and Solutions
Problem: 1
Machines K and L, both capable of manufacturing an industrial product, compare as follows:
Machine K Machine L
Investment Rs. 60,000 Rs. 1,00,000
Interest on borrowed capital 15% 15%
Operating cost (wages, power, etc.) per hour Rs. 12 Rs. 10
Production per hour 6 pieces 10 pieces
The factory whose overhead costs are Rs. 1,20,000 works effectively for 4,000 hours in 2 shifts during
the year. (i) Justify with appropriate calculations which of the two machines you would choose for
regular production. (ii) If only 4000 pieces are to be produced in a year, which machine would give the
lower cost per piece. (iii) For how many pieces of production per year would the cost of production be
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65
same on either machine? (For above comparisons, the cost of material may be excluded as being the
same on both machines.)
Solution:
Machine K Machine L
Annual interest charges (Rs. 60,000 x 15) / 100 (Rs. 1,00,000 x 15) / 100
(fixed cost) = Rs. 9,000 = Rs. 15,000
Annual operating charges 4,000 x 12 4,000 x 10
= Rs. 48,000 = Rs. 40,000
Total annual charges = Rs. 57,000 = Rs. 55,000
Annual output = 4,000 x 6 = 24,000 = 4,000 x 10 = 40,000
Cost per unit = 5,700 / 2,400 = 55,000 / 40,000
= Rs. 2.375 = Rs. 1.375
(i) Thus machine L should be chosen for regular production.
(ii) If only 4,000 pieces are to be produced in a year
Interest cost Rs. 9,000 Rs. 15,000
Operating cost (4,000 / 6) x 12 = Rs. 8,000 (4,000 / 10) x 10 = Rs. 4,000
Total cost = Rs. 17,000 = Rs. 19,000
Cost per unit (17,000 / 4,000) = Rs. 4.25 (19,000 / 4,000) = Rs. 4.75
Thus, machine K gives the lower cost per piece.
(iii) Interest charge = Rs. 9,000 = Rs. 15,000
Operating cost per piece = 12 / 6 = 2 = 10/10 = Re. 1
Let the production be = X units,
Then 2X + 9,000 = X + 15,000 or, 2X – X = 15,000 – 9,000 or, X = 6,000 pieces.
For 6,000 piece of production per year the cost of production will be the same (Rs. 21,000) on either
machine.
Problem: 2
A department of a company has to process a large number of components/month. The process equipment
time required is 36 minutes/component, whereas the requirement of an imported process chemical is 1.2
litres/component. The manual skilled manpower required is 12 minutes/component for polishing and
cleaning. The following additional data is available:
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Production Planning and Productivity Management
Availability/month Efficiency of utilisation
Equipment hour 500 85%
Imported chemicals 1000 95%
Skilled manpower - hours 250 65%
(i) What is the maximum possible production under the current conditions? (ii) If skilled manpower
availability is increased by overtime by 20%, what will be the impact on production
increase?
Solution:
(i) Actual Equipment Hrs. used = 500 × 85/100 = 425 Hrs.
Possible output = 425 × (60/36) = 708 Components
(ii) Imported chemicals = 1,000 × 95/100 = 950 litres, actually used;
Possible output = 950/1.2 = 792 Components
(iii) Skilled manpower Hrs. used = 250 × 65/100 = 162.5 Hrs.
Possible output =162.5 × (60/12) = 813 Components
The bottleneck capacity = 708 Components.
(1) Maximum possible production under the given conditions = 708 Components.
(2) There will be no impact on production increase if skilled manpower is increased by overtime by
20% as the bottleneck in output is equipment hours.
Problem: 3
A manufacturing enterprise has introduced a bonus system of wage payment on a slab-rate based on cost
of production towards labour and overheads.
The slab-rate being
1% - 10% saving in production cost 5% of saving
Between 11%-20% saving in production cost 15%
Between 21%-40% saving in production cost 30%
Between 41%-70% saving in production cost 40%
Above 70% saving in production cost 50%
The rate per hour for three workers A, B, C are Rs. 5, Rs. 5.50 and Rs. 5.25 respectively. The overhead
recovery rate is 500% of production wages and the material cost is Rs. 40 per unit. The standard cost of
production per unit is determined at Rs. 160 per unit.
If the time taken by A, B, C to finish 10 units is 26 hours, 30 hours and 16 hours respectively, what is the
amount of bonus earned by the individual workers and actual cost of production per unit?
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Solution:
A B C
Unit produced 10 10 10
Wage rate 5.00 5.50 5.25
Time taken 26 hours 30 hours 16 hours
Wage payable 130.00 165.00 84.00
Overhead recovery 650.00 825.00 420.00
Materials 400.00 400.00 400.00
Total cost of production 1,180.00 1,390.00 904.00
Standard cost of production 1,600.00 1,600.00 1,600.00
Saving in cost of production 420.00 210.00 696.00
% of savings 26.25% 13.13% 43.50%
Bonus slab 30% 15% 40%
Bonus Amount 126.00 31.50 278.40
Actual cost of production 1,306.00 1,421.50 1,182.40
Cost/unit (Rs.) 130.60 142.15 118.24
Problem: 4
Calculate the break-even point for the following:
Production Manager of a unit wants to know from what quantity he can use automatic machine against
semi-automatic machine.
Data Automatic Semi-automatic
Time for the job 2 mts 5 mts
Set up time 2 hrs 1.5 hrs
Cost per hour Rs. 20 Rs. 12
Solution:
Let x be the break-even quantity between automatic and semi-automatic machines. This means, for
volume of output V, the total cost of manufacture is the same on both automatic and semi-automatic
machines.
For quantity = x units
Total manufacturing cost on automatic machines =
2
2.0+
60
⎛ ⎞
⎜ ⎟
⎝ ⎠
x
× 20 Rs.
Total manufacturing cost on semi-automatic machines =
5
1.5+
60
⎛ ⎞
⎜ ⎟
⎝ ⎠
x
×12 Rs.
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Production Planning and Productivity Management
If ‘x’ is the break-even quantity, then
2
2.0+
60
⎛ x ⎞
⎜⎝ ⎟⎠ × 20 =
5
1.5+
60
⎛ x ⎞
⎜⎝ ⎟⎠ × 12
40 +
2
20
60
x × = 18 +
5
12
60
x ×
40 +
2
3
x
= 18 + x
x -
2
3
x
= 40 - 18 = 22
3
x
= 22
x = 66 units
Hence for quantity upto 65, a semi-automatic machine will be cheaper. For quantity 66, both semiautomatic
and automatic machines are equally costly. For quantity more than 66, automatic machine
becomes cheaper than semi-automatic machine.
Problem: 5
Two alternative set-ups, A and B are available for the manufacture of a component on a particular machine,
where the operating cost per hour is Rs. 20/-.
Set-up A Set-up B
Components/set-up 4,000 pieces 3,000 pieces
Set-up cost Rs. 300/- Rs.1,500/-
Production rate/hour 10 pieces 15 pieces
Which of these set-ups should be used for long range and economic production?
Solution:
Considering one set-up
Set-A Set-up B
Set-up cost per year Rs. 300/- Rs. 1,500/-
Operating hours / set-up
4000
10
= 400 hours
3000
15
= 200 hours
Operating cost 400 x 20 = Rs. 8,000 200 x 20 = Rs. 4,000
Total manufacturing cost 300 + 8,000 = Rs. 8,300 1,500 + 4,000 = Rs. 5,500
Manufacturing cost per piece
8300
4000
= Rs. 2.075
5500
3000
= Rs. 1.833
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69
Assuming that the machine is used for production for one year having 2,000 hours of working. For
annual production,
Set-up A Set-up B
No. of set-ups
2000
400
= 5
2000
200
= 10
Set-up cost per year 5 x 300 = Rs. 1,500 10 x 1,500 = Rs. 15,000
No. of units produced per year 2,000 x 10 = Rs. 20,000 2,000 x 15 = Rs. 30,000
Total annual manufacturing cost 1,500 + 40,000 = Rs. 41,500 15,000 + 40,000 = Rs. 55,000
Manufacturing cost per unit
8300
4000
= Rs. 2.075
5500
3000
= Rs. 1.833
Since the manufacturing cost for set B is less, use set-up B for long range and economic production.
2.2 Forecasting
Forecasting means peeping into the future. As future is unknown and is anybody’s guess but the business
leaders in the past have evolved certain systematic and scientific methods to know the future by scientific
analysis based on facts and possible consequences. Thus, this systematic method of probing the future is
called forecasting. In this way forecasting of sales refers to an act of making prediction about future sales
followed by a detailed analysis of facts related to future situations and forces which may affect the business
as a whole.
Foresight is not the whole of management, but at least it is an essential part of management and accordingly,
to foresee in this context means both to assess the future and make provisions for it, that is forecasting is
itself action already. Forecasting as a kind of future picture wherein proximate events are outlined with
some distinctness, while remote events appear progressively less distinct and it entails the running of the
business as foresee and provide means to run the business over a definite period.
As far as the marketing manager is concerned the sales forecast is an estimate of the amount of unit sales
for a specified future period under the proposed marketing plan or program. It may also be defined as an
estimate of sales in rupees of physical units for a specified future period under a proposed marketing plan
or program and under an assumed set of economic and other force outside the organisation for which the
forecast is made.
When we consider the function of production and operations management, no doubt Production and
Operation departments will produce goods as per the sales program given by the sales department, but it
has to prepare forecast regarding machine capacity required, materials required and time required for
production and so on. This needs the knowledge of what exactly happened in the production shop in
previous periods.
Making of a proper forecast requires the assessment of both controllable and uncontrollable factors (both
economic and non economic) inside and outside the organisation.
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Production Planning and Productivity Management
All business and industrial activities revolve around the sale and its future planning. To know what a
business will do we must know its future sales. So, sales forecasting is the most important activity in the
business because all other activities depend upon the sales of the concern. Sales forecasting as a guiding
factor for a firm because it enables the firm to concentrate its efforts to produce the required quantities, at
the right time at reasonable price and of the right quality. Sales forecasting is the basis of planning the
various activities i.e.; production activities, pricing policies, programme policies and strategies, personnel
policies as to recruitment, transfer, promotion, training, wages etc.
The period of forecasting, that is the time range selected for forecasting depends on the purpose for which
the forecast is made. The period may vary from one week to some years. Depending upon the period, the
forecast can be termed as ‘Short range forecasting’, medium range forecasting’ and ‘Long range forecasting’.
‘Short range forecasting period may be one week, two weeks or a couple of months. Medium range
forecasting period may vary from 3 to 6 months. Long range forecasting period may vary from one year to
any period. The objective of above said forecast is naturally different.
In general, short term forecasting will be of more useful in production planning. The manager who does
short range forecast must see that they are very nearer to the accuracy.
In long range forecast, the normal period used is generally 5 years. In some cases it may extends to 10 to 15
years also. The purpose of long range forecast is:
(i) To work out expected capital expenditure for future developments or to acquire new facilities,
(ii) To determine expected cash flow from sales,
(iii) To plan for future manpower requirements,
(iv) To plan for material requirement,
(v) To plan for Research and Development. Here much importance is given to long range growth factor.
In case of medium range forecasting the period may extend over to one or two years. The purpose of this
type of forecasting is:
(i) To determine budgetary control over expenses,
(ii) To determine dividend policy,
(iii) To find and control maintenance expenses,
(iv) To determine schedule of operations,
(v) To plan for capacity adjustments.
In case of short-term forecast, which extends from few weeks to three or six months and the following
purposes are generally served:
(i) To estimate the inventory requirement,
(ii) To provide transport facilities for finished goods,
(iii) To decide work loads for men and machines,
(iv) To find the working capital needed,
(v) To set-up of production run for the products,
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71
(vi) To fix sales quota,
(vii) To find the required overtime to meet the delivery promises.
Everyone who use the forecast for one purpose or the other expects that they need that forecast should be
accurate. But it is practically impossible to forecast accurately. But decisions are made everyday to run the
business by using the best information available with them. Management scientists have developed various
methods for forecasting. One has to decide which method has to be used to suit the information available
with him and to suit his needs. The manager, who is concerned with forecasting, must have knowledge of
factors influencing forecast. Various factors that influence the forecast are:
(i) Environmental changes,
(ii) Changes in the preference of the user,
(iii) Number of competitive products,
(iv) Disposable income of the consumer.
In forecasting the production important factors to be considered are:
(i) Demand from the marketing department,
(ii) Rate of labours absenteeism,
(iii) Availability of materials,
(iv) Available capacity of machines,
(v) Maintenance schedules,
(vi) Delivery date schedules.
Steps in forecasting
Whatever may be the method used for forecasting, the following steps are followed in forecasting.
(a) Determine the objective of forecast: What for you are making forecast? Is it for predicting the demand?
Is it to know the consumer’s preferences? Is it to study the trend? You have to spell out clearly the use
of forecast.
(b) Select the period over which the forecast will be made? Is it long-term forecast or medium-term forecast
or short-term forecast? What are your information needs over that period?
(c) Select the method you want to use for making the forecast. This method depends on the period selected
for the forecast and the information or data available on hand. It also depends on what you expect
from the information you get from the forecast. Select appropriate method for making forecast.
(d) Gather information to be used in the forecast. The data you use for making forecasting to produce the
result, which is of great use to you. The data may be collected by:
(i) Primary source: This data we will get from the records of the firm itself.
(ii) Secondary source: This is available from outside means, such as published data, magazines,
educational institutions etc.
(e) Make the forecast: Using the data collected in the selected method of forecasting, the forecast is made.
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Production Planning and Productivity Management
Forecasting Methods:
Methods or techniques of sales forecasting: Different authorities on marketing and production have devised
several methods or techniques of sales or demand forecasting. The sales forecasts may be result of what
market people or buyers say about the product or they may be the result of statistical and quantitative
techniques. The most common methods of sales forecasting are:
1. Survey of buyer’s inventions or the user’s expectation method: Under this system of sales forecasting
actual users of the product of the concern are contacted directly and they are asked about their intention
to buy the company’s products in an expected given future usually a year. Total sales forecasts of the
product then estimated on the basis of advice and willingness of various customers. This is most
direct method of sales forecasting.
The chief advantages of this method are:
(i) Sales forecast under this method is based on information received or collected from the actual
users whose buying actions will really decide the future demand. So, the estimates are correct.
(ii) It provides a subjective feel of the market and of the thinking behind the buying intention of the
actual uses. It may help the development of a new product in the market.
(iii) This method is more appropriate where users of the product are numbered and a new product is
to be introduced for which no previous records can be made available.
(iv) It is most suitable for short-run forecasting.
2. Collective opinion or sales force composite method: Under this method, views of salesmen, branch
manager, area manager and sales manager are secured for the different segments of the market.
Salesmen, being close to actual users are required to estimate expected sales in their respective territories
and sections. The estimates of individual salesmen are then consolidated to find out the total estimated
sales for the coming session. These estimates are then further examined by the successive executive
levels in the light of various factors like proposed changes in product design, advertising and selling
prices, competition etc. before they are finally emerged for forecasting.
3. Group executive judgement or executive judgement method: This is a process of combining, averaging
or evaluating, in some other way, the opinions and views of top executives. Opinions are sought from
the executives of different fields i.e., marketing; finance; production etc. and forecasts are made.
4. Experts’ opinions: Under this method, the organisation collects opinions from specialists in the field
outside the organisation. Opinions of experts given in the newspapers and journals for the trade,
wholesalers and distributors for company’s products, agencies or professional experts are taken. By
analysing these opinions and views of experts, deductions are made for the company’s sales, and
sales forecasts are done.
5. Market test method: Under this method seller sells his product in a part of the market for sometimes
and makes the assessment of sales for the full market on the bases of results of test sales. This method
is quite appropriate when the product is quite new in the market or good estimators are not available
or where buyers do not prepare their purchase plan.
6. Trend projection method: Under this method, a trend of company’s or industry’s sales is fixed with
the help of historical data relating to sales which are collected, observed or recorded at successive
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73
intervals of time. Such data is generally referred to as time series. The change in values of sales is
found out. The study may show that the sales sometimes are increasing and sometimes decreasing,
but a general trend in the long run will be either upward or downward. It cannot be both ways. This
trend is called secular trend. The sales forecasts with the help of this method are made on the assumption
that the same trend will continue in the future. The method which is generally used in fitting the
trend is the method of least squares or straight line trend method. With this method a straight line
trend is obtained. This line is called ‘line of best fit’. By using the formula of regression equation of Y
on X, the future sales are projected.
Calculation of trend.
The trend can be calculated by the least square method as follows:
(i) Find time deviations (X) of each period from a certain period and then find the sum of
time deviation ( ΣX).
(ii) Square the time deviation of each period (X2) and then find the sum of squares of each
period (ΣX 2).
(iii) Multiply time deviations with the sales of each period individually (XY) and add the
product of the column to find (ΣXY).
(iv) To find the trend (Y) this is equal to a + bX. The value of a and b may be determined by
either of the following two ways:
(a) Direct method. This method is applicable only when ΣX=0. To make ΣX=0, it is necessary that
the time deviations should be calculated exactly from the mid point of the series. Then, the values
of a and b will be calculated as follows:
a (average) =
Y
n
Σ
and b (rate of growth) = 2
XY
Y
Σ
Σ
This method is simple and direct.
(b) Indirect method. This method is somewhat difficult. This method can be applied in both the
cases where ΣX has any positive or negative values or ΣX is not equal to zero. The values of a and
b are calculated by solving the following two equations:
Σ Y = na + bΣ X
Σ XY = aΣ X + bΣ X2
By calculating the values of a and b in the above manner, the sales can be forecasted for any future
period by applying the formula Y = a + bX.
7. Moving average method: This is another statistical method to calculate the trend through moving
averages. It can be calculated as follows:
An appropriate period is to be determined for which the moving average is calculated. While
determining the period for moving averages, the normal cycle time of changes in the values of series
should be considered so that short-term fluctuations are eliminated. As far as possible, the period for
moving averages should be in odd numbers such as period of 3, 5 or 7 years. The period in even
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Production Planning and Productivity Management
numbers will create a problem in centralising the values of averages. The calculated values of moving
averages present the basis for determining the expected amount of sale.
8. Criteria of a good forecasting method: It cannot be said which method of sales forecasting is the best
because everyone has merits and demerits of its own. The suitability of a method depends on various
factors such as nature of theproduct, available time and past records, wealth and energy, degree of
accuracy and the forecaster etc. of an enterprise. However, in general, a good forecasting method
must possess the following qualifications.
(i) Accuracy: Accuracy of the forecasting figures is the life blood of the business because many
important plans and programmes, policies andstrategies are prepared and followed on the basis
of such estimates. If sales forecasts are wrong, the businessman suffer a big loss. Hence, the
method of forecasting to be applied must amount to maximum accuracy.
(ii) Simplicity: The method for forecasting should be very simple. If the method is difficult or technical,
then there is every possibility of mistake. Some information are collected from outside and that
will remain unanswered or inaccurate replies will be received, if the method is difficult.
Management must also be able to understand and have confidence in the method.
(iii) Economy: The method to be used should be economical taking into account the importance of
the accuracy of forecast. Costs must be weighed against the importance of the forecast to the
operations of the business.
(iv) Availability: The method should be such for which the relevant information may be available
immediately with reasonable accuracy. Moreover, the technique must give quick results and
useful information to the management.
(v) Stability: The data of forecasting should be such wherein the future changes are expected to be
minimum and are reliable for future planning for sometime.
(vi) Utility: The forecasting technique must be easily understandable and suitable to the management.
Problems and Solutions
Problem: 1
An investigation into the demand for colour TV sets in 5 towns has resulted in the following data:
Population of the town (in lakhs) X: 5 7 8 11 14
No of TV sets demanded (in thousands) Y: 9 13 11 15 19
Fit a linear regression of Y on X and estimate the demand for CTV sets for two towns with a population
of 10 lakhs and 20 lakhs.
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75
Solution:
Computation of trend values
Population Sales of CTV Squares of the Product of population and
(in lakhs) (in thousands) population sales of colour TV
X Y X² XY
5 9 25 45
7 13 49 91
8 11 64 88
11 15 121 165
14 19 196 266
ΣX = 45 Σy = 67 ΣX² = 455 ΣXY = 655
Regression equation of Y on X
Y = a + bX
To find the values of a and b, the following two equations are to be solved
ΣY = na + bΣX ... (i)
ΣXY = aΣX + bΣX2 ... (ii)
By putting the values we get
67 = 5a + 45b ... (iii)
655 = 45a + 455b ... (iv)
Multiplying equation (iii) by 9 and putting it as no. (v) we get,
603 = 45a + 405b ... (v)
By deducting equation (v) from equation (iv); we get 52 = 50b
b =
52
50
= 1.04
By putting the value of b in equation (iii), we get
67 = 5a + 45 × 1.04
or, 67 = 5a + 46.80
or, 67-46.80 = 5a
or, 5a = 20.20
or, a =
20.20
5
or a = 4.04
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Production Planning and Productivity Management
Now by putting the values of a, b and X (10 lakhs) in regression equation of Y on X, we get,
Y = a + bX
or, Y = 4.04 + 1.04 (10)
or, Y = 4.04 + 10.40 or 14.44 thousand CTV sets.
Similarly sales estimates for town having population of 20 lakhs, by putting the values of X, a and b in
regression equation can be found as
Y = 4.04 + 1.04 (20)
= 4.04 + 20.80 = 24.84 thousands CTV sets.
Hence expected demand for CTV for two towns will be 14.44 thousand and 24.84 thousand CTV sets.
Problem: 2
The annual sales of truck tyres manufactured by a company are as follows—
Year (X) 2002 2003 2004 2005 2006
Sales (‘000 units) (Y) 53 64 86 54 83
Fit a linear trend equation to the sales figures and estimate the sales for 2007.
Solution:
Computation of Trend Values
Years Time Deviation Sales in Squares of Product of time
from 2004 (‘000 units) time dev. deviations and sales
X Y mX² XY
2002 –2 53 4 –106
2003 –1 64 1 –64
2004 0 86 0 0
2005 +1 54 1 +54
2006 +2 83 4 +166
n = 5 ΣX = 0 ΣY = 340 ΣX² = 10 ΣXY = + 50
Regression equation of Y on X—
Y = a + bX
For calculating the values of a and b
a =
ΣY
n
=
340
5
or 68
b = 2
50
10
=
Σ
Σ
XY
X = 5
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77
Hence, regression equation comes to Y = 68 + 5X with the help of this equation, the trend value for
2007 can be calculated as follows—
Y2007 = 68 + 5(5) = 68 + 25 = 93
The estimated sales for 2007 will be 93,000 units.
Problem: 3.
From the following time series data of sale project the sales for the next three years.
Year 2001 2002 2003 2004 2005 2006 2007
Sales (`000 units) 80 90 92 83 94 99 92
Solution.
Computation of Trend Values
Years Time Deviation Sales in Squares of Product of time
from 2004 (`000 units) time dev. deviations and sales
X Y X² XY
2001 –3 80 9 –240
2002 –2 90 4 –180
2003 –1 92 1 –92
2004 0 83 0 0
2005 +1 94 1 +94
2006 +2 99 4 +198
2007 +3 92 9 +276
n = 5 ΣX = 0 ΣY = 630 ΣX² = 28 ΣXY = + 56
Regression equation of Y on X
Y = a + bX
To find the values of a and b
a =
ΣY
n
=
630
7
= 90
b = 2
XY
X
Σ
Σ =
56
28
= 2
Hence regression equation comes to Y = 90 + 2X. With the help of this equation we can project the
trend values for the next three years, i.e. 2008, 2009 and 2010.
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Production Planning and Productivity Management
Y2008 = 90 + 2(4) = 90 + 8 = 98 (000) units.
Y2009 = 90 + 2(5) = 90 + 10 = 100 (000) units.
Y2010 = 90 + 2(6) = 90+ 12= 102 (000) units.
Problem: 4
Project the trend of sales for the next 5 years from the following data –
Year 2003 2004 2005 2006 2007
Sales (‘000units) 120 140 120 150 170
Solution.
Calculation of trend values of sales
Years Sales Time deviation Squares of Product of time
(in lakh of Rs.) (from 2005) time deviation deviations and sales
Y X X² XY
2003 120 –2 4 –240
2004 140 –1 1 –140
2005 120 0 0 0
2006 150 +1 1 150
2007 170 +2 4 340
n = 5 ΣY = 700 ΣX = 0 ΣX² = 10 ΣXY = 110
Regression equation of Y on X
Y = a + bX
To find values of a and b
a =
Y
n
Σ
=
700
5
= 140
b = 2
XY
X
Σ
Σ =
110
10
= 11
Hence regression equation is a + bX or 140 + 11X. With the help of this equation we can project the
trend for the next five years as follows:
Y2008 = 140 + 11 × 3 = 140 + 33 = 173 lakh rupees.
Y2009 = 140 + 11 × 4 = 140 + 44 = 184 lakh rupees.
Y2010 = 140 + 11 × 5 = 140 + 55 = 195 lakh rupees.
Y2011 = 140 + 11 × 6 = 140 + 66 = 206 lakh rupees.
Y2012 = 140 + 11 × 7= 140 + 77 = 217 lakh rupees.
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79
Problem: 5
An investigation into the use of scooters in 5 towns has resulted in the following data:
Population in town
Population in town (X) 4 6 7 10 13
(in lakhs)
No. of scooters (Y) 4,400 6,600 5,700 8,000 10,300
Fit a linear regression of Y on X and estimate the number of scooters to be found in a town with a
population of 16 lakhs.
Solution:
Computation of trend value
Population No. of scooters Squares of Product of population and
(in lakhs) demanded population No. of scooters demanded
X Y X² XY
4 4,400 16 17,600
6 6,600 436 39,600
7 5,700 49 39,900
10 8,000 100 80,000
13 10,300 169 1,33,900
ΣX = 40 ΣY = 35,000 ΣX² = 370 ΣXY = 3,11,000
Regression equation of Y on X
Y = a + bX
To find the values of a and b we will have to solve the following two equations
ΣY = na + bΣX ... (i)
ΣXY = aΣX + bΣX2 ....(ii)
By putting the values, we get
35,000 = 5a + 40b ... (iii)
3,11,000 = 40a + 370b ... (iv)
By multiplying equation no. (iii) by 8 putting as equation (v) we get,
2,80,000 = 40a + 320b ... (v)
By subtracting equation (v) from equation (iv), we get
31,000 = 50b
or, 50b = 31,000
or, b =
31000
50
= 620
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Production Planning and Productivity Management
By substituting the value of b in equation no. (iii), we get
35,000 = 5a + 40b
or 35,000 = 5a + 40 × 620
or 35,000 = 5a + 24,800
or 10,200 = 5a
or a =
10200
5
= 2040
Now putting the value of a, b and X (16 lakhs) in regression equation of Y on X, we
get Y = a + bX
or, Y = 2040 + 620 (16)
or Y = 2040 + 9920
or Y = 11,960
Hence, the expected demand of scooters for a town with a population of 16 lakhs will be 11,960
scooters.
Problem 6.
An investigation into the demand for TV sets in 7 towns has resulted in the following data:
Population (m 000) X : 11 14 14 17 17 21 25
No. of TV sets demande Y : 15 27 27 30 34 38 46
Fit a linear regression of Y on X, and estimate the demand for TV sets for a town with a population of
30,000.
Solution
Population No. of TV sets Squares of Product of population and
(in ‘000) demanded population No. TV sets demanded
X Y X² XY
11 15 121 165
14 27 196 378
14 27 196 378
17 30 289 510
17 34 289 578
21 38 441 798
25 46 625 1150
ΣX = 119 ΣY = 217 ΣX² = 2157 ΣXY = 3957
n = 7
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81
Regression equation of Y on X:Y = a + bX
To find the value of a and b the equations are to be solved:
ΣY = na + bΣX ... (i)
ΣXY = aΣX + bΣX2 ... (ii)
By putting the values, we get
217 = 7a + 119b ...(iii)
3957 = 119a + 2157b ...(iv)
Multiplying equation no. (iii) by 17 and putting it as no. (v) we get
3689 = 119a + 2023b ...(v)
By deducting equation (v) from (iv)
we get 268 = 134b
or 134b = 268
or, b =
268
134
= 2
By substituting the value of b in equation no. (iii), we get
217 = 7a + 119 × 2
or 7a + 238 = 217
or 7a = 217 - 238 = -21 or a = -3
Now, by putting the values of a, b and X (i.e.,) in regression equation of Y on X, we get
Y = -3 + 2 × 30 = -3 + 60 = 57
Hence, the expected demand for TV sets for a town with a population of 30,000 will be 57 sets.
Problem 7:
An investigation into the demand for coolers in 5 towns has resulted in the following data:
Population of the town X : 5 7 8 11 14
(in lakhs)
No. of coolers demanded Y : 45 65 55 75 95
Fit a linear regression of Y on X and estimate the demand for coolers for a town with a population of
25 lakhs.
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Production Planning and Productivity Management
Solution:
Computation of demand for coolers for a population of 20 lakhs
Towns Population of No. of coolers Squares of Production and no.
town (in lakhs) demanded population of coolers demanded
X Y X² XY
A 5 45 25 225
B 7 65 49 455
C 8 55 64 440
D 11 75 121 825
E 14 95 196 1,330
n = 5 ΣX = 45 ΣY = 335 ΣX² = 455 ΣXY = 3,275
Regression equation of Y on X.
Y = a + bX
To find the values of a and b the following two regression equations are to be solved :
ΣY = na + bΣX .....(i)
ΣXY = aΣX + bΣX2 .....(ii)
By putting the values, we get
335 = 5a + 45b .... (iii)
3,275 = 45a + 455b .... (iv)
By multiplying equation (iii) by 9, we get
3,015 = 45a + 405b .... (v)
By subtracting equation (v) from (iv) we get
45a + 455b = 3,275
45a + 405b = 3,015
50b = 260
or b = 260/50 = 5.2
By putting the value of b in equation (iii), we get
335 = 5a + 45 × 5.2
or 5a = 335 - 234 = 101
or a = 101/5 = 20.2
By putting the value of a, b and X (which is 20) in regression equation of Y on X, we get
Y = a + bX
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83
Y = 20.5 + 5.2 (20)
Y = 20.2 + 104 = 124.2 or 124
or say expected demand for room coolers for a town having a population of 20 lakhs will be 124 room
coolers.
Problem: 8
An investigation into the demand for coolers in five towns has resulted in the following data:
Population of the town X : 4 6 7 10 13
(in lakhs)
No. of coolers demanded Y : 40 60 50 70 90
Fit a linear regression of Y on X and estimate the demand for coolers for a town with a population of
20 lakhs.
Solution:
Computation of trend values of sales.
Towns Population Demand for Squares of Product of Population Trend values
(in lakhs) room coolers population & demand XY (Y = a + bX)
X Y X² XY Y
A 4 40 16 160 20.40 + (5.2 x 4) = 41.2
B 6 60 36 360 20.4 + (5.2 x 6) = 51.6
C 7 50 49 350 20.4 + (5.2 x 7) = 56.8
D 10 70 100 700 20.4 + (5.2 x 10) = 72.4
E 13 90 169 1,170 20.4 + (5.2 x 13) = 88.0
n = 5 ΣX = 40 ΣY = 310 ΣX² = 370 ΣXY = 2,740 = 310
Regression equation of Y on X = Y = a + bX
To find out the value of a and b, the following two regression equations are to be solved:
ΣY = na + bΣX ... (i)
ΣXY = aΣX + bΣX2 ... (ii)
By putting the values in the above two equations
310 = 5a + 40b ...(iii)
2,740 = 40a + 370b ... (iv)
By multiplying the equation (iii) with 8 and deducting it from equation (iv)
2,480 = 40a + 320b ... (v)
2,740 = 40a + 370b ... (vi)
-260 = - 50b
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Production Planning and Productivity Management
or 50b = 260
or b = 260/50 = 5.2
By substituting the value of b in equation (iii)
310 = 5a + 40 × 5.2
or 5a = 310-208 = 102
or a = 102/5 = 20.4
Now by putting the values of a and b in regression equation of Y on X, we find the following equation:
Y = 20.4 + 5.2 (20) = 20.4 + 104 = 124.4 or say 124
Problem: 9
With the help of following data project the trend of sales for the next five years:
Years 2002 2003 2004 2005 2006 2007
Sales (in lakhs) 100 110 115 120 135 140
Solution:
Computation of trend values of sales
Year Time deviations from Sales Squares of Product of time
the middle of 2004 and (in lakh Rs.) time deviation deviation and sales
2005 assuring 5 years = 1
X Y X2 XY
2002 -5 100 25 -500
2003 -3 110 9 -330
2004 -1 115 1 -115
2005 +1 120 1 +120
2006 +3 135 9 +405
2007 + 5 140 25 +700
n = 6 ΣX = 0 ΣY = 720 ΣX² = 70 ΣXY = 280
Regression equation of Y on X:
Y = a + bX
To find the values of a and b
a =
ΣY
n
=
720
6
= 120
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85
b = 2
Σ
Σ
XY
X =
280
70
= 4
Sales forecast for the next years, i.e., 2008 to 2012
Y2008= 120 + 4 (+7) = 120 + 28 = Rs. 148 lakhs
Y2009 =120 + 4 (+9) = 120 + 36 = Rs. 156 lakhs
Y2010 = 120 + 4 (+11) = 120 + 44 = Rs. 164 lakhs.
Y2011 =120 + 4 (+13) = 120 + 52 = Rs. 172 lakhs.
Y2012 = 120 + 4 (+15) = 120 + 60 = Rs. 180 lakhs.
Problem: 10
There exists a relationship between expenditure on research and its annual profit. The details of the
expenditure for the last six years is given below. Estimate the profit when the expenditure is 6 units
Year Expenditure for research Annual Profit
(x) (y)
2001 2 20
2002 3 25
2003 5 34
2004 4 30
2005 11 40
2006 5 31
2007 6 ?
(One unit corresponds to 1 Crore Rs.)
Solution:
Year Expenditure for Annual Profit xy x²
research (x)
2001 2 20 40 4
2002 3 25 75 9
2003 5 34 170 25
2004 4 30 120 16
2005 11 40 440 121
2006 5 31 155 25
Total 30 180 1000 200
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Production Planning and Productivity Management
x =
30
6
= 5 and y =
180
6
= 30
The values a and b are computed as follows: for a linear regression equation
y = a + bX
b = 2 2
−
−
Σ
Σ
xy n x y
x nx
b =
1000 6 5 30
200 6 5 5
− × ×
− × × =
1000 900
200 150
−
− = 2
a = y – b x = 30 - 2 x 5 = 20
Thus, the model is y = 20 + 2x.
The profit when the expenditure is 6 units is
y = 20 + 2 × 6 = 32 units of Rs.
2.3 Capacity Planning and Utilization
Capacity Planning:
The effective management of capacity is the most important responsibility of production and operations
management. The objective of capacity management i.e., planning and control of capacity is to match the
level of operations to the level of demand.
Capacity planning is concerned with finding answers to the basic questions regarding capacity such as:
(i) What kind of capacity is needed?
(ii) How much capacity is needed?
(iii) When this capacity is needed?
Capacity planning is to be carried out keeping in mind future growth and expansion plans, market trends,
sales forecasting, etc. Capacity is the rate of productive capability of a facility. Capacity is usually expressed
as volume of output per period of time.
Capacity planning is required for the following:
• Sufficient capacity is required to meet the customers demand in time,
• Capacity affects the cost efficiency of operations,
• Capacity affects the scheduling system,
• Capacity creation requires an investment,
• Capacity planning is the first step when an organisation decides to produce more or new products.
Capacity planning is mainly of two types:
(i) Long-term capacity plans which are concerned with investments in new facilities and equipments.
These plans cover a time horizon of more than two years.
(ii) Short-term capacity plans which takes into account work-force size, overtime budgets, inventories
etc.
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87
Capacity refers to the maximum load an operating unit can handle. The operating unit might be a plant, a
department, a machine, a store or a worker. Capacity of a plant is the maximum rate of output (goods or
services) the plant can produce.
The production capacity of a facility or a firm is the maximum rate of production the facility or the firm is
capable of producing. It is usually expressed as volume of output per period of time (i.e., hour, day, week,
month, quarter etc.). Capacity indicates the ability of a firm to meet market demand - both current and
future.
Effective Capacity can be determined by the following factors:
Facilities - design, location, layout and environment.
Product - Product design and product-mix.
Process - Quantity and quality capabilities.
Human factors - Job content, Job design, motivation, compensation, training and experience of labour,
learning rates and absenteeism and labour turn over.
Operational factors - Scheduling, materials management, quality assurance, maintenance policies, and
equipment break-downs.
External factors - Product standards, safety regulations, union attitudes, pollution control standards.
Measurement of capacity
Capacity of a plant is usually expressed as the rate of output, i.e., in terms of units produced per period of
time (i.e., hour, shift, day, week, month etc.). But when firms are producing different types of products, it
is difficult to use volume of output of each product to express the capacity of the firm. In such cases,
capacity of the firm is expressed in terms of money value (production value) of the various products
produced put together.
Capacity Planning Decisions
Capacity planning involves activities such as:
(i) Assessing the capacity of existing facilities.
(ii) Forecasting the long-range future capacity needs.
(iii) Identifying and analysing sources of capacity for future needs.
(iv) Evaluating the alternative sources of capacity based on financial, technological and economical
considerations.
(v) Selecting a capacity alternative most suited to achieve strategic mission of the firm.
Capacity planning is necessary when an organisation decides to increase its production or introduce new
products into the market or to increase the volume of production to gain the advantages of economies of
scale. Once the existing capacity is evaluated and a need for new or expanded facilities is determined,
decisions regarding the facility location and process technology selection are undertaken.
When the long-range capacity needs are estimated through long-range forecasts for products, a firm may
find itself in one of the two following situations:
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Production Planning and Productivity Management
(i) A capacity shortage situation where present capacity is not enough to meet the forecast demand for
the product.
(ii) An excess or surplus capacity situation where the present capacity exceeds the expected future demand.
Factors affecting determination of plant capacity
(i) Capital investment required,
(ii) Changes in product design, process design, market conditions and product life cycles,
(iii) Flexibility for capacity additions,
(iv) Level of automation desired,
(v) Market demand for the product,
(vi) Product obsolescence and technology obsolescence and
(vii) Type of technology selected.
Forms of capacity planning:
Based on time-horizon
(i) Long-term capacity planning and
(ii) Short-term capacity planning
Based on amount of resources employed
(i) Finite capacity planning and
(ii) Infinite capacity planning
Factors Affecting Capacity Planning: Two kinds of factors affecting capacity planning are:
(i) Controllable Factors: amount of labour employed, facilities installed, machines, tooling, shifts of work
per day, days worked per week, overtime work, subcontracting, preventive maintenance and number
of production set ups.
(ii) Less Controllable Factors: absenteeism, labour performance, machine break-downs, material shortages,
scrap and rework, strike, lock-out, fire accidents etc.
Capacity Requirement Planning : Capacity requirement planning (CRP) is a technique which determines
what equipment and labour/personnel capacities are required to meet the production objectives (i.e., volume
of products) as per the master production schedule and material requirement planning (MRP-I).
Capacity Requirement Planning Strategies:
Two types of capacity planning strategies used are:
(i) “Level capacity” plan and
(ii) “Matching capacity with demand” plan.
Level capacity plan is based in “produce-to-stock and sell” approaches wherein the production systems
are operated at uniform production levels and finished goods inventories rise and fall depending upon
whether production level exceeds demand or vice versa from time period to time period (say every quarter
or every month).
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89
“Matching capacity with demand” Plan: In this plan, production capacity is matched with the demand in
each period (weekly, monthly or quarterly demand). Usually, material flows and machine capacity are
changed from quarter to quarter to match the demand. The main advantages are low levels of finished
goods inventory resulting in lesser inventory carrying costs. Also, the back-ordering cost is also reduced.
The disadvantages are high labour and material costs because of frequent changes in workforce (hiring,
training and lay-off costs, overtime or idle time cost or subcontracting costs).
Optimum Plant Capacity: Plant capacity has a great influence on cost of production with increasing volume
of production, economies of scale arises which results in reduction in average cost per unit produced.
For a given production facility, there is an optimum volume of output per year that results in the least
average unit cost. This level of output is called the “best operating level” of the plant.
As the volume of output increases outward from zero in a particular production facility, average unit costs
fall. These declining costs are because of the following reasons: (i) Fixed costs are spread over more units
produced, (ii) Plant construction costs are less, (iii) Reduced costs of purchased material due to quantity
discounts for higher volume of materials purchased and (iv) Cost advantages in mass production processes.
Longer production runs (i.e., higher batch quantity of products produced) have lesser setup cost per unit
of product produced, lesser scrap etc., resulting in savings which will reduce the cost of production per
unit. This is referred to as “economies of scale”. But this reduction in per unit cost will be only upto certain
volume of production. Additional volumes of outputs beyond this volume results in ever-increasing average
unit production cost. This increase in cost per unit arise from increased congestion of materials and workers,
which decreases efficiency of production, and due to other factors such as difficulty in scheduling, damaged
products, reduced employee morale due to excessive work pressure, increased use of overtime etc., resulting
in “diseconomies of scale”. Hence, the plant capacity should be such that the optimum level of production
which gives the minimum average cost of production per unit should be possible. This plant capacity is
referred to as optimum plant capacity.
Balancing the Capacity: In firms manufacturing many products (a product line or a product-mix) the load
on different machines and equipments vary due to changes in product-mix. When the output rates of
different machines do not match with the required output rate for the products to be produced, there will
be an imbalance between the work loads of different machines. This will result in some machine or equipment
becoming a “bottleneck work centre” thereby limiting the plant capacity which wills in-turn increase the
production costs per unit.
To overcome problem of imbalance between different machines, additional machines or equipments are
added to the bottleneck work-centre to increase the capacity of the bottle-neck work centre to match with
the capacity of other work centres. Adding new machines or equipments to bottleneck work centres to
remove the imbalance in capacity between various work centres is found to be economical than giving
excessive overtime to workers working in bottle-neck centres which increases production costs. Another
method to remove imbalance is to subcontract excess work load of bottleneck centres to outside vendors or
subcontractors. Another way to balance capacities is to try to change the productmix by manipulating the
sales for different products to arrive at a suitable product-mix which loads all work centres almost uniformly.
Implications of Plant Capacity
There are two major cost implications of plant capacity:
(i) Changes in output of an existing plant of certain installed capacity affect the production costs.
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Production Planning and Productivity Management
(ii) Changes in the plant capacity by changing the size of a plant have significant effects on costs.
Factors influencing Effective Capacity
The effective capacity is influenced by – (1) Forecasts of demand, (2) Plant and labour efficiency, (3)
Subcontracting, (4) Multiple shift operation, (5) Management policies.
Forecasts of demand: Demand forecast is going to influence the capacity plan in a
significant way. As such, it is very difficult to forecast the demand with accuracy as it changes significantly
with the product life-cycle stage, number of products. Products with long lifecycle usually exhibit steady
demand growth compared to one with shorter life-cycle. Thus the accuracy of forecast influences the capacity
planning.
Plant and labour efficiency: It is difficult to attain 100 per cent efficiency of plant and equipment. The
efficiency is less than 100 percent because of the enforced idle time due to machine breakdown, delays due
to scheduling and other reasons. The plant efficiency varies from equipment to equipment and from
organisation to organisation. Labour efficiency contributes to the overall capacity utilisation. The standard
time set by industrial engineer is for a representative or normal worker. But the actual workers differ in
their speed and efficiency. The actual efficiency of the labour should be considered for calculating efficiency.
Thus plant and labour efficiency are very much essential to arrive at realistic capacity planning.
Subcontracting: Subcontracting refers to off loading, some of the jobs to outside vendors thus hiring the
capacity to meet the requirements of the organisation. A careful analysis as to whether to make or to buy
should be done. An economic comparison between cost to make the component or buy the component is
to be made to take the decision.
Multiple shift operation: Multiple shifts are going to enhance the firm’s capacity
utilisation. But especially in the third shift the rejection rate is higher. Specially for process industries
where investment is very high it is recommended to have a multiple shifts.
Management policy: The management policy with regards to subcontracting, multiplicity of shifts (decision
regarding how many shifts to operate), which work stations or departments to be run for third shift, machine
replacement policy, etc., are going to affect the capacity planning.
Factors favouring over capacity and under capacity
It is very difficult to forecast demand as always there is an uncertainty associated with the demand. The
forecasted demand will be either higher or lower than the actual demand. So always there is a risk involved
in creating capacity based on projected demand. This gives rise to either over capacity or under capacity.
The over capacity is preferred when:
(a) Fixed cost of the capacity is not very high.
(b) Subcontracting is not possible because of secrecy of design and/or quality requirement.
(c) The time required to add capacity is long.
(d) The company cannot afford to miss the delivery, and cannot afford to loose the customer.
(e) There is an economic capacity size below which it is not economical to operate the plant.
The under capacity is preferred when:
(a) The time to build capacity is short.
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91
(b) Shortage of products does not affect the company (i.e., lost sales can be compensated).
(c) The technology changes fast, i.e., the rate of obsolescence of plant and equipment are high.
(d) The cost of creating the capacity is prohibitively high.
Aggregate Planning:
Aggregate planning is an intermediate term planning decision. It is the process of planning the quantity
and timing of output over the intermediate time horizon (3 months to one year). Within this range, the
physical facilities are assumed to be fixed for the planning period. Therefore, fluctuations in demand must
be met by varying labour and inventory schedule. Aggregate planning seeks the best combination to
minimise costs.
Production planning in the intermediate range of time is termed as ‘Aggregate Planning’. It is thus called
because the demand on facilities and available capacities is specified in aggregate quantities. For example
aggregate quantities of number of Automobile vehicles, Aggregate number of soaps etc. Here the total
expected demand is specified without regard to the product mix that makes up the specified figure.
While dealing with production problems, the planning process is normally divided in three categories.
(i) Long range Planning which deals with strategic decisions such as purchase of facilities, introduction
of new products, processes etc.
(ii) Short term planning which deals with day-to-day work, scheduling and sometimes inventory problems.
(iii) Intermediate Planning or Aggregate Planning, which is in between long range and short term planning,
which is concerned in generally acceptable planning taking the load on hand and the facilities available
into considerations. In aggregate planning the management formulates a general strategy by which
capacity can be made to satisfy demand in a most economical way during a specific moderate time
period, say for one year. The aggregate planning is made operational through a master schedule that
gives the manufacturing schedule (Products and dates of manufacture). Generally, day-to-day schedules
are prepared from master schedule. Facility planning and scheduling has got very close relationship
with aggregate planning.
Aggregate Planning Strategies:
The variables of the production system are labour, materials and capital. More labour effort is required to
generate higher volume of output. Hence, the employment and use of overtime (OT) are the two relevant
variables. Materials help to regulate output. The alternatives available to the company are inventories,
back ordering or subcontracting of items.
These controllable variables constitute pure strategies by which fluctuations in demand and uncertainties
in production activities can be accommodated.
Vary the size of the workforce: Output is controlled by hiring or laying off workers in proportion to changes
in demand.
Vary the hours worked: Maintain the stable workforce, but permit idle time when there is a slack and
permit overtime (OT) when demand is peak.
Vary inventory levels: Demand fluctuations can be met by large amount of inventory.
Subcontract: Upward shift in demand from low level. Constant production rates can be met by using
subcontractors to provide extra capacity.
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Production Planning and Productivity Management
Aggregate planning guidelines:
1. Determine corporate policy regarding controllable variables.
2. Use a good forecast as a basis for planning.
3. Plan in proper units of capacity.
4. Maintain the stable workforce.
5. Maintain needed control over inventories.
6. Maintain flexibility to change.
7. Respond to demand in a controlled manner.
8. Evaluate planning on a regular basis.
Properties of Aggregate Planning: To facilitate the production manager the aggregate planning must
have the following characteristics:
(i) Both out put and sales should be expressed in a logical overall unit of measuring. For example, an
automobile manufacturing can say 1000 vehicles per year, without giving the number of each verity
of vehicle. Similarly a paint industry can say 10,000 litres of paint and does not mention the quantities
of each colour.
(ii) Acceptable forecast for some reasonable planning period, say one year.
(iii) A method of identification and fixing the relevant costs associated with the plant. Availability of
alternatives for meeting the objective of the organization.
Ability to construct a model that will permit to take optimal or near optimal decisions for the sequence
of planning periods in the planning horizon.
(iv) Facilities that are considered fixed to carry out the objective.
Problems and Solutions
Problem 1:
A department works on 8 hours shift, 250 days a year and has the usage data of a machine, as given below:
Product Annual Processing time
demand (units) (standard time in hours)
X 300 4.0
Y 400 6.0
Z 500 3.0
Determine the number of machines required.
Solution:
Step 1: Calculate the processing time needed in hours to produce product x, y and z in the quantities
demanded using the standard time data.
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Product Annual Standard Processing
demand processing needed (Hrs.)
(units) per unit (Hrs.)
X 300 4.0 300 x 4 = 1200 Hrs.
Y 400 6.0 400 x 6 = 2400 Hrs.
Z 500 3.0 500 x 3 = 1500 Hrs.
Total = 5100 Hrs
Step 2 : Annual production capacity of one machine in standard hours
= 8 × 250 = 2000 hours per year
Step 3 : Number of machines required
=
Work load per year
Production capacity per machine =
5100
2000
= 2.55 machines = 3 machines.
Problem 2:
A steel plant has a design capacity of 50,000 tons of steel per day, effective capacity of 40,000 tons of steel
per day and an actual output of 36,000 tons of steel per day. Compute the efficiency of the plant and its
utilisation.
Solution:
Actual output
Efficiency of the plant =
Actual output 36000
100 90%
Effective Capacity 40000
⎛ ⎞ =⎜ ⎟× =
⎝ ⎠
Utilisation =
Actual output 36000
100 72%
Design Capacity 50000
⎛ ⎞⎛ ⎞ ⎜ ⎟=⎜ ⎟× =
⎝ ⎠ ⎝ ⎠
Problem 3:
An item is produced in a plant having a fixed cost of Rs. 6,000 per month, variable cost of rupees 2 per unit
and a selling price of Rs. 7 per unit. Determine
(a) The break-even volume.
(b) If 1000 units are produced and sold in a month, what would be the profit?
(c) How many units should be produced to earn a profit of Rs. 4000 per month?
Solution:
(a) Break-even-volume
Fixed cost (FC) = Rs. 6000 per month
Variable cost (VC) = Rs. 2 per unit
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Production Planning and Productivity Management
Selling price (SP) = Rs. 7 per unit
Let Q be the break even volume per month, then
Total cost = Fixed Cost + (Variable cost / unit) × Quantity
TC = FC + (VC ×Q) = 6000 + 2Q
Sales Revenue = Selling price per unit × Quantity = 7Q
For Q to be break-even volume,
Sales Revenue = Total cost
i.e., 7Q = 6000 + 2Q
5Q = 6000
Q =
6000
5
⎛ ⎞
⎜ ⎟
⎝ ⎠ = 1200 units / month
(b) For Q = 1000,
Profit = Sales Revenue - Total cost
= SR - (FC + VC × Q)
= (7 × 1000) - (6000 + 2 × 1000)
= (7000) - (6000 + 2000)
= Rs. 7000 - 8000 = -Rs 1000 (i.e., loss of Rs. 1000)
(c) For profit of Rs. 4000, What is Q?
SR = FC + (VC) Q + Profit
7Q = 6000 + 2Q + Profit
7Q - 2Q = Rs (6000 + 4000)
5Q = Rs. 10,000
Q =
10000
5
⎛ ⎞
⎜ ⎟
⎝ ⎠ = 2000 units
Problem 4:
A manager has to decide about the number of machines to be purchased. He has three options i.e., purchasing
one, or two or three machines. The data are given below.
Number of machine Annual fixed cost Corresponding range of output
One Rs. 12,000 0 to 300
Two Rs. 15,000 301 to 600
Three Rs. 21,000 601 to 900
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95
Variable cost is Rs. 20 per unit and revenue is Rs. 50 per unit
(a) Determine the break-even point for each range
(b) If projected demand is between 600 and 650 units how many machines should the manager purchase?
Solution:
(i) Break-even point
Let QBEP be the break even point.
FC = Fixed cost, R = Revenue per unit, VC = Variable cost
Then QBEPR = FC + (VC) QBEP
QBEP =
FC
(R – VC)
Let Q1 be the break-even-point for one machine option
Then, Q1=
12000
(50 – 20) =
12000
30
= 400 units
(Not within the range of 0 to 300)
Let Q2 be the break-even-point for two machines option.
Then, Q2 =
15000
(50 – 20) =
15000
30
= 500 units
(within the range of 301 to 600)
Let Q3 be the break-even-point for three machines option.
Then, Q3 =
21000
(50 – 20) =
21000
30
= 700 units
(with in the range of 601 to 900)
(ii) The projected demand is between 600 to 650 units.
The break even point for single machine option (i.e., 400 units) is not feasible because it exceeds the
range of volume that can be produced with one machine (i.e., 0 to 300).
Also, the break even point for 3 machines is 700 units which is more than the upper limit of projected
demand of 600 to 650 units and hence not feasible. For 2 machines option the break even volume is 500
units and volume range is 301 to 600.
Hence, the demand of 600 can be met with 2 machines and profit is earned because the production
volume of 600 is more than the break even volume of 500. If the manager wants to produce 650 units
with 3 machines, there will be loss because the break even volume with three machines is 700 units.
Hence, the manager would choose two machines and produce 600 units.
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Production Planning and Productivity Management
Problem 5:
A firm has four work centres, A, B, C & D, in series with individual capacities in units per day shown in the
figure below.
Work centres
Actual
Raw Output
materials (300)
(450) (360) (340) (400)
(i) Identify the bottle neck centre.
(ii) What is the system capacity?
(iii) What is the system efficiency?
Solution:
(i) The bottle neck centre is the work centre having the minimum capacity. Hence, work centre ‘C’ is
the bottleneck centre.
(ii) System capacity is the maximum units that are possible to produce in the system as a whole.
Hence, system capacity is the capacity of the bottle neck centre i.e., 340 units.
(iii) System efficiency =
Actual output
System capacity
=
300
340
x 100 (i.e., maximum possible output) = 88.23%
Problem 6.
A firm operates 6 days a week on single shift of 8 hours per day basis. There are 10 machines of the same
capacity in the firm. If the machines are utilised for 75 percent of the time at a system efficiency of 80
percent, what is the rated output in terms of standard hours per week?
Solution
Maximum number of hours of work possible per week
= (Number of machines) × (Machine hours worked per week)
= 10 ×6 × 8 = 480 hours
If the utilisation is 75% then number of hours worked = 480 × 0.75 = 360 hours.
Rated output = utilised hours × system efficiency = 360 × 0.8 = 288 standard hours.
Problem: 7
The order position (i.e., requirements of despatch) for the next twelve months in respect of a particular
product is as under:
A B C D
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97
Month Required units Month Required units
1 13,000 7 11,000
2 12,000 8 7,000
3 10,000 9 15,000
4 9,000 10 13,000
5 11,000 11 12,000
6 13,000 12 10,000
The production capacity or the shop is 10,000 units per month on regular basis and 3,000 units per
month on overtime basis. Sub-contracting can be relied upon up to a capacity of 3,000 units per month
after giving a lead time of 3 months. Cost data reveal as under: Rs. 5.00 per piece on regular basis Rs.
9.00 per piece on overtime basis Rs. 7.00 per piece on sub-contract basis Cost of carrying Inventory is
Re. 1.00 per unit per month. Assuming an initial inventory of 1,000 units and that no backlogging of
orders is permissible, suggest an optimal production schedule. Also work out the total cost on the
basis of the suggested schedule.
Solution:
The optimum production schedule is as follows:
Month Required No. of No. of Units Sub-contract Inventory
Units (‘000) Production (6000) (‘000 units) the end
Regular Over Order Delivered of month
Time Time placed for (‘000) units
1 13 10 2 — — 0
2 12 10 2 — — 0
3 10 10 0 3 — 0
4 9 10 0 1 — 1
5 11 10 0 — — 0
6 13 10 0 2 3 0
7 11 10 0 3 1 0
8 7 10 0 +2 — 3
9 15 10 0 — 2 0
10 13 10 0 — 3 0
11 12 10 0 — 2 0
12 10 10 0 — — 0
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Production Planning and Productivity Management
Cost of production on regular basis = Rs. 1,20,000 × 5 = Rs. 6,00,000;
Cost of production on overtime = Rs. 4,000 × 9 = Rs. 36,000; Cost of sub-contracting
= Rs. 11,000 × 7 = Rs. 77,000
Cost of carrying inventory = Rs. 4,000 × 1 = Rs. 4,000; Total cost on the basis of the suggested schedule=
(Rs.6,00,000 + Rs. 36,000 + Rs. 77,000 + Rs. 4,000) = Rs. 7,17,000
Problem: 8
A manufacturing company has a product line consisting of five work stations in series. The individual
workstation capacities are given. The actual output of the line is 500 units per shift.
Calculate (i) System capacity (ii) Efficiency of the production line
Workstation No. A B C D E
Capacity/Shift 600 650 650 550 600
Solution:
(i) The capacity of the system is decided by the workstation with minimum capacity/shift, i.e., the
bottleneck. In the given example, the work station ‘D’ is having a capacity of 550 units/ shift
which is a minimum.
Therefore, the system capacity = 550 units/shift. (ii) The actual output of the line = 500 units/shift.
Therefore, the system efficiency =
Actual capacity
System capacity x 100 =
500
550
x 100 = 90.91 %
Problem: 9
A company intends to buy a machine having a capacity to produce 1,70,000 good parts per annum. The
machine constitutes a part of the total product line. The system efficiency of the product line is 85%.
(i) Find the system capacity.
(ii) If the time required to produce each part is 100 seconds and the machine works for 2000 hours per
year. If the utilisation of the machine is 60% and the efficiency of the machine is 90%, compute the
output of the machine.
(iii) Calculate the number of machines required?
Solution:
(i) System capacity =
Actual output / annum
System efficiency =
1,70,000
0.85
= 2,00,000 units / annum
=
2,00,000
2,000 = 100 units/hours
(ii) Output per annum = Unit capacity × % utilisation × efficiency
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99
Unit capacity =
60 60 sec
100 sec per unit
×
= 36 units
Output per hour = 36 × 0.6 × 0.9 = 19.44 units = 20 units.
(iii) Number of machines required =
System capacity
Output per hour =
100
20
= 5 machines
Problem: 10
The following activities constitute a work cycle.
(i) Find the total time, theoretical output obtained from the machine.
(ii) Calculate the number of machines required to produce the three components from the information
given below.
Sr. No. Activity Time (min)
1. Unloading 0.25
2. Inspection 0.35
3. Loading job on machine table 0.40
4. Machine operation time 0.90
Components A B C
1. Setup time per batch 25 min 55 min 45 min
2. Operation time (min/piece) 1.75 3.0 2.1
3. Batch size 350 550 575
4. Production per month 2450 4400 2875
Solution:
(i) Total cycle time (T) = 0.25 + 0.35 + 0.40 + 0.90 = 1.90 min.
(ii) Output of the machine
Output =
60
1.9
= 31.5 ≈ 31 units.
(iii) Number of machines required
Assume that the plant works on the single shift basis per day of 8 hours each.
The total time required for the processing the components is given by
Total time required = Setup time + operation time.
For component A,
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Production Planning and Productivity Management
Total time required = Setup time + operation time
=
Production quantity Setup time
Batch size Batch
⎡⎛ ⎞ ⎛ ⎞ ⎤ ⎢⎜⎝ ⎟⎠ × ⎜⎝ ⎟⎠ ⎥ ⎣ ⎦
+ Operation time
=
2450 25 1.75
2450
350 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 2.916+71.458=74.374 hrs.
For component B,
Total time required =
4400 55 3
4400
550 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 22/3+220=227.33 hrs.
For component C,
Total time required =
2875 45 2.1
2875
575 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 3.75+100.625=104.375hrs.
Total time (hrs) required to process all the three components
= 74.374 + 227.33 + 104.375 = 406.079 hrs. Total number of hours available (assuming 25 working
days) per month = 8 × 25 = 200 hrs.
Number of machines required =
Total number of machine hours required
Total number of hours available
=
406.079
200
= 2.030 ≈ 2 machines.
Assuming a machine efficiency of 85% and operator efficiency of 75%, the number of machines required
are:
Total hours required per month =
406.079
0.85 × 0.75 = 636.98 hrs.
Number of machines required =
636.98
200
= 3.18 ≈ 4 machines.
Problem: 11
Three components are to be manufactured on three machines i.e. Center lathe, Milling machine and
Cylindrical grinding machine.
(i) Calculate the number of machines required of each kind to produce the components if the plant works
for 48 hours per week.
(ii) Calculate the number of machines required assuming the machine efficiency of 75%.
(iii) How do you reduce the number of machines. The following information is given:
Operation Management
101
Machine Component A Component B Component C
Setup operation Setup operation setup operation
1 Center lathe 30 min 2min 55min 2.5 min 40 min 1.5 min
2 Milling machine 45 min 8 min 30 min 4 min – –
3 Cylindrical grinding 50 min 8 min 60 min 8 min 60 min 10 min
Other details
Lot size 350 400 600
Quantity 1750 4000 3000
demanded / month
Solution:
The total time required to process the required components on the machines
(i) Center Lathe
(a) Total time required for Component A=
1750 30 2
1750
350 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 60.83 hours
(b) Total time required for Component B =
4000 55 2.5
4000
400 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 175.832 hours
(c) Total time required for Component C =
3000 40 1.5
4000
600 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 78.33 hours
Total time required to process the components on center lathe
= a +b+ c = 60.83 + 175.83 + 78.333 = 314.993 hrs/month.
Available time per machine per month = 48 × 4 = 192 hours.
Total hours required / month
No. of Lathe machines required =
Total hours required/ month
Total hours available/ month =
314.993
192
= 1.64 ≈ 2 nos.
If the machine efficiency is considered as 85%, then
No. of lathes required =
Total hours required/ month
Total No. of hours available / month ×machine efficiency
=
314.993
192 × 0.75 = 2.18 ≈ 3 machines
(ii) Milling Machine
Total time required to process all the components per month
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Production Planning and Productivity Management
1750 45 1750 8 4000 30 4000 4
350 60 60 400 60 60
⎛ ⎞⎛ ⎞
⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠
× + × + × + × = 508.749 hours.
Number of milling machines required
=
Total hours required/ month
Total hours available/ month =
508.749
192
= 3.53 ≈ 4 nos.
Cylindrical Grinding Machines
Total time required to process all the components per month
=
1750 50 10 4000 60 8 3000 60 10
1750 4000 3000
350 60 60 400 60 60 600 60 60
⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎜ × + × ⎟ + ⎜ × + × ⎟ + ⎜ × + × ⎟
⎝ ⎠⎝ ⎠ ⎝ ⎠
= [4.166 + 291.666] + [10+533.333] + [5+500] = 1344.165 hours
Number of milling machines required =
Total hours required/ month
Total hours available/ month =
1344.165
192
= 7 machines
If the machine efficiency is considered as 75%,
Number of milling machine required =
1344.165
192 × 0.75 = 9.33 ≈ 10 machines
(iii) Reduction in number of machines
(a) By introducing the second and third shift, the number of hours available will be increased
and hence the number of machines required will be reduced.
(b) By increasing the utilisation of the machine. The availability of the machine will be increased
by proper maintenance which reduces the break down and hence the down time. The
production time will be increased and hence the plant utilisation.
Problem: 12
Machines A and B are both capable of processing the product. The following informations is given
Particular Machine A Machine B
Investment Rs. 75,000 Rs. 80,000
Interest on Capital invested 10% 15%
Hourly charge (wage + power) Rs. 10 Rs. 8
Pieces produced per hour 5 8
Annual operating hours 2000 2000
Which machine will give the lower cost per unit of production, if run for the whole year? If only 4000
pieces are to be produced in a year, which machine would give the lower cost per piece.
Operation Management
103
Solution:
Computation of cost per unit of production of machines
Particulars Machine A Machine B
Interest (fixed cost) Rs. 7,500 Rs. 12,000
Variable cost (hourly charge x Rs. 20,000 Rs. 16,000
annual operating hours)
Total cost Rs. 27,500 Rs. 28,000
Total Output 5 x 2000 = 10,000 8 x 2000 = 16,000
Unit cost Rs. 2.75 Rs. 1.75
If the output is 4000 units per annum
Particulars Machine A Machine B
Interest (fixed cost) Rs. 7,500 Rs. 7,500
Variable cost (10 x 800) Rs. 8,000 Rs. 4,000
(8 x 500)
Total cost Rs. 15,500 Rs. 16,000
Unit cost Rs. 3.89 Rs. 4.00
Note: 800 hours will be required to produce the commodity with machine A and 500 hrs on machine B.
Problem : 13
ABC. Co. has developed a forecast for the group of items that has the following demand pattern
Quarter Demand Cumulative demand
1 270 270
2 220 490
3 470 960
4 670 1630
5 450 2080
6 270 2350
7 200 2550
8 370 3920
The firm estimates that it costs Rs. 150 per unit to increase production rate Rs. 200 per unit to decrease
the production rate, Rs. 50 per unit per quarter to carry the items in inventory and Rs. 100 per unit if
subcontracted. Compare the costs of the pure strategies.
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Production Planning and Productivity Management
Solution:
Different pure strategies are
Plan I In this pure strategy, the actual demand is met by varying the work force size. This means that
during the period of low demand, the company must fire the workers and during the period of high
demand the company must hire workers. These two steps involve associated costs. In this strategy,
the production units will be equal to the demand and values in each period. The cost of the plan is
computed in the table below,
Quarter Demand Cost of increasing Cost of decreasing Total cost of
Production level (Rs) Production level (Rs) plan (Rs.)
1 270 — — —
2 220 — 50 x 200 = 10,000 10,000
3 470 250 x 150 = 37,500 — 37,500
4 670 200 x 150 = 30,000 — 30,000
5 450 — 220 x 200 = 44,000 44,000
6 270 — 180 x 200 = 36,000 36,000
7 200 — 70 x 200 = 14,000 14,000
8 370 170 x 150 = 25,500 — 25,500
Total 1,97,000
Plan II In this plan, the company computes the average demand and sets its production capacity to
this average demand. This results in excess of units in some periods and also shortage of units during
some other periods. The excess units will be carried as inventory for future use and shortage of units
can be fulfilled using future inventory. The cost of the plan II is computer in the table. The plan incurs
a maximum shortage of 255 units during 5 periods. The firm might decide to carry 255 units from the
beginning of period 1 to avoid shortage. The total cost of the plan is Rs. 96,000.
Quar- Demand Cumu Production Cumu. Inventory Adjusted Cost of
ter forecast lative level prod. inventory with holding
demand level 255 at inventory
beginning Rs
of period 1
1 270 270 365 365 95 350 17,500
2 220 490 365 730 240 495 24,750
3 470 960 365 1095 135 390 19,500
4 670 1630 365 1460 –170 85 4,250
5 450 2080 365 1825 –255 0 0
6 270 2350 365 2190 –160 95 4,750
7 200 2550 365 2555 5 260 13,000
8 370 3920 365 2920 0 255 12,750
Total 96,500
Operation Management
105
Plan III
The additional demand other than the normal capacity is met by subcontracting. The cost of the plan
III amounts to Rs. 1,32,000 as shown in table below.
Quarter Demand Production Subcontract Incremental cost @
forecast units units Rs. 100/units
1 270 200 70 70 x 100 = 7,000
2 220 200 20 20 x 100 = 2,000
3 470 200 270 270 x 100 = 27,000
4 670 200 470 470 x 100 = 47,000
5 450 200 250 250 x 100 = 25,000
6 270 200 70 70 x 100 = 7,000
7 200 200 0 0
8 370 200 170 170 x 100 = 17,000
Total = 1,32,000
The total cost of pure strategies is given below. On observation Plan II (Changing inventory levels)
has the least cost.
Plan Total cost (Rs)
Plan I 1,97,000
Plan II 96,500
Plan III 1,32,000
Problem: 14
A company manufactures the consumer durable products and the company intends to develop an aggregate
plan for six months starting from January through June. The following information is available.
Demand and working days.
Month Jan Feb Mar Apr May June
Demand 500 600 650 800 900 800
Working day 22 19 21 21 22 20
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Production Planning and Productivity Management
Cost details
Materials Rs. 100/ unit
Inventory carrying cost Rs. 10/unit/month
Cost of stockout Rs. 20/unit/month
Cost subcontracting Rs. 200/unit
Hiring and training cost Rs. 50/worker
Lay off cost Rs. 100/worker
Labour hours required Rs. 4/unit
Regular time cost (forfirst 8 hrs) Rs. 12.50/hours
Overtime cost Rs. 18.75/hr
Beginning inventory 200 units
Safety stock required Nil
Work out the cost of the following strategies
1. Produce exactly to meet demand — vary the work force.
2. Constant work force — vary inventory and allow shortages
3. Constant work force and use subcontracting.
Solution:
Strategy I: Produce exactly to meet demand by varying work force.
Assumption: Opening workforce equals the first month’s requirements.
Table: Aggregate production planning requirements
Jan Feb Mar Apr May June Total
Beginning Inventory 200 0 0 0 0 0
Forcasted demand 500 600 650 800 900 800
Production requirement 300 600 650 800 900 800
(demand + safety stock –
beginning inventory
Ending inventory 0 0 0 0 0 0
(beginning inventory+
Production requirement –
Demand forecast)
Operation Management
107
Plan I — Exact Production, vary Work Force
Jan Feb Mar Apr May June Total
Production requirement 300 460 650 800 900 800
Production hours required 1200 2400 2600 3200 3600 3200
(production requirement
× 4 hr/unit)
Working days per month 22 19 21 21 22 20
Hours per month per worker 176 152 168 168 176 160
(working days × 8 hrs/day)
No. of workers’ required 7 16 15 19 20 20
(production hrs required +
hrs per month per worker
New worker hired (assuming 0 9 0 4 1 0
opening work force equal to first
months requirement of 7 workers)
Hiring cost 0 450 0 200 50 0 700
(workers hired × Rs. 50)
Workers laid off 0 0 1 0 0 0
Lay off cost 0 0 100 0 0 0 100
(workers laid off × 100)
Regular production cost
(production hrs required 15,000 30,000 32,500 40,000 45,000 40,000 2,02,500
× 12.50 Rs./hrs)
Total 2,03,300
Plan II — Constant Work Force, vary Inventory and Stockout
* Assume a constant work force of 10.
Jan Feb Mar Apr May June Total
Beginning inventory 200 140 – 80 – 310 – 690 –1150
Working days per month 22 19 21 21 22 20
Production hrs available 1760 1520 1680 1680 1760 1600
(working days/month×8 hrs/day
× 10 workers)
Actual production 440 380 420 420 440 400
(production hrs available
÷ 4 hours/unit)
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Production Planning and Productivity Management
Jan Feb Mar Apr May June Total
Forecasted demand 500 600 650 800 900 800
Ending inventory (beginning 140 – 80 – 310 – 690 –1150 –1550
inventory + actual)
Shortage cost 0 1600 6200 13800 23000 31000 75600
(unit short × Rs.20/unit)
Units excess (ending inventory 140 0 0 0 0 0
– safety stock)
Inventory cost (unit excess × 10) 1400 0 0 0 0 0 1400
Regular production cost 22000 19000 21000 21000 22000 20000 125000
(production hrs required
× 12.50 Rs./ hrs)
Total 202000
Plan III — Constant Work Force Subcontract
Jan Feb Mar Apr May June Total
Production requirement 300 460 650 800 900 800
Working days per month 22 19 21 21 22 20
Production hrs available 1760 1520 680 1680 1760 1600
(working days × 8 hrs/day
× 10 workers)
Actual production (production 440 380 420 420 440 400
hrs available ÷ 4 hours per unit)
Unit subcontracted (production 0 220 230 380 460 400
requirements – actual production)
Subcontracting cost 0 8000 23000 38000 46000 40000 155000
(units subcontracted ×Rs.100)
Regular production cost 22000 19000 21000 21000 22000 20000 125000
(production hrs required
× 12.50 Rs./hrs)
Total 280000
Note: Assume a constant work force of 10.
600 - 140 = 460 units of beginning inventory in February.
Operation Management
109
Summary of the Plans
Plan Hiring Lay off Subcon– RT. Short– excess Total
tract prod age inven. cost
Plan I – Exact production 700 100 – 2,02,500 – – 2,03,300
vary work force
Plan II – Constant work – – – 1,25,000 75,600 1,400 2,02,000
force vary inventory
and shortages
Plan III – Constant work – – 155000 1,25,000 – – 2,80,000
Problem: 15
A company is considering the expansion of a manufacturing process by adding more 1-Ton capacity furnaces.
Each batch (1 ton) must undergo 30 minutes of furnace time, including load and unload operations. However
the furnace is used only 80% of the time due to power restriction in other parts of the system. The required
output for the new layout is to be 16 tons/shift (8 hours). Plant (system) efficiency is estimated at 50% of
system capacity.
(a) Determine system capacity and the number of furnaces required
(b) Estimate the percentage of time, the furnaces will be idle.
Solution:
(a) Required system capacity
=
16 tons/shift
0.5
= 32 tons / shift =
32
8 × 0.8 = 5 tons / hour
Individual furnace capacity =
1 ton
0.50 hour
= 2 ton/hour per furnace
Number of furnaces required =
5 tons/hour
2 ton / hour per furnace = 2.5 (say) ≈ 3 furnaces.
(b) Percentage of idle time:
Total hours available / shift = 3 furnaces × 8 hours = 24 furnace-hour
Total hours of actual use/shift = (24 -8) = 16 ton × 0.5 hour/ton = 8 furnace-hour
Idle time = 16 furnace-hour % of idle time = 16/24 = 67%
Problem: 16
Annual demand for a manufacturing company is expected to be as follows
Units demanded 8,000 10,000 15,000 20,000
Probability 0.50 0.20 0.20 0.10
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Production Planning and Productivity Management
Selling price is Rs. 35 per unit. The existing manufacturing facility has annual fixed operating cost of
Rs. 2,06,000. Variable manufacturing costs are Rs. 7.75 per unit at the 8000 unit output level, Rs. 5 at
the 10,000 unit level, Rs. 5.33 at the 15000 unit level and Rs: 7.42 at the 20,000 unit output level.
An expanded facility under consideration would require Rs. 2,50,000 fixed operating costs annually.
Variable costs would average Rs. 9.40 at the 8000 unit level, Rs. 5.20 at 10,000 unit level, Rs. 3.80 at the
15000 unit level, and Rs. 4.90 at the 20000 level.
To maximise net earnings, which size facility should be selected?
Solution:
Expected net revenue of existing facility:
Expected variable cost
= [7.75×8000×0.5 + 5×10000×0.2 + 5.33×15000×0.2+ 7.42×20000×0.1]
= 31000+10000+15990+14840=Rs.71.830
Expected total cost = fixed cost + variable cost = 2,00,000 + 71,830 = Rs. 2,71,830
Expected sales = 35 [8000×0.5+10000×0.2 + 15000×0.2 + 20000×0.1]= Rs.3,85,000
Expected net revenue = 3,85,000-2,71,830 = Rs. 1,13,170
Expected net revenue of expanded facility: Expected variable cost
= [9.40×8000×0.5 + 5.20×10,000×0.2 + 3.80×15000×0.2 + 4.90×2000×0.1 ]
= 37600+10400+11400+980=Rs. 60,380
Expected total cost = fixed cost + variable cost = 2,50,000 + 60,380 = Rs.3,10,380 Expected net revenue
= 3,85,000-3,10,380 = Rs. 74,620. Therefore, the existing facility maximises expected net earnings.
Problem: 17
A manufacturer has the following information on its major product
Regular - time production capacity = 2600 units/period.
Over time production costs = Rs. 12 per unit.
Inventory costs = Rs. 2 per unit per period (based on closing inventory)
Backlog costs = Rs. 5 per unit per period.
Opening inventory 400 units.
Demand (in units) for periods 1, 2, 3, 4, is 4000, 3200, 2000 and 2800 respectively. Develop a level output
plan that yields zero inventory at the end of period 4. What costs result from this plan?
Operation Management
111
Solution:
Period Demand Output Closing Inventory Regular output Overtime
(units) (units) (units) (units) output
400
1 4000 2900 –700 2600 300
2 3200 2900 –1000 2600 300
3 2000 2900 –100 2600 300
4 2800 2900 0 2600 300
Average 3000 Total(–)1800
Total Cost = Overtime + inventory + backlogs = (300×4×12) + (0×2) + (1800 ×5) = Rs.23,400.
Problem: 18
M Ltd. produces a product which has a 6-month demand cycle, as shown. Each unit requires 10 worker
hours to be produced, at a labour cost of Rs. 6 per hour regular rate (or Rs. 9 per hour overtime). The total
cost per unit is estimated at Rs. 200, but units can be subcontracted at a cost of Rs. 208 per unit. There are
currently 20 workers employed in the subject department and hiring and training costs for additional
workers are Rs. 300 per person, whereas layoff costs are Rs. 400 per person. Company policy is to retain a
safety stock equal to 20% of the monthly forecast, and each month’ s safety stock becomes the opening
inventory for the next month. There are currently 50 units in stock carried at a cost of Rs. 2 per unit-month.
Stockouts have been assigned a cost of Rs. 20 per unit-month.
January February March April May June
Forecast demand 300 500 400 100 200 300
Work days 22 19 21 21 22 20
Work hour at 8 per day 176 152 168 168 176 160
Three aggregate plans are proposed.
Plan I. Vary the work-force size to accommodate demand.
Plan II. Maintain a constant work-force of 20, and use overtime and idle times to meet demand.
Plan III. Maintain a constant workforce of 20 and build inventory or incur a stock out cost. The firm
must begin January with the 50-unit inventory on hand.
Compare the costs of the three plans.
Solution:
We must first determine what the production requirements are as adjusted to include a safety stock of
20 per cent of next months forecast. Beginning with a January inventory of 50, each subsequent month’s
inventory reflects the difference between the forecast demand and the production requirement of the
previous month.
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Production Planning and Productivity Management
January February March April May June
Forecast demand 300 500 400 100 200 300
Work days 22 19 21 21 22 20
Work hour at 8 per day 176 152 168 168 176 160
Plan I (Vary workforce size)
Jan Feb Mar Apr May June Total
(in Rs.)
Production Required 310 540 380 40 220 320
Production hrs. Required 3100 5400 3800 400 2200 3200
Available Hrs./worker 176 152 168 168 176 160
No. of worker Required 18 36 23 3 13 20
No. of worker Hired – 18 – – 10 7
Hiring Cost 5400 – 3000 2100 10.500
No. of workers laid-off 2 – 13 20 – –
Lay off cost 800 – 5200 8000 – – 14,000
Plan II (Use overtime and idle time) (based on constant 20-work force)
Jan Feb Mar April May June Total
(in Rs.)
Production Required 310 540 380 40 220 320
Production hrs. Required 3100 5400 3800 400 2200 3200
Available Hrs./worker 176 152 168 168 176 160
Total Available Hrs. 3520 3040 3360 3360 3520 320
O.T. hrs. Required 2360 440 – 0
O.T. Premium – 7080 1320 – – 0 8,400
Idle hours 420 – – 2960 1320 0
Idle Time Cost 2520 – – 17,760 7920 0 28,200
Operation Management
113
Plan III (Used inventory and stockouts on a constant 20 - worker force)
Jan Feb Mar April May June Total
(in Rs.)
Production Required 310 540 380 40 220 320
Cumulative 310 850 1230 1270 1490 1810
Requirement
Available Hours 3520 3040 3360 3360 3520 3200
Unit produced 352 304 336 336 352 320
Cumulative Production 352 656 992 1328 1680 2000
Units Short — 194 238 — — —
Shortage cost — 3880 4760 — — —
Excess units 42 — — 58 190 190 8,640
Inventory Cost 84 — — 116 380 380 960
Note that Plan III assumes that a stockout cost is incurred if safety stock is not maintained at prescribe
level of 20% of forecast. The firm is in effect managing the safety stock level to yield a specified degree
of production by absorbing the cost of carrying the safety stock as a policy decision.
Summary:
Plan I - 10,500 (Hiring) + 14,000 (Layoff) = Rs.24,500
Plan II - 8,400 (OT) + 28,200 (IT) = Rs. 36,600
Plan III - 8,640 (Stockout) + 960 (Inventory) = Rs. 9,600
Thus, Plan III is the preferred plan.
Problem: 19
X Garment Products produces garment. While planning for next year production following demand
(quarterwise) pattern was noticed.
Quarter I II III IV
Demand 7000 10000 9000 10000
At present it is running in single shift operation having rate of production 80 units. As and when
required X.G.P. runs a second shift by hiring extra workers, in which the production is only 60 units.
The extra workers, once hired, must be kept for any period equal to a quarter or its’ multiples. There
is also a provision for giving over time to the workers, which is limited to 25% of the regular hours.
However, the O.T. provision is only for the quarters where the production is run in a single shift. The
productivity during O.T. is 20% more than that during regular time. The O.T. wages are quite attractive,
being at a premium of 50% over the normal wages, which are Rs. 150 per day. X.G.P pays the same
wages to all its workers including the temporary ones hired for the second shift. In each shift 20
workers are required.
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Production Planning and Productivity Management
The cost of change over from a single shift working to double shift working is Rs.30000, and that from
a double shift to a single shift working is only Rs.20000 These change over costs are onetime costs,
incurred only at the time the shift working changes are made.
The cost accounting section has worked out the inventory holding cost for the products which comes
to Rs.30 per unit per month. A quarter is of three months and every month consists of approximately
25 working days.
X.G.P.’s back ordering costs in it are quite heavy, at Rs. 100 per unit per month. An order once delayed
can only be accepted in the next quarter or one next to it, i.e. multiple of a quarter.
There is an initial inventory of 1000 units, which is the amount of safety stock that is required to be
kept at all times.
Compute and compare the aggregate production plans which provide for:
1. Production at a continuous rate of 9000 units per quarter.
2. Running a single-shift for the first half of the year and a double shift for the second
half of the year. (Wherever possible, use OT to the maximum)
Solution:
(i) Aggregate Plan-I (Constant rate of production)
In single shift possible unit/quarter=80 units/day × 75day/quarter=6000 units /quarter
Which is not sufficient to reach constant 9000 units/quarter
So OT option may be explored
= (25 ÷100 × 75 day/quarter) × (120/100) × 80 units/day = 1800 units/quarter.
By inclusion of OT option it was not possible to reach 9000 unit/quarter.
Introducing 2nd shift operation:
The production per quarter = 60 units /day × 75days/quarter = 4500units/quarter
As per given condition as 2nd shift operation is put in force option of O.T. to be discarded.
Thus total production possible in double-shift = 6000+4500 units/quarter.
The relevant cost of 9000 unit per quarter. Regular time wages = 20 × 2 × 150 × 75 = Rs.4,50,000 Cost of
change over from single shift to double shift = Rs.30,000/-
Operation Management
115
Cost of inventory carrying
Quarter 1 2 3 4
Opening (inventory) 1000 3000 2000 2000
Production–(units) 9000 9000 9000 9000
Demand–(units) 7000 10000 9000 10000
End inventory–(units) 3000 2000 2000 1000
Average inventory (units) 2000 2500 2000 1500
Cost of carrying inventory (Rs) 30×3×2000 30×3×2500 30×3×2000 30×3×1500
=1,80,000 =2,25,000 =1,80,000 = 1,35,000
The total relevant costs over the entire planing
= Regular time wage for year + O.T. + Costs of changeover + inventory cost + Backlog costs
= Rs.4,50,000×4 + 0 + Rs.30,000 + Rs. 1,80,000 + Rs.2,25,000 + Rs. 1,80,000 + Rs. 1,35,000 + 0
= Rs.25,50,000
Aggregate Plan 2 (Single shift for quarter I & II, double shift for quarter III and IV, O.T. to be used to
maximum)
Production Plan
Quarter 1 2 3 4
Regular time production 6000 6000 10500 10500
O.T. 2400 2400 – –
Quarter-I
Production 8400
Opening invetory 1000
9400 units
Demand 7000
Inventory at the end of quarter 2400 units
Average inventory at the end of quarter = (1000 + 2400) ÷2 = 1700 units.
Quarter-II
Production 8400
Opening invetory 2400
10800 units
Demand 10000
Inventory at the end of quarter 800 units
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Production Planning and Productivity Management
[Here the stock is lower than safety stock] Average inventory
= (2400 + 800) ÷ 2 = 1600 units
Quarter-III
Now the safety stock has to be made up to the 1000 units, i.e. 200 units (1000-800) are demanded over
9000 unit demanded.
Production 8400
Beginning invetory 2400
10800 units
Demand 10000
Inventory at the end of quarter 800 units
Average inventory = (800 + 1300) ÷ 2 = 1050 units.
Quarter -IV
Production 8400
Initial invetory 2400
10800 units
Demand 10000
Quarter End inventory 1300 units
Average inventory = (1300+1800) ÷ 2 = 1550 units.
The relevant costs for aggregate plan-2 Regular time wages
= 2 single shift + 2 double shift
= 2,25,000×2+4,50,000×2 = Rs. 13,50,000
Overtime wages for 1st 2 quarters = 225000 × (25/100) × (150/100) × 2
= Rs. 168750
Inventory carrying cost = 3 × 30× (1700+ 1600+ 1050+1550)
= Rs. 5,31,000
Change over cost = Rs. 30000
Total relevant cost = Rs.(13,50,000+1,68,750 + 5,31,000 + 30,000)
= Rs. 20,79,750
The aggregate plan-2 is less costly.
Operation Management
117
Problem: 20
Machines A and B are both capable of manufacturing a product. They compare as follows:
Machine A Machine B
Investment Rs. 50,000/– Rs. 80,000/–
Interest on capital invested 15% per annum 15% per annum
Hourly charges (Wages + Power) Rs. 10/– Rs. 8/–
No. of pieces produced per hour 5 8
Annual operating hours 2,000 2,000
(i) Which machine will have the lower cost per unit of output, if run for the whole year?
(ii) If only 4000 pieces are to be produced in a year, which machine would have the lower cost per
piece?
(iii) Will your answer to (i) above vary if you informed that 12.5% of the output of machine B gets
rejected at the inspection stage. If so, what would be the new solution?
Solution:
Data Machine A Machine B
Annual interest charges Rs. 50,000 ×
100
15
Rs. 80,000 ×
100
15
= Rs.7,500/– = Rs. 12,000/–
Annual operating charges Rs. 10×2,000 Rs. 8 × 2,000
= Rs. 20,000 = Rs. 16,000
Total annual charge 7,500 + 20,000 12,000 + 16,000
= Rs. 27,500 = Rs. 28,000
Annual production (units) 5 ×2,000 = 10,000 nos 8 ×2,000 = 16,000 nos
for 2000 hours
Cost per unit = 10,000
27,500
= Rs2.75 = 16,000
28,000
= Rs1.75
Machine ‘B’ gives the lower cost per unit if run for the whole year (for 2000 hours),
(ii) If only 4000 pieces are to be produced in an year:
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Production Planning and Productivity Management
Data Machine A Machine B
Operating hours required for
8
4,000
=500hrs.
8
4,000
=500hrs.
Operating charges Rs. 10×500= Rs. 5,000/– Rs.8 × 500 =Rs.4,000/–
Interest charges Rs. 7,500/– Rs. 12,000/–
Total annual charges Rs.(5000 + 7500) Rs.(4000 + 12000 )
= Rs. 12,500 = Rs. 16,000
Cost per unit = Rs.3.125/– = Rs. 4/–
Machine ‘A’ gives lower cost per unit.
(iii) If 12.5% of output of Machine B is rejected, net annual production
from Machine B = 16,000 x
(100-12.5)
100
= 16,000 x
87.5
100
=14,000
Cost per unit =
28,000
14,000 = Rs. 2/-
Even though, unit cost of production on Machine B increases from Rs. 1.75 to Rs. 2.0, still machine B
continues to be cheaper, if used for 2000 hours in the year.
Problem:21
Methods P and Q are both capable of manufacturing a product. They compare as follows
Data Method P Method Q
Fixture – cost Rs. 24,000/– Rs. 16,000/–
– life 6 months 4 months
Tooling – cost Rs. 2,500/– Rs. 4,800/–
– life 300 pieces 500 pieces
Processing time per piece 6mts 4 mts
The annual requirement is 1500 nos. Operating cost per hour of the process is Rs. 128 for both processes.
Material cost is same in each case.
Which method would you choose for production during a period of one year?
Solution:
Data Method P Method Q
Cost of manufacture per year
Fixture cost Rs. 24,000 x 2 = Rs. 48,000/–
= Rs. 48,000/– Rs. 16,000x3
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119
(2 nos of fixtures are required per year in method P and 3 nos required in method Q)
Tooling cost = 2,560×
300
Rs.1,500
= 4,800×
300
Rs.1,500
= 2560 x5 = 4800 x 3
= Rs.12,800 = Rs.14,400
Operating hours to produce 1500 nos.
1500 6
60
×
=150hrs.
1500 4
60
×
=100hrs.
Operating cost per year Rs. 128x150 Rs. 128x100
= Rs. 19,200/– = Rs. 12,800/–
Total manufacturing cost per year Rs. 48,000 /– Rs. 48,000 /–
Rs. 12,800 /– Rs. 14,400 /–
Rs. 19,200 /– Rs. 12,800 /–
Rs. 80,000 /– Rs. 75,200 /–
Since method Q is cheaper than method P, method ‘Q’ is the choice for production during the whole
one year/period.
analysis is the study of the entire process to determine whether operations can be eliminated,
combined or the sequence changed. Operation analysis aims to determine the one best way and can be
applied to method, materials, tools equipment layout, working conditions and human requirements of
each operation.
Job standardisation consists in determining the one best way of performing a job under the means at
command of recording the exact method along with the time for each element of operation and establishing
means to maintain the standard conditions.
Another term connected with time and motion study is the job analysis. Job analysis is the determination
of essential factors in a specific kind of work and of the qualifications of a worker necessary for its
performance.
Time study aims at determining the best manner of doing a job and timing the performance of the job
when done in the best manner.
In motion study the work is divided into fundamental motions and in time study work is divided into
elements of operations. In both cases attempts are made to remove useless motions and improve combination
and sequences of motions and operations. In motion study the best way of doing a work is determined by
motion analysis and operators are trained to follow the method so determined but in time study the best
method is determined by analysis of the methods and equipment, used and motions only roughly considered
and that too indirectly. In time study, setting of production standards, standards for cost purposes and
wage incentives are emphasised. The measurement of human effort is a difficult job which can only be
solved by using scientific method and industrial experience combined with knowledge of psychology.
The use of scientific method involves experiment measurement and elimination of variables connected
with a job.
The variables connected with a job are the method of manufacture, tools and equipments, material, working
conditions, worker concerned and time required to perform the job. In order to measure the last variable
time, the other variables must be eliminated by standardising. In going to proceed for time study, it is first
necessary to standardise the method and conditions of work and to define what an average worker is.
Time study has two sides, mechanical and human.
Before commencing the time study, the time study man should ensure and ascertain the following:
• That motion studies have been carried out so that planning of work, work places and appliances are
satisfactory.
• That the operations can be performed in the correct; sequence without interruption.
• That the human effort involved is minimum.
• That the worker in question has average skill and diligence necessary for the work.
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55
Work Study:
It is a general term for the techniques: methods study and work measurement which are used in the
examination; of human work in all its contexts and systematically investigate all factors leading to
improvement of efficiency.
Work study aims at finding the best and most efficient way of using the available resources—men, materials,
money and machinery. Once the method study has developed an improved procedure for doing a work
the work measurement or time study will study the time to complete a job.
Method Study:
It is the systematic investigation of the existing method of doing a job in order to develop and install an
easy, rapid, efficient, effective and less fatiguing procedure for doing the same job and at minimum cost.
This is achieved by eliminating unnecessary motions involved in a certain operation or by changing the
sequence of operation or the process itself.
Methods study can be made by the help of both motion study and time study.
The methods study programme must include the following features:–
(a) Uniform application,
(b) Established standard practice,
(c) Continuous review,
(d) Credit distribution.
A new and improved method developed in one department should be spread out to the entire plant
preferably with further improvements.
A new method must not be forgotten between orders as it happens sometimes in batch production. Methods
department should always aim at improved and better ways of doing jobs.
For successful control of methods study, the enthusiastic cooperation of every employee is required. To
gain employee cooperation, distribution of credit is essential. It has been correctly said that a good methods
department rarely takes credit for an original idea. Its success lies in getting new ways and methods adopted
promptly, universally, continuously and cooperatively towards the improvement of productivity.
Job Evaluation:
Job evaluation is the ranking grading, and weighing of essential work characteristics of all jobs in order to
find out or rate the worth of jobs. It is a systematic approach to ascertain the labour worth of each job and
is a very important concern of all employers.
Job evaluation aims at fairness and consistency so far as all wages and salaries are concerned within an
organisation and when systematic and impartial, it stimulates, confidence of the employees. There are
three steps for evaluations of all jobs :–
(i) Preparation of preliminary description of each existing job.
(ii) Analysing each job to arrive at final job descriptions and specifications.
(iii) Analysing each job according to its approved description in order to determine its worth or value.
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Production Planning and Productivity Management
Job Description and Specifications: The understanding of the job content or job description is the primary
requirement.
Job specifications are derived from the job descriptions which have already been approved. The specification
help determining the qualification required of the individual desired for the position. This in turn guides
the personnel department in the selection of employees and also guides shop executives in the placement
of workmen.
Systems of Valuation: There are several systems of job evaluation.
The fundamental criteria in valuation of a job into account are to make a specific list of factors which affect
job values. The many factors are:
(i) Qualifications required of the worker,
(ii) Job difficulties,
(iii) Job responsibilities,
(iv) Working conditions.
All these factors are to be analysed in detail in order to complete the job description. The list of factors, the
manner in which they are apprised and the method of finding out relative worth and money values
distinguishes the various systems of valuation.
The systems of valuations which are commonly adopted are given below:
1. The ranking or grading method,
2. The factor comparison method,
3. Point rating method.
Ranking or Grading Method: Under this system the titles of all jobs are written on cards and the grading is
done by several competent judges. The hourly rates to be paid for different jobs are suggested by the
judges without any consideration to the existing wage. The ranks or grades assigned to each job by all the
judges are averaged and this average is considered the “score” for that job. Hourly rates are then fixed for
jobs according to their ranking.
Factor Comparison Method: The factor comparison method analyses the job into much greater detail than
the grading method. It ranks each job with respect to each factor that characterise the job and the factors
are taken one at a time.
All jobs are compared and ranked first with respect to mental requirements, then skill, then physical
requirements and after that responsibility and lastly working conditions. The total worth of the job is
obtained by adding together money values which are assigned separately to the various levels of rank in
each factor. Factor comparison method is more accurate than the simple ranking systems, since the separate
factors are analysed comparatively. This method is flexible.
Point Rating Method: There are three methods of analytical evaluation of a job. They are:
1. Straight point method.
2. Weighted point method.
3. Valuation of jobs directly in money method, not specifying any maximum weight.
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57
Straight Point Method: This method assigns equal weights for each characteristic. When evaluating a job
under this system, it is assumed that all the characteristics have ranges of values between same maximum
and minimum points.
Weighted Point Method: In this method different points are assigned to the different characteristics of
doing jobs.
Direct to Money Methods: After selecting the job characteristics, ten key jobs whose rates are believed to
be correct, are taken and the present wage rates of these jobs are distributed to the job characteristics by
each analyst. The jobs are then ranked by the analysts for each characteristic in order of the degree to which
that characteristic is present. This serves as a check to show up any errors made in the original distribution
of the wages rate to the various characteristics.
Problems and Solutions
Problem: 1
Continuous stopwatch study observations for a job are given. Compute the standard time for the job, if the
total allowances are 15%.
Ele. Description Cycle time (min) P.R.
No. 1 2 3 4 5 6 7 8 9 10
A Loosen vice 0.09 0.49 0.89 1.31 1.70 2.09 2.50 2.88 3.29 3.71 90
B Set bar length 0.16 0.56 1.38 1.38 1.76 2.16 2.57 2.95 3.36 3.78 110
C Switch m/c 0.28 0.67 1.49 1.49 1.88 2.28 2.68 3.07 3.40 3.90 120
D Unlock arm & 0.41 0.80 1.61 1.61 2.00 2.41 2.80 3.20 3.62 4.03 100
set saw
Solution:
The individual element cycle timing is computed from the cumulative cycle times as shown in table
below:
Ele. Cycle time (min) Avg. Normal
No. 1 2 3 4 5 6 7 8 9 10 time time
A 0.09 0.08 0.09 0.10 0.09 0.09 0.09 0.08 0.09 0.09 0.089 0.080
B 0.07 0.07 0.06 0.07 0.06 0.07 0.07 0.07 0.07 0.07 0.068 0.075
C 0.12 0.11 0.12 0.11 0.12 0.12 0.11 0.12 0.13 0.12 0.118 0.142
D 0.13 0.13 0.14 0.12 0.12 0.13 0.12 0.13 0.13 0.13 0.128 0.128
Total 0.425
Standard time =
0.425
1 − 0.15 = 0.500 minutes.
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Production Planning and Productivity Management
Problem: 2
The work - study engineer carries out the work sampling study. The following observations were made for
a machine shop.
Total number of observations 7000
No. Working activities 1200
Ratio between manual to machine elements 2:1
Average rating factor 120%
Total number of jobs produced during study 800 units
Rest and personal allowances 17%
Compute the standard time for the job.
Solution:
(i) Overall time per unit (To) =
Duration of study
Number of jobs produced during study =
120 60
800
×
= 9 min.
(ii) Effective time per piece (Te) = To ×
Productive observations
Total observations
= 9 ×
5800
7000
= 7.46 min.
The effective time is to be segregated into manual time and machine element time.
Machine controlled time per piece (Tm) = 7.46 × 1/3 = 2.49 min
Hand controlled time per piece (Th) = 7.46 × 2/3 = 4.97 min
Normal time per piece = Tm + Th × performance rating = 2.49 + 4.97 × 1.2 = 8.46 min.
Standard time per piece = 8.46 (1 + 0.17) = 9.9 minutes.
Problem: 3
The time study of a machinery operation recorded cycle times of 8.0, 7.0, 8.0 and 9.0 minutes. The analyst
rated the observed worker as 90%. The firm uses a 0.15 allowance fraction. Compute the standard time.
Solution:
Average cycle time =
8.0 7.0 8.0 9.0
4
+ + +
= 8.0 minutes.
Normal time = 8.0 × 0.9 = 7.2 minutes.
Standard time =
7.2
(1-0.15) = 8.47 minutes.
The standard time for this machinery operation would be set at 8.47 minutes, which is greater than
the average cycle time observed. The average cycle time was adjusted for the rating factor (90%) and
the allowance fraction (0.15).
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59
Problem: 4
An analyst wants to obtain a cycle time estimate that is within ± 5% of the true value. A preliminary run of
20 cycles took 40 minutes to complete and had a calculated standard deviation of 0.3 minutes. What is the
coefficient of variation to be used for computing the sample size for the forthcoming time study?
Solution:
Standard deviation of sample(s) = 0.3 min/cycle.
Mean of sample = x =
40 min
20 cycle = 2 min./cycle;
V =
s
x
=
0.3
2
= 0.15
Problem: 5
A job has been time standard for 20 observations. The mean actual time was 5.83 minutes and the standard
deviation of the time is estimated to be 2.04 minutes. How many total observations should be taken for
95% confidence that the mean actual time has been determined within 10%?
Solution:
n =
2 Zs
Ax
⎛ ⎞
⎜ ⎟
⎝ ⎠ =
( )
( )
2 1.96 2.04
0.10 5.83
⎡ ⎤
⎢ ⎥
⎣ ⎦
= 47
Therefore, a total of 47 observations should be made. Since 20 observations have already been made,
only 27 more are necessary.
Problem: 6
An analyst has observed a job long enough to become familiar with it and has divided it into five elements.
The element times for the first four cycles and a performance rating for each element are given in the
following table,
Element Cycle Cycle Cycle Cycle Performance
1 2 3 4 Rating (%)
1 1.246 1.328 1.298 1.306 90
2 0.972 0.895 0.798 0.919 100
3 0.914 1.875 1.964 1.972 100
4 2.121 2.198 2.146 2.421 110
5 1.253 1.175 1.413 2.218 100
(a) Do any of the times look like outliners, i.e. probable errors in reading or recording data that
should not be included in the analysis?
(b) Compute an estimated normal time for the job based on the data available at this stage of the study.
(c) On the basis of the data available, what sample size should be taken to estimate the time for
element 2 within 5% of the true mean time with 95% confidence?
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Production Planning and Productivity Management
Solution:
(a) The times for element 3 in cycle 1 and for element 5 in cycle 4 are suspect and should be
disregarded.
(b) The following estimates are made on the basis of the remaining times
Element Mean actual time Performance Rating (%) Normal time
1 1.295 90 1.116
2 0.896 100 0.896
3 1.937 100 1.937
4 2.222 110 2.444
5 1.28 100 1.28
Normal time for total job = 7.723
(c) For element 2:
x = 0.896
S =
( )2
2
1
x
x
n
n
−
′
′ −
Σ
Σ =
( )2 3.227174 – 3.584
4
3
= 0.0728
n =
2 Zs
Ax
⎛ ⎞
⎜ ⎟
⎝ ⎠ =
( )
( )
2 1.96 0.0728
0.05 0.896
⎡ ⎤
⎢ ⎥
⎣ ⎦
= 10.14
The analyst probably would want to use more than 10 observation, so that workers would have more
confidence in the standard. A Company might make it a general practice to use at least say 15 or more
observations.
Problem: 7
Stopwatch time study figure for a job which is continuous in nature are given below. Calculate the Standard
Time for the job assuming that the sample size is adequate, and total allowances are 15 percent.
Ele. Description Cycle time (min) P.R.
No. per cycle 1 2 3 4 5 6 7 8 9 10
1 A 0.10 0.50 0.90 1.32 1.71 2.10 2.51 2.89 3.30 3.72 90
2 B 0.17 0.57 0.96 1.39 1.77 2.17 2.58 2.96 3.37 3.79 110
3 C 0.29 0.68 1.08 1.50 1.89 2.29 2.69 3.08 3.41 3.91 120
4 B 0.15 0.81 1.22 1.62 2.01 2.42 2.81 3.21 3.63 4.04 100
Solution:
From the continuous study figure the individual time figures are derived.
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61
Cycle time (min) Normal
Ele. Description 1 2 3 4 5 6 7 8 9 10 Arithmetic time of
No. per cycle Average element
(min)
1 A 0.10 0.08 0.09 0.10 0.09 0.09 0.09 0.08 0.09 0.09 0.090 0.081
2 B 0.07 0.07 0.06 0.07 0.06 0.07 0.07 0.07 0.07 0.07 0.068 0.075
3 C 0.12 0.11 0.12 0.11 0.12 0.12 0.11 0.12 0.13 0.12 0.118 0.142
4 D 0.13 0.13 0.14 0.12 0.12 0.13 0.12 0.13 0.13 0.13 0.128 0.128
Total time = 0.426 min
Standard time = 0.426 ÷ (1 - 0.15) = 0.501 min
2.1 Production Planning and Control Introduction
Production planning control can be viewed as the nervous system of a production operation. The primary
concern of production planning and control is the delivery of products to customers or to inventory stocks
according to some predetermined schedule. All the activities in the manufacturing or production cycle
must be planned, coordinated, organised, and controlled to achieve this objective. From a long-term point
of view (usually from seven to ten years or more) production planning largely deals with plant construction
and location and with product-line, design and development. Short-range planning (from several months
to a year) focuses on such areas as inventory goals and wage budgets. In plans projected over a two-to-five
year period, capital-equipment budgeting and plant capacity and layout are the major concern. Production
planning and control normally reflects the short range activities and focuses on the issues and problems
that arise in the planned utilisation of the labour force, materials, and physical facilities that are required
for manufacturing the products in accordance with the primary objectives of the firm.
Production systems are usually designed to produce a variety of products and are, therefore, complex. In
such complex systems, anything can happen and usually it is so. Therefore, it is vital to exercise some kind
of control over the production activities. Control is possible only when everything is planned. Production
planning and control is thus a very important aspect of production management.
Objectives of production planning and control
The ultimate objective of production planning and control is to contribute to the profits of the enterprise.
This is accomplished by keeping the customers satisfied through the meeting of delivery schedules. Further,
the specific objectives of production planning and control are to establish the routes and schedules for
work that will ensure the optimum utilisation of raw materials, labourers, and machines to provide the
means for ensuring the operation of the plant in accordance with these plans. Production planning and
control is essentially concerned with the control of work-in-process. To control work-in-process effectively
it becomes necessary to control not only the flow of material but also the utilisation of people and machines.
Production planning and control fulfils these objectives by focusing on the following points:
Analysing the orders to determine the raw materials and parts that will be required for their completion,
Answering questions from customers and salesmen concerning the status of their orders,
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Production Planning and Productivity Management
Assisting the costing department in making cost estimates of orders,
Assisting the human resource departments in the manpower planning and assignment of men to
particular jobs,
Controlling the stock of finished parts and products,
Determining the necessary tools required for manufacturing,
Direction and control of the movement of materials through production process,
Initiating changes in orders as requested by customers while orders are in process,
Issuing requisitions for the purchase of necessary materials,
Issuing requisitions for the purchase or manufacture of necessary tools and parts,
Keeping the up-to-date records scheduled and in process,
Maintaining stocks of materials and parts,
Notifying sales and accounting of the acceptance of orders in terms of production feasibility,
Preparing the route sheets and schedules showing the sequence of operation required to produce
particular products,
Production of work orders to initiate production activities,
Receiving and evaluating reports of progress on particular orders and initiating corrective action, if
necessary,
Receiving orders from customers,
Revising plans when production activities cannot conform to original plans and when revisions in
scheduled production are necessary because of rush orders.
Production control involves the following functions:
Planning the production operations in detail,
Routing, i.e., laying down the path for the work to follow and the order in which the various operations
will be carried out,
Scheduling, i.e., establishing the quantity of work to be done, and fixing the time table for performing
the operations,
Dispatching, i.e., issuing the necessary orders, and taking necessary steps to ensure that the time
targets set in the schedules are effectively achieved,
Follow-up, taking necessary steps to check up whether work proceeds according to predetermined
plans and how far there are variances from the standards set earlier,
Inspection, i.e., conducting occasional check-ups of the products manufactured or assembled to ensure
high quality of the production.
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63
Figure : Techniques of Production Control
Basic types of production control:
Production control can be of six types:
• Block control
This type of control is most prominent in textiles and book and magazine printing. In these industries
it is necessary to keep things separated and this is the fundamental reason why industries resort to
block control.
• Flow control
This type of control is commonly applied in industries like chemicals, petroleum, glass, and some
areas of food manufacturing and processing. Once the production system is thoroughly designed, the
production planning and control department controls the rate of flow of work into the system and
checks it as it comes out of the system. But, under this method, routing and scheduling are done when
the plant is laid out. That is to say, the production line which is established is well balanced and
sequenced before production operations begin; this type of control is more prevalent in continuous
production systems.
• Load control
Load control is typically found wherever a particular bottleneck machine exists in the process of
manufacturing.
• Order control
The most, common type of production control is called order control. This type of control is commonly
employed in companies with intermittent production systems, the so-called job-lot shops. Under this
method, orders come into the shop for different quantities for different products. Therefore, production
planning and control must be based, on the individual orders.
• Special project control
Special production control is necessary in certain projects like the construction of bridges, office
buildings, schools, colleges, universities, hospitals and any other construction industries. Under this
type of control, instead of having sets of elaborate forms for tooling and scheduling, a man or a group
of men keeps in close contact with the work.
• Batch control
Batch control is another important, type of production control which is frequently found in the food
processing industries. Thus, production control in batch-system of control operates with a set of
ingredients that are proportionally related and handled one batch at a time.
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Production Planning and Productivity Management
Production planning and control in continuous-production systems.
Production systems may be continuous or intermittent. The continuous production systems are characterised by:
Fixed-path material handling equipment,
High volume of production,
Product layouts,
Production of standardised products,
Production to stock or long-range orders,
The use of special-purpose machines or automation.
Production planning and control in continuous-production systems involve two activities:
Assuring that supply of raw materials and supplies are on hand to keep the production system supplied
and assuring that finished products are moved from the production-system,
Maintaining a constant rate of flow of the production, so that the system can operate near capacity in
some case or can meet the quantity requirements of the production.
Production planning in intermittent production systems:
The intermittent production systems are characterized by the following:
General purpose production machines are normally utilised and process layout is favoured.
Materials handling equipment is typically of the varied path type such as hand trucks and forklift
trucks.
Relatively high cost, skilled labour is needed to turn out the various quantities and types of products.
The company generally manufactures a wide variety of products; for the majority of items, sales
volumes and consequently production order sizes are small in relation to the total production.
Problems and Solutions
Problem: 1
Machines K and L, both capable of manufacturing an industrial product, compare as follows:
Machine K Machine L
Investment Rs. 60,000 Rs. 1,00,000
Interest on borrowed capital 15% 15%
Operating cost (wages, power, etc.) per hour Rs. 12 Rs. 10
Production per hour 6 pieces 10 pieces
The factory whose overhead costs are Rs. 1,20,000 works effectively for 4,000 hours in 2 shifts during
the year. (i) Justify with appropriate calculations which of the two machines you would choose for
regular production. (ii) If only 4000 pieces are to be produced in a year, which machine would give the
lower cost per piece. (iii) For how many pieces of production per year would the cost of production be
Operation Management
65
same on either machine? (For above comparisons, the cost of material may be excluded as being the
same on both machines.)
Solution:
Machine K Machine L
Annual interest charges (Rs. 60,000 x 15) / 100 (Rs. 1,00,000 x 15) / 100
(fixed cost) = Rs. 9,000 = Rs. 15,000
Annual operating charges 4,000 x 12 4,000 x 10
= Rs. 48,000 = Rs. 40,000
Total annual charges = Rs. 57,000 = Rs. 55,000
Annual output = 4,000 x 6 = 24,000 = 4,000 x 10 = 40,000
Cost per unit = 5,700 / 2,400 = 55,000 / 40,000
= Rs. 2.375 = Rs. 1.375
(i) Thus machine L should be chosen for regular production.
(ii) If only 4,000 pieces are to be produced in a year
Interest cost Rs. 9,000 Rs. 15,000
Operating cost (4,000 / 6) x 12 = Rs. 8,000 (4,000 / 10) x 10 = Rs. 4,000
Total cost = Rs. 17,000 = Rs. 19,000
Cost per unit (17,000 / 4,000) = Rs. 4.25 (19,000 / 4,000) = Rs. 4.75
Thus, machine K gives the lower cost per piece.
(iii) Interest charge = Rs. 9,000 = Rs. 15,000
Operating cost per piece = 12 / 6 = 2 = 10/10 = Re. 1
Let the production be = X units,
Then 2X + 9,000 = X + 15,000 or, 2X – X = 15,000 – 9,000 or, X = 6,000 pieces.
For 6,000 piece of production per year the cost of production will be the same (Rs. 21,000) on either
machine.
Problem: 2
A department of a company has to process a large number of components/month. The process equipment
time required is 36 minutes/component, whereas the requirement of an imported process chemical is 1.2
litres/component. The manual skilled manpower required is 12 minutes/component for polishing and
cleaning. The following additional data is available:
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Production Planning and Productivity Management
Availability/month Efficiency of utilisation
Equipment hour 500 85%
Imported chemicals 1000 95%
Skilled manpower - hours 250 65%
(i) What is the maximum possible production under the current conditions? (ii) If skilled manpower
availability is increased by overtime by 20%, what will be the impact on production
increase?
Solution:
(i) Actual Equipment Hrs. used = 500 × 85/100 = 425 Hrs.
Possible output = 425 × (60/36) = 708 Components
(ii) Imported chemicals = 1,000 × 95/100 = 950 litres, actually used;
Possible output = 950/1.2 = 792 Components
(iii) Skilled manpower Hrs. used = 250 × 65/100 = 162.5 Hrs.
Possible output =162.5 × (60/12) = 813 Components
The bottleneck capacity = 708 Components.
(1) Maximum possible production under the given conditions = 708 Components.
(2) There will be no impact on production increase if skilled manpower is increased by overtime by
20% as the bottleneck in output is equipment hours.
Problem: 3
A manufacturing enterprise has introduced a bonus system of wage payment on a slab-rate based on cost
of production towards labour and overheads.
The slab-rate being
1% - 10% saving in production cost 5% of saving
Between 11%-20% saving in production cost 15%
Between 21%-40% saving in production cost 30%
Between 41%-70% saving in production cost 40%
Above 70% saving in production cost 50%
The rate per hour for three workers A, B, C are Rs. 5, Rs. 5.50 and Rs. 5.25 respectively. The overhead
recovery rate is 500% of production wages and the material cost is Rs. 40 per unit. The standard cost of
production per unit is determined at Rs. 160 per unit.
If the time taken by A, B, C to finish 10 units is 26 hours, 30 hours and 16 hours respectively, what is the
amount of bonus earned by the individual workers and actual cost of production per unit?
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67
Solution:
A B C
Unit produced 10 10 10
Wage rate 5.00 5.50 5.25
Time taken 26 hours 30 hours 16 hours
Wage payable 130.00 165.00 84.00
Overhead recovery 650.00 825.00 420.00
Materials 400.00 400.00 400.00
Total cost of production 1,180.00 1,390.00 904.00
Standard cost of production 1,600.00 1,600.00 1,600.00
Saving in cost of production 420.00 210.00 696.00
% of savings 26.25% 13.13% 43.50%
Bonus slab 30% 15% 40%
Bonus Amount 126.00 31.50 278.40
Actual cost of production 1,306.00 1,421.50 1,182.40
Cost/unit (Rs.) 130.60 142.15 118.24
Problem: 4
Calculate the break-even point for the following:
Production Manager of a unit wants to know from what quantity he can use automatic machine against
semi-automatic machine.
Data Automatic Semi-automatic
Time for the job 2 mts 5 mts
Set up time 2 hrs 1.5 hrs
Cost per hour Rs. 20 Rs. 12
Solution:
Let x be the break-even quantity between automatic and semi-automatic machines. This means, for
volume of output V, the total cost of manufacture is the same on both automatic and semi-automatic
machines.
For quantity = x units
Total manufacturing cost on automatic machines =
2
2.0+
60
⎛ ⎞
⎜ ⎟
⎝ ⎠
x
× 20 Rs.
Total manufacturing cost on semi-automatic machines =
5
1.5+
60
⎛ ⎞
⎜ ⎟
⎝ ⎠
x
×12 Rs.
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Production Planning and Productivity Management
If ‘x’ is the break-even quantity, then
2
2.0+
60
⎛ x ⎞
⎜⎝ ⎟⎠ × 20 =
5
1.5+
60
⎛ x ⎞
⎜⎝ ⎟⎠ × 12
40 +
2
20
60
x × = 18 +
5
12
60
x ×
40 +
2
3
x
= 18 + x
x -
2
3
x
= 40 - 18 = 22
3
x
= 22
x = 66 units
Hence for quantity upto 65, a semi-automatic machine will be cheaper. For quantity 66, both semiautomatic
and automatic machines are equally costly. For quantity more than 66, automatic machine
becomes cheaper than semi-automatic machine.
Problem: 5
Two alternative set-ups, A and B are available for the manufacture of a component on a particular machine,
where the operating cost per hour is Rs. 20/-.
Set-up A Set-up B
Components/set-up 4,000 pieces 3,000 pieces
Set-up cost Rs. 300/- Rs.1,500/-
Production rate/hour 10 pieces 15 pieces
Which of these set-ups should be used for long range and economic production?
Solution:
Considering one set-up
Set-A Set-up B
Set-up cost per year Rs. 300/- Rs. 1,500/-
Operating hours / set-up
4000
10
= 400 hours
3000
15
= 200 hours
Operating cost 400 x 20 = Rs. 8,000 200 x 20 = Rs. 4,000
Total manufacturing cost 300 + 8,000 = Rs. 8,300 1,500 + 4,000 = Rs. 5,500
Manufacturing cost per piece
8300
4000
= Rs. 2.075
5500
3000
= Rs. 1.833
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69
Assuming that the machine is used for production for one year having 2,000 hours of working. For
annual production,
Set-up A Set-up B
No. of set-ups
2000
400
= 5
2000
200
= 10
Set-up cost per year 5 x 300 = Rs. 1,500 10 x 1,500 = Rs. 15,000
No. of units produced per year 2,000 x 10 = Rs. 20,000 2,000 x 15 = Rs. 30,000
Total annual manufacturing cost 1,500 + 40,000 = Rs. 41,500 15,000 + 40,000 = Rs. 55,000
Manufacturing cost per unit
8300
4000
= Rs. 2.075
5500
3000
= Rs. 1.833
Since the manufacturing cost for set B is less, use set-up B for long range and economic production.
2.2 Forecasting
Forecasting means peeping into the future. As future is unknown and is anybody’s guess but the business
leaders in the past have evolved certain systematic and scientific methods to know the future by scientific
analysis based on facts and possible consequences. Thus, this systematic method of probing the future is
called forecasting. In this way forecasting of sales refers to an act of making prediction about future sales
followed by a detailed analysis of facts related to future situations and forces which may affect the business
as a whole.
Foresight is not the whole of management, but at least it is an essential part of management and accordingly,
to foresee in this context means both to assess the future and make provisions for it, that is forecasting is
itself action already. Forecasting as a kind of future picture wherein proximate events are outlined with
some distinctness, while remote events appear progressively less distinct and it entails the running of the
business as foresee and provide means to run the business over a definite period.
As far as the marketing manager is concerned the sales forecast is an estimate of the amount of unit sales
for a specified future period under the proposed marketing plan or program. It may also be defined as an
estimate of sales in rupees of physical units for a specified future period under a proposed marketing plan
or program and under an assumed set of economic and other force outside the organisation for which the
forecast is made.
When we consider the function of production and operations management, no doubt Production and
Operation departments will produce goods as per the sales program given by the sales department, but it
has to prepare forecast regarding machine capacity required, materials required and time required for
production and so on. This needs the knowledge of what exactly happened in the production shop in
previous periods.
Making of a proper forecast requires the assessment of both controllable and uncontrollable factors (both
economic and non economic) inside and outside the organisation.
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Production Planning and Productivity Management
All business and industrial activities revolve around the sale and its future planning. To know what a
business will do we must know its future sales. So, sales forecasting is the most important activity in the
business because all other activities depend upon the sales of the concern. Sales forecasting as a guiding
factor for a firm because it enables the firm to concentrate its efforts to produce the required quantities, at
the right time at reasonable price and of the right quality. Sales forecasting is the basis of planning the
various activities i.e.; production activities, pricing policies, programme policies and strategies, personnel
policies as to recruitment, transfer, promotion, training, wages etc.
The period of forecasting, that is the time range selected for forecasting depends on the purpose for which
the forecast is made. The period may vary from one week to some years. Depending upon the period, the
forecast can be termed as ‘Short range forecasting’, medium range forecasting’ and ‘Long range forecasting’.
‘Short range forecasting period may be one week, two weeks or a couple of months. Medium range
forecasting period may vary from 3 to 6 months. Long range forecasting period may vary from one year to
any period. The objective of above said forecast is naturally different.
In general, short term forecasting will be of more useful in production planning. The manager who does
short range forecast must see that they are very nearer to the accuracy.
In long range forecast, the normal period used is generally 5 years. In some cases it may extends to 10 to 15
years also. The purpose of long range forecast is:
(i) To work out expected capital expenditure for future developments or to acquire new facilities,
(ii) To determine expected cash flow from sales,
(iii) To plan for future manpower requirements,
(iv) To plan for material requirement,
(v) To plan for Research and Development. Here much importance is given to long range growth factor.
In case of medium range forecasting the period may extend over to one or two years. The purpose of this
type of forecasting is:
(i) To determine budgetary control over expenses,
(ii) To determine dividend policy,
(iii) To find and control maintenance expenses,
(iv) To determine schedule of operations,
(v) To plan for capacity adjustments.
In case of short-term forecast, which extends from few weeks to three or six months and the following
purposes are generally served:
(i) To estimate the inventory requirement,
(ii) To provide transport facilities for finished goods,
(iii) To decide work loads for men and machines,
(iv) To find the working capital needed,
(v) To set-up of production run for the products,
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71
(vi) To fix sales quota,
(vii) To find the required overtime to meet the delivery promises.
Everyone who use the forecast for one purpose or the other expects that they need that forecast should be
accurate. But it is practically impossible to forecast accurately. But decisions are made everyday to run the
business by using the best information available with them. Management scientists have developed various
methods for forecasting. One has to decide which method has to be used to suit the information available
with him and to suit his needs. The manager, who is concerned with forecasting, must have knowledge of
factors influencing forecast. Various factors that influence the forecast are:
(i) Environmental changes,
(ii) Changes in the preference of the user,
(iii) Number of competitive products,
(iv) Disposable income of the consumer.
In forecasting the production important factors to be considered are:
(i) Demand from the marketing department,
(ii) Rate of labours absenteeism,
(iii) Availability of materials,
(iv) Available capacity of machines,
(v) Maintenance schedules,
(vi) Delivery date schedules.
Steps in forecasting
Whatever may be the method used for forecasting, the following steps are followed in forecasting.
(a) Determine the objective of forecast: What for you are making forecast? Is it for predicting the demand?
Is it to know the consumer’s preferences? Is it to study the trend? You have to spell out clearly the use
of forecast.
(b) Select the period over which the forecast will be made? Is it long-term forecast or medium-term forecast
or short-term forecast? What are your information needs over that period?
(c) Select the method you want to use for making the forecast. This method depends on the period selected
for the forecast and the information or data available on hand. It also depends on what you expect
from the information you get from the forecast. Select appropriate method for making forecast.
(d) Gather information to be used in the forecast. The data you use for making forecasting to produce the
result, which is of great use to you. The data may be collected by:
(i) Primary source: This data we will get from the records of the firm itself.
(ii) Secondary source: This is available from outside means, such as published data, magazines,
educational institutions etc.
(e) Make the forecast: Using the data collected in the selected method of forecasting, the forecast is made.
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Production Planning and Productivity Management
Forecasting Methods:
Methods or techniques of sales forecasting: Different authorities on marketing and production have devised
several methods or techniques of sales or demand forecasting. The sales forecasts may be result of what
market people or buyers say about the product or they may be the result of statistical and quantitative
techniques. The most common methods of sales forecasting are:
1. Survey of buyer’s inventions or the user’s expectation method: Under this system of sales forecasting
actual users of the product of the concern are contacted directly and they are asked about their intention
to buy the company’s products in an expected given future usually a year. Total sales forecasts of the
product then estimated on the basis of advice and willingness of various customers. This is most
direct method of sales forecasting.
The chief advantages of this method are:
(i) Sales forecast under this method is based on information received or collected from the actual
users whose buying actions will really decide the future demand. So, the estimates are correct.
(ii) It provides a subjective feel of the market and of the thinking behind the buying intention of the
actual uses. It may help the development of a new product in the market.
(iii) This method is more appropriate where users of the product are numbered and a new product is
to be introduced for which no previous records can be made available.
(iv) It is most suitable for short-run forecasting.
2. Collective opinion or sales force composite method: Under this method, views of salesmen, branch
manager, area manager and sales manager are secured for the different segments of the market.
Salesmen, being close to actual users are required to estimate expected sales in their respective territories
and sections. The estimates of individual salesmen are then consolidated to find out the total estimated
sales for the coming session. These estimates are then further examined by the successive executive
levels in the light of various factors like proposed changes in product design, advertising and selling
prices, competition etc. before they are finally emerged for forecasting.
3. Group executive judgement or executive judgement method: This is a process of combining, averaging
or evaluating, in some other way, the opinions and views of top executives. Opinions are sought from
the executives of different fields i.e., marketing; finance; production etc. and forecasts are made.
4. Experts’ opinions: Under this method, the organisation collects opinions from specialists in the field
outside the organisation. Opinions of experts given in the newspapers and journals for the trade,
wholesalers and distributors for company’s products, agencies or professional experts are taken. By
analysing these opinions and views of experts, deductions are made for the company’s sales, and
sales forecasts are done.
5. Market test method: Under this method seller sells his product in a part of the market for sometimes
and makes the assessment of sales for the full market on the bases of results of test sales. This method
is quite appropriate when the product is quite new in the market or good estimators are not available
or where buyers do not prepare their purchase plan.
6. Trend projection method: Under this method, a trend of company’s or industry’s sales is fixed with
the help of historical data relating to sales which are collected, observed or recorded at successive
Operation Management
73
intervals of time. Such data is generally referred to as time series. The change in values of sales is
found out. The study may show that the sales sometimes are increasing and sometimes decreasing,
but a general trend in the long run will be either upward or downward. It cannot be both ways. This
trend is called secular trend. The sales forecasts with the help of this method are made on the assumption
that the same trend will continue in the future. The method which is generally used in fitting the
trend is the method of least squares or straight line trend method. With this method a straight line
trend is obtained. This line is called ‘line of best fit’. By using the formula of regression equation of Y
on X, the future sales are projected.
Calculation of trend.
The trend can be calculated by the least square method as follows:
(i) Find time deviations (X) of each period from a certain period and then find the sum of
time deviation ( ΣX).
(ii) Square the time deviation of each period (X2) and then find the sum of squares of each
period (ΣX 2).
(iii) Multiply time deviations with the sales of each period individually (XY) and add the
product of the column to find (ΣXY).
(iv) To find the trend (Y) this is equal to a + bX. The value of a and b may be determined by
either of the following two ways:
(a) Direct method. This method is applicable only when ΣX=0. To make ΣX=0, it is necessary that
the time deviations should be calculated exactly from the mid point of the series. Then, the values
of a and b will be calculated as follows:
a (average) =
Y
n
Σ
and b (rate of growth) = 2
XY
Y
Σ
Σ
This method is simple and direct.
(b) Indirect method. This method is somewhat difficult. This method can be applied in both the
cases where ΣX has any positive or negative values or ΣX is not equal to zero. The values of a and
b are calculated by solving the following two equations:
Σ Y = na + bΣ X
Σ XY = aΣ X + bΣ X2
By calculating the values of a and b in the above manner, the sales can be forecasted for any future
period by applying the formula Y = a + bX.
7. Moving average method: This is another statistical method to calculate the trend through moving
averages. It can be calculated as follows:
An appropriate period is to be determined for which the moving average is calculated. While
determining the period for moving averages, the normal cycle time of changes in the values of series
should be considered so that short-term fluctuations are eliminated. As far as possible, the period for
moving averages should be in odd numbers such as period of 3, 5 or 7 years. The period in even
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Production Planning and Productivity Management
numbers will create a problem in centralising the values of averages. The calculated values of moving
averages present the basis for determining the expected amount of sale.
8. Criteria of a good forecasting method: It cannot be said which method of sales forecasting is the best
because everyone has merits and demerits of its own. The suitability of a method depends on various
factors such as nature of theproduct, available time and past records, wealth and energy, degree of
accuracy and the forecaster etc. of an enterprise. However, in general, a good forecasting method
must possess the following qualifications.
(i) Accuracy: Accuracy of the forecasting figures is the life blood of the business because many
important plans and programmes, policies andstrategies are prepared and followed on the basis
of such estimates. If sales forecasts are wrong, the businessman suffer a big loss. Hence, the
method of forecasting to be applied must amount to maximum accuracy.
(ii) Simplicity: The method for forecasting should be very simple. If the method is difficult or technical,
then there is every possibility of mistake. Some information are collected from outside and that
will remain unanswered or inaccurate replies will be received, if the method is difficult.
Management must also be able to understand and have confidence in the method.
(iii) Economy: The method to be used should be economical taking into account the importance of
the accuracy of forecast. Costs must be weighed against the importance of the forecast to the
operations of the business.
(iv) Availability: The method should be such for which the relevant information may be available
immediately with reasonable accuracy. Moreover, the technique must give quick results and
useful information to the management.
(v) Stability: The data of forecasting should be such wherein the future changes are expected to be
minimum and are reliable for future planning for sometime.
(vi) Utility: The forecasting technique must be easily understandable and suitable to the management.
Problems and Solutions
Problem: 1
An investigation into the demand for colour TV sets in 5 towns has resulted in the following data:
Population of the town (in lakhs) X: 5 7 8 11 14
No of TV sets demanded (in thousands) Y: 9 13 11 15 19
Fit a linear regression of Y on X and estimate the demand for CTV sets for two towns with a population
of 10 lakhs and 20 lakhs.
Operation Management
75
Solution:
Computation of trend values
Population Sales of CTV Squares of the Product of population and
(in lakhs) (in thousands) population sales of colour TV
X Y X² XY
5 9 25 45
7 13 49 91
8 11 64 88
11 15 121 165
14 19 196 266
ΣX = 45 Σy = 67 ΣX² = 455 ΣXY = 655
Regression equation of Y on X
Y = a + bX
To find the values of a and b, the following two equations are to be solved
ΣY = na + bΣX ... (i)
ΣXY = aΣX + bΣX2 ... (ii)
By putting the values we get
67 = 5a + 45b ... (iii)
655 = 45a + 455b ... (iv)
Multiplying equation (iii) by 9 and putting it as no. (v) we get,
603 = 45a + 405b ... (v)
By deducting equation (v) from equation (iv); we get 52 = 50b
b =
52
50
= 1.04
By putting the value of b in equation (iii), we get
67 = 5a + 45 × 1.04
or, 67 = 5a + 46.80
or, 67-46.80 = 5a
or, 5a = 20.20
or, a =
20.20
5
or a = 4.04
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Production Planning and Productivity Management
Now by putting the values of a, b and X (10 lakhs) in regression equation of Y on X, we get,
Y = a + bX
or, Y = 4.04 + 1.04 (10)
or, Y = 4.04 + 10.40 or 14.44 thousand CTV sets.
Similarly sales estimates for town having population of 20 lakhs, by putting the values of X, a and b in
regression equation can be found as
Y = 4.04 + 1.04 (20)
= 4.04 + 20.80 = 24.84 thousands CTV sets.
Hence expected demand for CTV for two towns will be 14.44 thousand and 24.84 thousand CTV sets.
Problem: 2
The annual sales of truck tyres manufactured by a company are as follows—
Year (X) 2002 2003 2004 2005 2006
Sales (‘000 units) (Y) 53 64 86 54 83
Fit a linear trend equation to the sales figures and estimate the sales for 2007.
Solution:
Computation of Trend Values
Years Time Deviation Sales in Squares of Product of time
from 2004 (‘000 units) time dev. deviations and sales
X Y mX² XY
2002 –2 53 4 –106
2003 –1 64 1 –64
2004 0 86 0 0
2005 +1 54 1 +54
2006 +2 83 4 +166
n = 5 ΣX = 0 ΣY = 340 ΣX² = 10 ΣXY = + 50
Regression equation of Y on X—
Y = a + bX
For calculating the values of a and b
a =
ΣY
n
=
340
5
or 68
b = 2
50
10
=
Σ
Σ
XY
X = 5
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77
Hence, regression equation comes to Y = 68 + 5X with the help of this equation, the trend value for
2007 can be calculated as follows—
Y2007 = 68 + 5(5) = 68 + 25 = 93
The estimated sales for 2007 will be 93,000 units.
Problem: 3.
From the following time series data of sale project the sales for the next three years.
Year 2001 2002 2003 2004 2005 2006 2007
Sales (`000 units) 80 90 92 83 94 99 92
Solution.
Computation of Trend Values
Years Time Deviation Sales in Squares of Product of time
from 2004 (`000 units) time dev. deviations and sales
X Y X² XY
2001 –3 80 9 –240
2002 –2 90 4 –180
2003 –1 92 1 –92
2004 0 83 0 0
2005 +1 94 1 +94
2006 +2 99 4 +198
2007 +3 92 9 +276
n = 5 ΣX = 0 ΣY = 630 ΣX² = 28 ΣXY = + 56
Regression equation of Y on X
Y = a + bX
To find the values of a and b
a =
ΣY
n
=
630
7
= 90
b = 2
XY
X
Σ
Σ =
56
28
= 2
Hence regression equation comes to Y = 90 + 2X. With the help of this equation we can project the
trend values for the next three years, i.e. 2008, 2009 and 2010.
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Production Planning and Productivity Management
Y2008 = 90 + 2(4) = 90 + 8 = 98 (000) units.
Y2009 = 90 + 2(5) = 90 + 10 = 100 (000) units.
Y2010 = 90 + 2(6) = 90+ 12= 102 (000) units.
Problem: 4
Project the trend of sales for the next 5 years from the following data –
Year 2003 2004 2005 2006 2007
Sales (‘000units) 120 140 120 150 170
Solution.
Calculation of trend values of sales
Years Sales Time deviation Squares of Product of time
(in lakh of Rs.) (from 2005) time deviation deviations and sales
Y X X² XY
2003 120 –2 4 –240
2004 140 –1 1 –140
2005 120 0 0 0
2006 150 +1 1 150
2007 170 +2 4 340
n = 5 ΣY = 700 ΣX = 0 ΣX² = 10 ΣXY = 110
Regression equation of Y on X
Y = a + bX
To find values of a and b
a =
Y
n
Σ
=
700
5
= 140
b = 2
XY
X
Σ
Σ =
110
10
= 11
Hence regression equation is a + bX or 140 + 11X. With the help of this equation we can project the
trend for the next five years as follows:
Y2008 = 140 + 11 × 3 = 140 + 33 = 173 lakh rupees.
Y2009 = 140 + 11 × 4 = 140 + 44 = 184 lakh rupees.
Y2010 = 140 + 11 × 5 = 140 + 55 = 195 lakh rupees.
Y2011 = 140 + 11 × 6 = 140 + 66 = 206 lakh rupees.
Y2012 = 140 + 11 × 7= 140 + 77 = 217 lakh rupees.
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79
Problem: 5
An investigation into the use of scooters in 5 towns has resulted in the following data:
Population in town
Population in town (X) 4 6 7 10 13
(in lakhs)
No. of scooters (Y) 4,400 6,600 5,700 8,000 10,300
Fit a linear regression of Y on X and estimate the number of scooters to be found in a town with a
population of 16 lakhs.
Solution:
Computation of trend value
Population No. of scooters Squares of Product of population and
(in lakhs) demanded population No. of scooters demanded
X Y X² XY
4 4,400 16 17,600
6 6,600 436 39,600
7 5,700 49 39,900
10 8,000 100 80,000
13 10,300 169 1,33,900
ΣX = 40 ΣY = 35,000 ΣX² = 370 ΣXY = 3,11,000
Regression equation of Y on X
Y = a + bX
To find the values of a and b we will have to solve the following two equations
ΣY = na + bΣX ... (i)
ΣXY = aΣX + bΣX2 ....(ii)
By putting the values, we get
35,000 = 5a + 40b ... (iii)
3,11,000 = 40a + 370b ... (iv)
By multiplying equation no. (iii) by 8 putting as equation (v) we get,
2,80,000 = 40a + 320b ... (v)
By subtracting equation (v) from equation (iv), we get
31,000 = 50b
or, 50b = 31,000
or, b =
31000
50
= 620
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Production Planning and Productivity Management
By substituting the value of b in equation no. (iii), we get
35,000 = 5a + 40b
or 35,000 = 5a + 40 × 620
or 35,000 = 5a + 24,800
or 10,200 = 5a
or a =
10200
5
= 2040
Now putting the value of a, b and X (16 lakhs) in regression equation of Y on X, we
get Y = a + bX
or, Y = 2040 + 620 (16)
or Y = 2040 + 9920
or Y = 11,960
Hence, the expected demand of scooters for a town with a population of 16 lakhs will be 11,960
scooters.
Problem 6.
An investigation into the demand for TV sets in 7 towns has resulted in the following data:
Population (m 000) X : 11 14 14 17 17 21 25
No. of TV sets demande Y : 15 27 27 30 34 38 46
Fit a linear regression of Y on X, and estimate the demand for TV sets for a town with a population of
30,000.
Solution
Population No. of TV sets Squares of Product of population and
(in ‘000) demanded population No. TV sets demanded
X Y X² XY
11 15 121 165
14 27 196 378
14 27 196 378
17 30 289 510
17 34 289 578
21 38 441 798
25 46 625 1150
ΣX = 119 ΣY = 217 ΣX² = 2157 ΣXY = 3957
n = 7
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81
Regression equation of Y on X:Y = a + bX
To find the value of a and b the equations are to be solved:
ΣY = na + bΣX ... (i)
ΣXY = aΣX + bΣX2 ... (ii)
By putting the values, we get
217 = 7a + 119b ...(iii)
3957 = 119a + 2157b ...(iv)
Multiplying equation no. (iii) by 17 and putting it as no. (v) we get
3689 = 119a + 2023b ...(v)
By deducting equation (v) from (iv)
we get 268 = 134b
or 134b = 268
or, b =
268
134
= 2
By substituting the value of b in equation no. (iii), we get
217 = 7a + 119 × 2
or 7a + 238 = 217
or 7a = 217 - 238 = -21 or a = -3
Now, by putting the values of a, b and X (i.e.,) in regression equation of Y on X, we get
Y = -3 + 2 × 30 = -3 + 60 = 57
Hence, the expected demand for TV sets for a town with a population of 30,000 will be 57 sets.
Problem 7:
An investigation into the demand for coolers in 5 towns has resulted in the following data:
Population of the town X : 5 7 8 11 14
(in lakhs)
No. of coolers demanded Y : 45 65 55 75 95
Fit a linear regression of Y on X and estimate the demand for coolers for a town with a population of
25 lakhs.
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Production Planning and Productivity Management
Solution:
Computation of demand for coolers for a population of 20 lakhs
Towns Population of No. of coolers Squares of Production and no.
town (in lakhs) demanded population of coolers demanded
X Y X² XY
A 5 45 25 225
B 7 65 49 455
C 8 55 64 440
D 11 75 121 825
E 14 95 196 1,330
n = 5 ΣX = 45 ΣY = 335 ΣX² = 455 ΣXY = 3,275
Regression equation of Y on X.
Y = a + bX
To find the values of a and b the following two regression equations are to be solved :
ΣY = na + bΣX .....(i)
ΣXY = aΣX + bΣX2 .....(ii)
By putting the values, we get
335 = 5a + 45b .... (iii)
3,275 = 45a + 455b .... (iv)
By multiplying equation (iii) by 9, we get
3,015 = 45a + 405b .... (v)
By subtracting equation (v) from (iv) we get
45a + 455b = 3,275
45a + 405b = 3,015
50b = 260
or b = 260/50 = 5.2
By putting the value of b in equation (iii), we get
335 = 5a + 45 × 5.2
or 5a = 335 - 234 = 101
or a = 101/5 = 20.2
By putting the value of a, b and X (which is 20) in regression equation of Y on X, we get
Y = a + bX
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Y = 20.5 + 5.2 (20)
Y = 20.2 + 104 = 124.2 or 124
or say expected demand for room coolers for a town having a population of 20 lakhs will be 124 room
coolers.
Problem: 8
An investigation into the demand for coolers in five towns has resulted in the following data:
Population of the town X : 4 6 7 10 13
(in lakhs)
No. of coolers demanded Y : 40 60 50 70 90
Fit a linear regression of Y on X and estimate the demand for coolers for a town with a population of
20 lakhs.
Solution:
Computation of trend values of sales.
Towns Population Demand for Squares of Product of Population Trend values
(in lakhs) room coolers population & demand XY (Y = a + bX)
X Y X² XY Y
A 4 40 16 160 20.40 + (5.2 x 4) = 41.2
B 6 60 36 360 20.4 + (5.2 x 6) = 51.6
C 7 50 49 350 20.4 + (5.2 x 7) = 56.8
D 10 70 100 700 20.4 + (5.2 x 10) = 72.4
E 13 90 169 1,170 20.4 + (5.2 x 13) = 88.0
n = 5 ΣX = 40 ΣY = 310 ΣX² = 370 ΣXY = 2,740 = 310
Regression equation of Y on X = Y = a + bX
To find out the value of a and b, the following two regression equations are to be solved:
ΣY = na + bΣX ... (i)
ΣXY = aΣX + bΣX2 ... (ii)
By putting the values in the above two equations
310 = 5a + 40b ...(iii)
2,740 = 40a + 370b ... (iv)
By multiplying the equation (iii) with 8 and deducting it from equation (iv)
2,480 = 40a + 320b ... (v)
2,740 = 40a + 370b ... (vi)
-260 = - 50b
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Production Planning and Productivity Management
or 50b = 260
or b = 260/50 = 5.2
By substituting the value of b in equation (iii)
310 = 5a + 40 × 5.2
or 5a = 310-208 = 102
or a = 102/5 = 20.4
Now by putting the values of a and b in regression equation of Y on X, we find the following equation:
Y = 20.4 + 5.2 (20) = 20.4 + 104 = 124.4 or say 124
Problem: 9
With the help of following data project the trend of sales for the next five years:
Years 2002 2003 2004 2005 2006 2007
Sales (in lakhs) 100 110 115 120 135 140
Solution:
Computation of trend values of sales
Year Time deviations from Sales Squares of Product of time
the middle of 2004 and (in lakh Rs.) time deviation deviation and sales
2005 assuring 5 years = 1
X Y X2 XY
2002 -5 100 25 -500
2003 -3 110 9 -330
2004 -1 115 1 -115
2005 +1 120 1 +120
2006 +3 135 9 +405
2007 + 5 140 25 +700
n = 6 ΣX = 0 ΣY = 720 ΣX² = 70 ΣXY = 280
Regression equation of Y on X:
Y = a + bX
To find the values of a and b
a =
ΣY
n
=
720
6
= 120
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85
b = 2
Σ
Σ
XY
X =
280
70
= 4
Sales forecast for the next years, i.e., 2008 to 2012
Y2008= 120 + 4 (+7) = 120 + 28 = Rs. 148 lakhs
Y2009 =120 + 4 (+9) = 120 + 36 = Rs. 156 lakhs
Y2010 = 120 + 4 (+11) = 120 + 44 = Rs. 164 lakhs.
Y2011 =120 + 4 (+13) = 120 + 52 = Rs. 172 lakhs.
Y2012 = 120 + 4 (+15) = 120 + 60 = Rs. 180 lakhs.
Problem: 10
There exists a relationship between expenditure on research and its annual profit. The details of the
expenditure for the last six years is given below. Estimate the profit when the expenditure is 6 units
Year Expenditure for research Annual Profit
(x) (y)
2001 2 20
2002 3 25
2003 5 34
2004 4 30
2005 11 40
2006 5 31
2007 6 ?
(One unit corresponds to 1 Crore Rs.)
Solution:
Year Expenditure for Annual Profit xy x²
research (x)
2001 2 20 40 4
2002 3 25 75 9
2003 5 34 170 25
2004 4 30 120 16
2005 11 40 440 121
2006 5 31 155 25
Total 30 180 1000 200
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Production Planning and Productivity Management
x =
30
6
= 5 and y =
180
6
= 30
The values a and b are computed as follows: for a linear regression equation
y = a + bX
b = 2 2
−
−
Σ
Σ
xy n x y
x nx
b =
1000 6 5 30
200 6 5 5
− × ×
− × × =
1000 900
200 150
−
− = 2
a = y – b x = 30 - 2 x 5 = 20
Thus, the model is y = 20 + 2x.
The profit when the expenditure is 6 units is
y = 20 + 2 × 6 = 32 units of Rs.
2.3 Capacity Planning and Utilization
Capacity Planning:
The effective management of capacity is the most important responsibility of production and operations
management. The objective of capacity management i.e., planning and control of capacity is to match the
level of operations to the level of demand.
Capacity planning is concerned with finding answers to the basic questions regarding capacity such as:
(i) What kind of capacity is needed?
(ii) How much capacity is needed?
(iii) When this capacity is needed?
Capacity planning is to be carried out keeping in mind future growth and expansion plans, market trends,
sales forecasting, etc. Capacity is the rate of productive capability of a facility. Capacity is usually expressed
as volume of output per period of time.
Capacity planning is required for the following:
• Sufficient capacity is required to meet the customers demand in time,
• Capacity affects the cost efficiency of operations,
• Capacity affects the scheduling system,
• Capacity creation requires an investment,
• Capacity planning is the first step when an organisation decides to produce more or new products.
Capacity planning is mainly of two types:
(i) Long-term capacity plans which are concerned with investments in new facilities and equipments.
These plans cover a time horizon of more than two years.
(ii) Short-term capacity plans which takes into account work-force size, overtime budgets, inventories
etc.
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87
Capacity refers to the maximum load an operating unit can handle. The operating unit might be a plant, a
department, a machine, a store or a worker. Capacity of a plant is the maximum rate of output (goods or
services) the plant can produce.
The production capacity of a facility or a firm is the maximum rate of production the facility or the firm is
capable of producing. It is usually expressed as volume of output per period of time (i.e., hour, day, week,
month, quarter etc.). Capacity indicates the ability of a firm to meet market demand - both current and
future.
Effective Capacity can be determined by the following factors:
Facilities - design, location, layout and environment.
Product - Product design and product-mix.
Process - Quantity and quality capabilities.
Human factors - Job content, Job design, motivation, compensation, training and experience of labour,
learning rates and absenteeism and labour turn over.
Operational factors - Scheduling, materials management, quality assurance, maintenance policies, and
equipment break-downs.
External factors - Product standards, safety regulations, union attitudes, pollution control standards.
Measurement of capacity
Capacity of a plant is usually expressed as the rate of output, i.e., in terms of units produced per period of
time (i.e., hour, shift, day, week, month etc.). But when firms are producing different types of products, it
is difficult to use volume of output of each product to express the capacity of the firm. In such cases,
capacity of the firm is expressed in terms of money value (production value) of the various products
produced put together.
Capacity Planning Decisions
Capacity planning involves activities such as:
(i) Assessing the capacity of existing facilities.
(ii) Forecasting the long-range future capacity needs.
(iii) Identifying and analysing sources of capacity for future needs.
(iv) Evaluating the alternative sources of capacity based on financial, technological and economical
considerations.
(v) Selecting a capacity alternative most suited to achieve strategic mission of the firm.
Capacity planning is necessary when an organisation decides to increase its production or introduce new
products into the market or to increase the volume of production to gain the advantages of economies of
scale. Once the existing capacity is evaluated and a need for new or expanded facilities is determined,
decisions regarding the facility location and process technology selection are undertaken.
When the long-range capacity needs are estimated through long-range forecasts for products, a firm may
find itself in one of the two following situations:
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Production Planning and Productivity Management
(i) A capacity shortage situation where present capacity is not enough to meet the forecast demand for
the product.
(ii) An excess or surplus capacity situation where the present capacity exceeds the expected future demand.
Factors affecting determination of plant capacity
(i) Capital investment required,
(ii) Changes in product design, process design, market conditions and product life cycles,
(iii) Flexibility for capacity additions,
(iv) Level of automation desired,
(v) Market demand for the product,
(vi) Product obsolescence and technology obsolescence and
(vii) Type of technology selected.
Forms of capacity planning:
Based on time-horizon
(i) Long-term capacity planning and
(ii) Short-term capacity planning
Based on amount of resources employed
(i) Finite capacity planning and
(ii) Infinite capacity planning
Factors Affecting Capacity Planning: Two kinds of factors affecting capacity planning are:
(i) Controllable Factors: amount of labour employed, facilities installed, machines, tooling, shifts of work
per day, days worked per week, overtime work, subcontracting, preventive maintenance and number
of production set ups.
(ii) Less Controllable Factors: absenteeism, labour performance, machine break-downs, material shortages,
scrap and rework, strike, lock-out, fire accidents etc.
Capacity Requirement Planning : Capacity requirement planning (CRP) is a technique which determines
what equipment and labour/personnel capacities are required to meet the production objectives (i.e., volume
of products) as per the master production schedule and material requirement planning (MRP-I).
Capacity Requirement Planning Strategies:
Two types of capacity planning strategies used are:
(i) “Level capacity” plan and
(ii) “Matching capacity with demand” plan.
Level capacity plan is based in “produce-to-stock and sell” approaches wherein the production systems
are operated at uniform production levels and finished goods inventories rise and fall depending upon
whether production level exceeds demand or vice versa from time period to time period (say every quarter
or every month).
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“Matching capacity with demand” Plan: In this plan, production capacity is matched with the demand in
each period (weekly, monthly or quarterly demand). Usually, material flows and machine capacity are
changed from quarter to quarter to match the demand. The main advantages are low levels of finished
goods inventory resulting in lesser inventory carrying costs. Also, the back-ordering cost is also reduced.
The disadvantages are high labour and material costs because of frequent changes in workforce (hiring,
training and lay-off costs, overtime or idle time cost or subcontracting costs).
Optimum Plant Capacity: Plant capacity has a great influence on cost of production with increasing volume
of production, economies of scale arises which results in reduction in average cost per unit produced.
For a given production facility, there is an optimum volume of output per year that results in the least
average unit cost. This level of output is called the “best operating level” of the plant.
As the volume of output increases outward from zero in a particular production facility, average unit costs
fall. These declining costs are because of the following reasons: (i) Fixed costs are spread over more units
produced, (ii) Plant construction costs are less, (iii) Reduced costs of purchased material due to quantity
discounts for higher volume of materials purchased and (iv) Cost advantages in mass production processes.
Longer production runs (i.e., higher batch quantity of products produced) have lesser setup cost per unit
of product produced, lesser scrap etc., resulting in savings which will reduce the cost of production per
unit. This is referred to as “economies of scale”. But this reduction in per unit cost will be only upto certain
volume of production. Additional volumes of outputs beyond this volume results in ever-increasing average
unit production cost. This increase in cost per unit arise from increased congestion of materials and workers,
which decreases efficiency of production, and due to other factors such as difficulty in scheduling, damaged
products, reduced employee morale due to excessive work pressure, increased use of overtime etc., resulting
in “diseconomies of scale”. Hence, the plant capacity should be such that the optimum level of production
which gives the minimum average cost of production per unit should be possible. This plant capacity is
referred to as optimum plant capacity.
Balancing the Capacity: In firms manufacturing many products (a product line or a product-mix) the load
on different machines and equipments vary due to changes in product-mix. When the output rates of
different machines do not match with the required output rate for the products to be produced, there will
be an imbalance between the work loads of different machines. This will result in some machine or equipment
becoming a “bottleneck work centre” thereby limiting the plant capacity which wills in-turn increase the
production costs per unit.
To overcome problem of imbalance between different machines, additional machines or equipments are
added to the bottleneck work-centre to increase the capacity of the bottle-neck work centre to match with
the capacity of other work centres. Adding new machines or equipments to bottleneck work centres to
remove the imbalance in capacity between various work centres is found to be economical than giving
excessive overtime to workers working in bottle-neck centres which increases production costs. Another
method to remove imbalance is to subcontract excess work load of bottleneck centres to outside vendors or
subcontractors. Another way to balance capacities is to try to change the productmix by manipulating the
sales for different products to arrive at a suitable product-mix which loads all work centres almost uniformly.
Implications of Plant Capacity
There are two major cost implications of plant capacity:
(i) Changes in output of an existing plant of certain installed capacity affect the production costs.
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Production Planning and Productivity Management
(ii) Changes in the plant capacity by changing the size of a plant have significant effects on costs.
Factors influencing Effective Capacity
The effective capacity is influenced by – (1) Forecasts of demand, (2) Plant and labour efficiency, (3)
Subcontracting, (4) Multiple shift operation, (5) Management policies.
Forecasts of demand: Demand forecast is going to influence the capacity plan in a
significant way. As such, it is very difficult to forecast the demand with accuracy as it changes significantly
with the product life-cycle stage, number of products. Products with long lifecycle usually exhibit steady
demand growth compared to one with shorter life-cycle. Thus the accuracy of forecast influences the capacity
planning.
Plant and labour efficiency: It is difficult to attain 100 per cent efficiency of plant and equipment. The
efficiency is less than 100 percent because of the enforced idle time due to machine breakdown, delays due
to scheduling and other reasons. The plant efficiency varies from equipment to equipment and from
organisation to organisation. Labour efficiency contributes to the overall capacity utilisation. The standard
time set by industrial engineer is for a representative or normal worker. But the actual workers differ in
their speed and efficiency. The actual efficiency of the labour should be considered for calculating efficiency.
Thus plant and labour efficiency are very much essential to arrive at realistic capacity planning.
Subcontracting: Subcontracting refers to off loading, some of the jobs to outside vendors thus hiring the
capacity to meet the requirements of the organisation. A careful analysis as to whether to make or to buy
should be done. An economic comparison between cost to make the component or buy the component is
to be made to take the decision.
Multiple shift operation: Multiple shifts are going to enhance the firm’s capacity
utilisation. But especially in the third shift the rejection rate is higher. Specially for process industries
where investment is very high it is recommended to have a multiple shifts.
Management policy: The management policy with regards to subcontracting, multiplicity of shifts (decision
regarding how many shifts to operate), which work stations or departments to be run for third shift, machine
replacement policy, etc., are going to affect the capacity planning.
Factors favouring over capacity and under capacity
It is very difficult to forecast demand as always there is an uncertainty associated with the demand. The
forecasted demand will be either higher or lower than the actual demand. So always there is a risk involved
in creating capacity based on projected demand. This gives rise to either over capacity or under capacity.
The over capacity is preferred when:
(a) Fixed cost of the capacity is not very high.
(b) Subcontracting is not possible because of secrecy of design and/or quality requirement.
(c) The time required to add capacity is long.
(d) The company cannot afford to miss the delivery, and cannot afford to loose the customer.
(e) There is an economic capacity size below which it is not economical to operate the plant.
The under capacity is preferred when:
(a) The time to build capacity is short.
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91
(b) Shortage of products does not affect the company (i.e., lost sales can be compensated).
(c) The technology changes fast, i.e., the rate of obsolescence of plant and equipment are high.
(d) The cost of creating the capacity is prohibitively high.
Aggregate Planning:
Aggregate planning is an intermediate term planning decision. It is the process of planning the quantity
and timing of output over the intermediate time horizon (3 months to one year). Within this range, the
physical facilities are assumed to be fixed for the planning period. Therefore, fluctuations in demand must
be met by varying labour and inventory schedule. Aggregate planning seeks the best combination to
minimise costs.
Production planning in the intermediate range of time is termed as ‘Aggregate Planning’. It is thus called
because the demand on facilities and available capacities is specified in aggregate quantities. For example
aggregate quantities of number of Automobile vehicles, Aggregate number of soaps etc. Here the total
expected demand is specified without regard to the product mix that makes up the specified figure.
While dealing with production problems, the planning process is normally divided in three categories.
(i) Long range Planning which deals with strategic decisions such as purchase of facilities, introduction
of new products, processes etc.
(ii) Short term planning which deals with day-to-day work, scheduling and sometimes inventory problems.
(iii) Intermediate Planning or Aggregate Planning, which is in between long range and short term planning,
which is concerned in generally acceptable planning taking the load on hand and the facilities available
into considerations. In aggregate planning the management formulates a general strategy by which
capacity can be made to satisfy demand in a most economical way during a specific moderate time
period, say for one year. The aggregate planning is made operational through a master schedule that
gives the manufacturing schedule (Products and dates of manufacture). Generally, day-to-day schedules
are prepared from master schedule. Facility planning and scheduling has got very close relationship
with aggregate planning.
Aggregate Planning Strategies:
The variables of the production system are labour, materials and capital. More labour effort is required to
generate higher volume of output. Hence, the employment and use of overtime (OT) are the two relevant
variables. Materials help to regulate output. The alternatives available to the company are inventories,
back ordering or subcontracting of items.
These controllable variables constitute pure strategies by which fluctuations in demand and uncertainties
in production activities can be accommodated.
Vary the size of the workforce: Output is controlled by hiring or laying off workers in proportion to changes
in demand.
Vary the hours worked: Maintain the stable workforce, but permit idle time when there is a slack and
permit overtime (OT) when demand is peak.
Vary inventory levels: Demand fluctuations can be met by large amount of inventory.
Subcontract: Upward shift in demand from low level. Constant production rates can be met by using
subcontractors to provide extra capacity.
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Production Planning and Productivity Management
Aggregate planning guidelines:
1. Determine corporate policy regarding controllable variables.
2. Use a good forecast as a basis for planning.
3. Plan in proper units of capacity.
4. Maintain the stable workforce.
5. Maintain needed control over inventories.
6. Maintain flexibility to change.
7. Respond to demand in a controlled manner.
8. Evaluate planning on a regular basis.
Properties of Aggregate Planning: To facilitate the production manager the aggregate planning must
have the following characteristics:
(i) Both out put and sales should be expressed in a logical overall unit of measuring. For example, an
automobile manufacturing can say 1000 vehicles per year, without giving the number of each verity
of vehicle. Similarly a paint industry can say 10,000 litres of paint and does not mention the quantities
of each colour.
(ii) Acceptable forecast for some reasonable planning period, say one year.
(iii) A method of identification and fixing the relevant costs associated with the plant. Availability of
alternatives for meeting the objective of the organization.
Ability to construct a model that will permit to take optimal or near optimal decisions for the sequence
of planning periods in the planning horizon.
(iv) Facilities that are considered fixed to carry out the objective.
Problems and Solutions
Problem 1:
A department works on 8 hours shift, 250 days a year and has the usage data of a machine, as given below:
Product Annual Processing time
demand (units) (standard time in hours)
X 300 4.0
Y 400 6.0
Z 500 3.0
Determine the number of machines required.
Solution:
Step 1: Calculate the processing time needed in hours to produce product x, y and z in the quantities
demanded using the standard time data.
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93
Product Annual Standard Processing
demand processing needed (Hrs.)
(units) per unit (Hrs.)
X 300 4.0 300 x 4 = 1200 Hrs.
Y 400 6.0 400 x 6 = 2400 Hrs.
Z 500 3.0 500 x 3 = 1500 Hrs.
Total = 5100 Hrs
Step 2 : Annual production capacity of one machine in standard hours
= 8 × 250 = 2000 hours per year
Step 3 : Number of machines required
=
Work load per year
Production capacity per machine =
5100
2000
= 2.55 machines = 3 machines.
Problem 2:
A steel plant has a design capacity of 50,000 tons of steel per day, effective capacity of 40,000 tons of steel
per day and an actual output of 36,000 tons of steel per day. Compute the efficiency of the plant and its
utilisation.
Solution:
Actual output
Efficiency of the plant =
Actual output 36000
100 90%
Effective Capacity 40000
⎛ ⎞ =⎜ ⎟× =
⎝ ⎠
Utilisation =
Actual output 36000
100 72%
Design Capacity 50000
⎛ ⎞⎛ ⎞ ⎜ ⎟=⎜ ⎟× =
⎝ ⎠ ⎝ ⎠
Problem 3:
An item is produced in a plant having a fixed cost of Rs. 6,000 per month, variable cost of rupees 2 per unit
and a selling price of Rs. 7 per unit. Determine
(a) The break-even volume.
(b) If 1000 units are produced and sold in a month, what would be the profit?
(c) How many units should be produced to earn a profit of Rs. 4000 per month?
Solution:
(a) Break-even-volume
Fixed cost (FC) = Rs. 6000 per month
Variable cost (VC) = Rs. 2 per unit
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Production Planning and Productivity Management
Selling price (SP) = Rs. 7 per unit
Let Q be the break even volume per month, then
Total cost = Fixed Cost + (Variable cost / unit) × Quantity
TC = FC + (VC ×Q) = 6000 + 2Q
Sales Revenue = Selling price per unit × Quantity = 7Q
For Q to be break-even volume,
Sales Revenue = Total cost
i.e., 7Q = 6000 + 2Q
5Q = 6000
Q =
6000
5
⎛ ⎞
⎜ ⎟
⎝ ⎠ = 1200 units / month
(b) For Q = 1000,
Profit = Sales Revenue - Total cost
= SR - (FC + VC × Q)
= (7 × 1000) - (6000 + 2 × 1000)
= (7000) - (6000 + 2000)
= Rs. 7000 - 8000 = -Rs 1000 (i.e., loss of Rs. 1000)
(c) For profit of Rs. 4000, What is Q?
SR = FC + (VC) Q + Profit
7Q = 6000 + 2Q + Profit
7Q - 2Q = Rs (6000 + 4000)
5Q = Rs. 10,000
Q =
10000
5
⎛ ⎞
⎜ ⎟
⎝ ⎠ = 2000 units
Problem 4:
A manager has to decide about the number of machines to be purchased. He has three options i.e., purchasing
one, or two or three machines. The data are given below.
Number of machine Annual fixed cost Corresponding range of output
One Rs. 12,000 0 to 300
Two Rs. 15,000 301 to 600
Three Rs. 21,000 601 to 900
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95
Variable cost is Rs. 20 per unit and revenue is Rs. 50 per unit
(a) Determine the break-even point for each range
(b) If projected demand is between 600 and 650 units how many machines should the manager purchase?
Solution:
(i) Break-even point
Let QBEP be the break even point.
FC = Fixed cost, R = Revenue per unit, VC = Variable cost
Then QBEPR = FC + (VC) QBEP
QBEP =
FC
(R – VC)
Let Q1 be the break-even-point for one machine option
Then, Q1=
12000
(50 – 20) =
12000
30
= 400 units
(Not within the range of 0 to 300)
Let Q2 be the break-even-point for two machines option.
Then, Q2 =
15000
(50 – 20) =
15000
30
= 500 units
(within the range of 301 to 600)
Let Q3 be the break-even-point for three machines option.
Then, Q3 =
21000
(50 – 20) =
21000
30
= 700 units
(with in the range of 601 to 900)
(ii) The projected demand is between 600 to 650 units.
The break even point for single machine option (i.e., 400 units) is not feasible because it exceeds the
range of volume that can be produced with one machine (i.e., 0 to 300).
Also, the break even point for 3 machines is 700 units which is more than the upper limit of projected
demand of 600 to 650 units and hence not feasible. For 2 machines option the break even volume is 500
units and volume range is 301 to 600.
Hence, the demand of 600 can be met with 2 machines and profit is earned because the production
volume of 600 is more than the break even volume of 500. If the manager wants to produce 650 units
with 3 machines, there will be loss because the break even volume with three machines is 700 units.
Hence, the manager would choose two machines and produce 600 units.
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Production Planning and Productivity Management
Problem 5:
A firm has four work centres, A, B, C & D, in series with individual capacities in units per day shown in the
figure below.
Work centres
Actual
Raw Output
materials (300)
(450) (360) (340) (400)
(i) Identify the bottle neck centre.
(ii) What is the system capacity?
(iii) What is the system efficiency?
Solution:
(i) The bottle neck centre is the work centre having the minimum capacity. Hence, work centre ‘C’ is
the bottleneck centre.
(ii) System capacity is the maximum units that are possible to produce in the system as a whole.
Hence, system capacity is the capacity of the bottle neck centre i.e., 340 units.
(iii) System efficiency =
Actual output
System capacity
=
300
340
x 100 (i.e., maximum possible output) = 88.23%
Problem 6.
A firm operates 6 days a week on single shift of 8 hours per day basis. There are 10 machines of the same
capacity in the firm. If the machines are utilised for 75 percent of the time at a system efficiency of 80
percent, what is the rated output in terms of standard hours per week?
Solution
Maximum number of hours of work possible per week
= (Number of machines) × (Machine hours worked per week)
= 10 ×6 × 8 = 480 hours
If the utilisation is 75% then number of hours worked = 480 × 0.75 = 360 hours.
Rated output = utilised hours × system efficiency = 360 × 0.8 = 288 standard hours.
Problem: 7
The order position (i.e., requirements of despatch) for the next twelve months in respect of a particular
product is as under:
A B C D
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97
Month Required units Month Required units
1 13,000 7 11,000
2 12,000 8 7,000
3 10,000 9 15,000
4 9,000 10 13,000
5 11,000 11 12,000
6 13,000 12 10,000
The production capacity or the shop is 10,000 units per month on regular basis and 3,000 units per
month on overtime basis. Sub-contracting can be relied upon up to a capacity of 3,000 units per month
after giving a lead time of 3 months. Cost data reveal as under: Rs. 5.00 per piece on regular basis Rs.
9.00 per piece on overtime basis Rs. 7.00 per piece on sub-contract basis Cost of carrying Inventory is
Re. 1.00 per unit per month. Assuming an initial inventory of 1,000 units and that no backlogging of
orders is permissible, suggest an optimal production schedule. Also work out the total cost on the
basis of the suggested schedule.
Solution:
The optimum production schedule is as follows:
Month Required No. of No. of Units Sub-contract Inventory
Units (‘000) Production (6000) (‘000 units) the end
Regular Over Order Delivered of month
Time Time placed for (‘000) units
1 13 10 2 — — 0
2 12 10 2 — — 0
3 10 10 0 3 — 0
4 9 10 0 1 — 1
5 11 10 0 — — 0
6 13 10 0 2 3 0
7 11 10 0 3 1 0
8 7 10 0 +2 — 3
9 15 10 0 — 2 0
10 13 10 0 — 3 0
11 12 10 0 — 2 0
12 10 10 0 — — 0
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Production Planning and Productivity Management
Cost of production on regular basis = Rs. 1,20,000 × 5 = Rs. 6,00,000;
Cost of production on overtime = Rs. 4,000 × 9 = Rs. 36,000; Cost of sub-contracting
= Rs. 11,000 × 7 = Rs. 77,000
Cost of carrying inventory = Rs. 4,000 × 1 = Rs. 4,000; Total cost on the basis of the suggested schedule=
(Rs.6,00,000 + Rs. 36,000 + Rs. 77,000 + Rs. 4,000) = Rs. 7,17,000
Problem: 8
A manufacturing company has a product line consisting of five work stations in series. The individual
workstation capacities are given. The actual output of the line is 500 units per shift.
Calculate (i) System capacity (ii) Efficiency of the production line
Workstation No. A B C D E
Capacity/Shift 600 650 650 550 600
Solution:
(i) The capacity of the system is decided by the workstation with minimum capacity/shift, i.e., the
bottleneck. In the given example, the work station ‘D’ is having a capacity of 550 units/ shift
which is a minimum.
Therefore, the system capacity = 550 units/shift. (ii) The actual output of the line = 500 units/shift.
Therefore, the system efficiency =
Actual capacity
System capacity x 100 =
500
550
x 100 = 90.91 %
Problem: 9
A company intends to buy a machine having a capacity to produce 1,70,000 good parts per annum. The
machine constitutes a part of the total product line. The system efficiency of the product line is 85%.
(i) Find the system capacity.
(ii) If the time required to produce each part is 100 seconds and the machine works for 2000 hours per
year. If the utilisation of the machine is 60% and the efficiency of the machine is 90%, compute the
output of the machine.
(iii) Calculate the number of machines required?
Solution:
(i) System capacity =
Actual output / annum
System efficiency =
1,70,000
0.85
= 2,00,000 units / annum
=
2,00,000
2,000 = 100 units/hours
(ii) Output per annum = Unit capacity × % utilisation × efficiency
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99
Unit capacity =
60 60 sec
100 sec per unit
×
= 36 units
Output per hour = 36 × 0.6 × 0.9 = 19.44 units = 20 units.
(iii) Number of machines required =
System capacity
Output per hour =
100
20
= 5 machines
Problem: 10
The following activities constitute a work cycle.
(i) Find the total time, theoretical output obtained from the machine.
(ii) Calculate the number of machines required to produce the three components from the information
given below.
Sr. No. Activity Time (min)
1. Unloading 0.25
2. Inspection 0.35
3. Loading job on machine table 0.40
4. Machine operation time 0.90
Components A B C
1. Setup time per batch 25 min 55 min 45 min
2. Operation time (min/piece) 1.75 3.0 2.1
3. Batch size 350 550 575
4. Production per month 2450 4400 2875
Solution:
(i) Total cycle time (T) = 0.25 + 0.35 + 0.40 + 0.90 = 1.90 min.
(ii) Output of the machine
Output =
60
1.9
= 31.5 ≈ 31 units.
(iii) Number of machines required
Assume that the plant works on the single shift basis per day of 8 hours each.
The total time required for the processing the components is given by
Total time required = Setup time + operation time.
For component A,
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Production Planning and Productivity Management
Total time required = Setup time + operation time
=
Production quantity Setup time
Batch size Batch
⎡⎛ ⎞ ⎛ ⎞ ⎤ ⎢⎜⎝ ⎟⎠ × ⎜⎝ ⎟⎠ ⎥ ⎣ ⎦
+ Operation time
=
2450 25 1.75
2450
350 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 2.916+71.458=74.374 hrs.
For component B,
Total time required =
4400 55 3
4400
550 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 22/3+220=227.33 hrs.
For component C,
Total time required =
2875 45 2.1
2875
575 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 3.75+100.625=104.375hrs.
Total time (hrs) required to process all the three components
= 74.374 + 227.33 + 104.375 = 406.079 hrs. Total number of hours available (assuming 25 working
days) per month = 8 × 25 = 200 hrs.
Number of machines required =
Total number of machine hours required
Total number of hours available
=
406.079
200
= 2.030 ≈ 2 machines.
Assuming a machine efficiency of 85% and operator efficiency of 75%, the number of machines required
are:
Total hours required per month =
406.079
0.85 × 0.75 = 636.98 hrs.
Number of machines required =
636.98
200
= 3.18 ≈ 4 machines.
Problem: 11
Three components are to be manufactured on three machines i.e. Center lathe, Milling machine and
Cylindrical grinding machine.
(i) Calculate the number of machines required of each kind to produce the components if the plant works
for 48 hours per week.
(ii) Calculate the number of machines required assuming the machine efficiency of 75%.
(iii) How do you reduce the number of machines. The following information is given:
Operation Management
101
Machine Component A Component B Component C
Setup operation Setup operation setup operation
1 Center lathe 30 min 2min 55min 2.5 min 40 min 1.5 min
2 Milling machine 45 min 8 min 30 min 4 min – –
3 Cylindrical grinding 50 min 8 min 60 min 8 min 60 min 10 min
Other details
Lot size 350 400 600
Quantity 1750 4000 3000
demanded / month
Solution:
The total time required to process the required components on the machines
(i) Center Lathe
(a) Total time required for Component A=
1750 30 2
1750
350 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 60.83 hours
(b) Total time required for Component B =
4000 55 2.5
4000
400 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 175.832 hours
(c) Total time required for Component C =
3000 40 1.5
4000
600 60 60
⎛ ⎞ ⎛ ⎞ ⎜⎝ × ⎟⎠ + ⎜⎝ × ⎟⎠ = 78.33 hours
Total time required to process the components on center lathe
= a +b+ c = 60.83 + 175.83 + 78.333 = 314.993 hrs/month.
Available time per machine per month = 48 × 4 = 192 hours.
Total hours required / month
No. of Lathe machines required =
Total hours required/ month
Total hours available/ month =
314.993
192
= 1.64 ≈ 2 nos.
If the machine efficiency is considered as 85%, then
No. of lathes required =
Total hours required/ month
Total No. of hours available / month ×machine efficiency
=
314.993
192 × 0.75 = 2.18 ≈ 3 machines
(ii) Milling Machine
Total time required to process all the components per month
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Production Planning and Productivity Management
1750 45 1750 8 4000 30 4000 4
350 60 60 400 60 60
⎛ ⎞⎛ ⎞
⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠
× + × + × + × = 508.749 hours.
Number of milling machines required
=
Total hours required/ month
Total hours available/ month =
508.749
192
= 3.53 ≈ 4 nos.
Cylindrical Grinding Machines
Total time required to process all the components per month
=
1750 50 10 4000 60 8 3000 60 10
1750 4000 3000
350 60 60 400 60 60 600 60 60
⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎜ × + × ⎟ + ⎜ × + × ⎟ + ⎜ × + × ⎟
⎝ ⎠⎝ ⎠ ⎝ ⎠
= [4.166 + 291.666] + [10+533.333] + [5+500] = 1344.165 hours
Number of milling machines required =
Total hours required/ month
Total hours available/ month =
1344.165
192
= 7 machines
If the machine efficiency is considered as 75%,
Number of milling machine required =
1344.165
192 × 0.75 = 9.33 ≈ 10 machines
(iii) Reduction in number of machines
(a) By introducing the second and third shift, the number of hours available will be increased
and hence the number of machines required will be reduced.
(b) By increasing the utilisation of the machine. The availability of the machine will be increased
by proper maintenance which reduces the break down and hence the down time. The
production time will be increased and hence the plant utilisation.
Problem: 12
Machines A and B are both capable of processing the product. The following informations is given
Particular Machine A Machine B
Investment Rs. 75,000 Rs. 80,000
Interest on Capital invested 10% 15%
Hourly charge (wage + power) Rs. 10 Rs. 8
Pieces produced per hour 5 8
Annual operating hours 2000 2000
Which machine will give the lower cost per unit of production, if run for the whole year? If only 4000
pieces are to be produced in a year, which machine would give the lower cost per piece.
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103
Solution:
Computation of cost per unit of production of machines
Particulars Machine A Machine B
Interest (fixed cost) Rs. 7,500 Rs. 12,000
Variable cost (hourly charge x Rs. 20,000 Rs. 16,000
annual operating hours)
Total cost Rs. 27,500 Rs. 28,000
Total Output 5 x 2000 = 10,000 8 x 2000 = 16,000
Unit cost Rs. 2.75 Rs. 1.75
If the output is 4000 units per annum
Particulars Machine A Machine B
Interest (fixed cost) Rs. 7,500 Rs. 7,500
Variable cost (10 x 800) Rs. 8,000 Rs. 4,000
(8 x 500)
Total cost Rs. 15,500 Rs. 16,000
Unit cost Rs. 3.89 Rs. 4.00
Note: 800 hours will be required to produce the commodity with machine A and 500 hrs on machine B.
Problem : 13
ABC. Co. has developed a forecast for the group of items that has the following demand pattern
Quarter Demand Cumulative demand
1 270 270
2 220 490
3 470 960
4 670 1630
5 450 2080
6 270 2350
7 200 2550
8 370 3920
The firm estimates that it costs Rs. 150 per unit to increase production rate Rs. 200 per unit to decrease
the production rate, Rs. 50 per unit per quarter to carry the items in inventory and Rs. 100 per unit if
subcontracted. Compare the costs of the pure strategies.
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Production Planning and Productivity Management
Solution:
Different pure strategies are
Plan I In this pure strategy, the actual demand is met by varying the work force size. This means that
during the period of low demand, the company must fire the workers and during the period of high
demand the company must hire workers. These two steps involve associated costs. In this strategy,
the production units will be equal to the demand and values in each period. The cost of the plan is
computed in the table below,
Quarter Demand Cost of increasing Cost of decreasing Total cost of
Production level (Rs) Production level (Rs) plan (Rs.)
1 270 — — —
2 220 — 50 x 200 = 10,000 10,000
3 470 250 x 150 = 37,500 — 37,500
4 670 200 x 150 = 30,000 — 30,000
5 450 — 220 x 200 = 44,000 44,000
6 270 — 180 x 200 = 36,000 36,000
7 200 — 70 x 200 = 14,000 14,000
8 370 170 x 150 = 25,500 — 25,500
Total 1,97,000
Plan II In this plan, the company computes the average demand and sets its production capacity to
this average demand. This results in excess of units in some periods and also shortage of units during
some other periods. The excess units will be carried as inventory for future use and shortage of units
can be fulfilled using future inventory. The cost of the plan II is computer in the table. The plan incurs
a maximum shortage of 255 units during 5 periods. The firm might decide to carry 255 units from the
beginning of period 1 to avoid shortage. The total cost of the plan is Rs. 96,000.
Quar- Demand Cumu Production Cumu. Inventory Adjusted Cost of
ter forecast lative level prod. inventory with holding
demand level 255 at inventory
beginning Rs
of period 1
1 270 270 365 365 95 350 17,500
2 220 490 365 730 240 495 24,750
3 470 960 365 1095 135 390 19,500
4 670 1630 365 1460 –170 85 4,250
5 450 2080 365 1825 –255 0 0
6 270 2350 365 2190 –160 95 4,750
7 200 2550 365 2555 5 260 13,000
8 370 3920 365 2920 0 255 12,750
Total 96,500
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105
Plan III
The additional demand other than the normal capacity is met by subcontracting. The cost of the plan
III amounts to Rs. 1,32,000 as shown in table below.
Quarter Demand Production Subcontract Incremental cost @
forecast units units Rs. 100/units
1 270 200 70 70 x 100 = 7,000
2 220 200 20 20 x 100 = 2,000
3 470 200 270 270 x 100 = 27,000
4 670 200 470 470 x 100 = 47,000
5 450 200 250 250 x 100 = 25,000
6 270 200 70 70 x 100 = 7,000
7 200 200 0 0
8 370 200 170 170 x 100 = 17,000
Total = 1,32,000
The total cost of pure strategies is given below. On observation Plan II (Changing inventory levels)
has the least cost.
Plan Total cost (Rs)
Plan I 1,97,000
Plan II 96,500
Plan III 1,32,000
Problem: 14
A company manufactures the consumer durable products and the company intends to develop an aggregate
plan for six months starting from January through June. The following information is available.
Demand and working days.
Month Jan Feb Mar Apr May June
Demand 500 600 650 800 900 800
Working day 22 19 21 21 22 20
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Production Planning and Productivity Management
Cost details
Materials Rs. 100/ unit
Inventory carrying cost Rs. 10/unit/month
Cost of stockout Rs. 20/unit/month
Cost subcontracting Rs. 200/unit
Hiring and training cost Rs. 50/worker
Lay off cost Rs. 100/worker
Labour hours required Rs. 4/unit
Regular time cost (forfirst 8 hrs) Rs. 12.50/hours
Overtime cost Rs. 18.75/hr
Beginning inventory 200 units
Safety stock required Nil
Work out the cost of the following strategies
1. Produce exactly to meet demand — vary the work force.
2. Constant work force — vary inventory and allow shortages
3. Constant work force and use subcontracting.
Solution:
Strategy I: Produce exactly to meet demand by varying work force.
Assumption: Opening workforce equals the first month’s requirements.
Table: Aggregate production planning requirements
Jan Feb Mar Apr May June Total
Beginning Inventory 200 0 0 0 0 0
Forcasted demand 500 600 650 800 900 800
Production requirement 300 600 650 800 900 800
(demand + safety stock –
beginning inventory
Ending inventory 0 0 0 0 0 0
(beginning inventory+
Production requirement –
Demand forecast)
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107
Plan I — Exact Production, vary Work Force
Jan Feb Mar Apr May June Total
Production requirement 300 460 650 800 900 800
Production hours required 1200 2400 2600 3200 3600 3200
(production requirement
× 4 hr/unit)
Working days per month 22 19 21 21 22 20
Hours per month per worker 176 152 168 168 176 160
(working days × 8 hrs/day)
No. of workers’ required 7 16 15 19 20 20
(production hrs required +
hrs per month per worker
New worker hired (assuming 0 9 0 4 1 0
opening work force equal to first
months requirement of 7 workers)
Hiring cost 0 450 0 200 50 0 700
(workers hired × Rs. 50)
Workers laid off 0 0 1 0 0 0
Lay off cost 0 0 100 0 0 0 100
(workers laid off × 100)
Regular production cost
(production hrs required 15,000 30,000 32,500 40,000 45,000 40,000 2,02,500
× 12.50 Rs./hrs)
Total 2,03,300
Plan II — Constant Work Force, vary Inventory and Stockout
* Assume a constant work force of 10.
Jan Feb Mar Apr May June Total
Beginning inventory 200 140 – 80 – 310 – 690 –1150
Working days per month 22 19 21 21 22 20
Production hrs available 1760 1520 1680 1680 1760 1600
(working days/month×8 hrs/day
× 10 workers)
Actual production 440 380 420 420 440 400
(production hrs available
÷ 4 hours/unit)
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Production Planning and Productivity Management
Jan Feb Mar Apr May June Total
Forecasted demand 500 600 650 800 900 800
Ending inventory (beginning 140 – 80 – 310 – 690 –1150 –1550
inventory + actual)
Shortage cost 0 1600 6200 13800 23000 31000 75600
(unit short × Rs.20/unit)
Units excess (ending inventory 140 0 0 0 0 0
– safety stock)
Inventory cost (unit excess × 10) 1400 0 0 0 0 0 1400
Regular production cost 22000 19000 21000 21000 22000 20000 125000
(production hrs required
× 12.50 Rs./ hrs)
Total 202000
Plan III — Constant Work Force Subcontract
Jan Feb Mar Apr May June Total
Production requirement 300 460 650 800 900 800
Working days per month 22 19 21 21 22 20
Production hrs available 1760 1520 680 1680 1760 1600
(working days × 8 hrs/day
× 10 workers)
Actual production (production 440 380 420 420 440 400
hrs available ÷ 4 hours per unit)
Unit subcontracted (production 0 220 230 380 460 400
requirements – actual production)
Subcontracting cost 0 8000 23000 38000 46000 40000 155000
(units subcontracted ×Rs.100)
Regular production cost 22000 19000 21000 21000 22000 20000 125000
(production hrs required
× 12.50 Rs./hrs)
Total 280000
Note: Assume a constant work force of 10.
600 - 140 = 460 units of beginning inventory in February.
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Summary of the Plans
Plan Hiring Lay off Subcon– RT. Short– excess Total
tract prod age inven. cost
Plan I – Exact production 700 100 – 2,02,500 – – 2,03,300
vary work force
Plan II – Constant work – – – 1,25,000 75,600 1,400 2,02,000
force vary inventory
and shortages
Plan III – Constant work – – 155000 1,25,000 – – 2,80,000
Problem: 15
A company is considering the expansion of a manufacturing process by adding more 1-Ton capacity furnaces.
Each batch (1 ton) must undergo 30 minutes of furnace time, including load and unload operations. However
the furnace is used only 80% of the time due to power restriction in other parts of the system. The required
output for the new layout is to be 16 tons/shift (8 hours). Plant (system) efficiency is estimated at 50% of
system capacity.
(a) Determine system capacity and the number of furnaces required
(b) Estimate the percentage of time, the furnaces will be idle.
Solution:
(a) Required system capacity
=
16 tons/shift
0.5
= 32 tons / shift =
32
8 × 0.8 = 5 tons / hour
Individual furnace capacity =
1 ton
0.50 hour
= 2 ton/hour per furnace
Number of furnaces required =
5 tons/hour
2 ton / hour per furnace = 2.5 (say) ≈ 3 furnaces.
(b) Percentage of idle time:
Total hours available / shift = 3 furnaces × 8 hours = 24 furnace-hour
Total hours of actual use/shift = (24 -8) = 16 ton × 0.5 hour/ton = 8 furnace-hour
Idle time = 16 furnace-hour % of idle time = 16/24 = 67%
Problem: 16
Annual demand for a manufacturing company is expected to be as follows
Units demanded 8,000 10,000 15,000 20,000
Probability 0.50 0.20 0.20 0.10
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Production Planning and Productivity Management
Selling price is Rs. 35 per unit. The existing manufacturing facility has annual fixed operating cost of
Rs. 2,06,000. Variable manufacturing costs are Rs. 7.75 per unit at the 8000 unit output level, Rs. 5 at
the 10,000 unit level, Rs. 5.33 at the 15000 unit level and Rs: 7.42 at the 20,000 unit output level.
An expanded facility under consideration would require Rs. 2,50,000 fixed operating costs annually.
Variable costs would average Rs. 9.40 at the 8000 unit level, Rs. 5.20 at 10,000 unit level, Rs. 3.80 at the
15000 unit level, and Rs. 4.90 at the 20000 level.
To maximise net earnings, which size facility should be selected?
Solution:
Expected net revenue of existing facility:
Expected variable cost
= [7.75×8000×0.5 + 5×10000×0.2 + 5.33×15000×0.2+ 7.42×20000×0.1]
= 31000+10000+15990+14840=Rs.71.830
Expected total cost = fixed cost + variable cost = 2,00,000 + 71,830 = Rs. 2,71,830
Expected sales = 35 [8000×0.5+10000×0.2 + 15000×0.2 + 20000×0.1]= Rs.3,85,000
Expected net revenue = 3,85,000-2,71,830 = Rs. 1,13,170
Expected net revenue of expanded facility: Expected variable cost
= [9.40×8000×0.5 + 5.20×10,000×0.2 + 3.80×15000×0.2 + 4.90×2000×0.1 ]
= 37600+10400+11400+980=Rs. 60,380
Expected total cost = fixed cost + variable cost = 2,50,000 + 60,380 = Rs.3,10,380 Expected net revenue
= 3,85,000-3,10,380 = Rs. 74,620. Therefore, the existing facility maximises expected net earnings.
Problem: 17
A manufacturer has the following information on its major product
Regular - time production capacity = 2600 units/period.
Over time production costs = Rs. 12 per unit.
Inventory costs = Rs. 2 per unit per period (based on closing inventory)
Backlog costs = Rs. 5 per unit per period.
Opening inventory 400 units.
Demand (in units) for periods 1, 2, 3, 4, is 4000, 3200, 2000 and 2800 respectively. Develop a level output
plan that yields zero inventory at the end of period 4. What costs result from this plan?
Operation Management
111
Solution:
Period Demand Output Closing Inventory Regular output Overtime
(units) (units) (units) (units) output
400
1 4000 2900 –700 2600 300
2 3200 2900 –1000 2600 300
3 2000 2900 –100 2600 300
4 2800 2900 0 2600 300
Average 3000 Total(–)1800
Total Cost = Overtime + inventory + backlogs = (300×4×12) + (0×2) + (1800 ×5) = Rs.23,400.
Problem: 18
M Ltd. produces a product which has a 6-month demand cycle, as shown. Each unit requires 10 worker
hours to be produced, at a labour cost of Rs. 6 per hour regular rate (or Rs. 9 per hour overtime). The total
cost per unit is estimated at Rs. 200, but units can be subcontracted at a cost of Rs. 208 per unit. There are
currently 20 workers employed in the subject department and hiring and training costs for additional
workers are Rs. 300 per person, whereas layoff costs are Rs. 400 per person. Company policy is to retain a
safety stock equal to 20% of the monthly forecast, and each month’ s safety stock becomes the opening
inventory for the next month. There are currently 50 units in stock carried at a cost of Rs. 2 per unit-month.
Stockouts have been assigned a cost of Rs. 20 per unit-month.
January February March April May June
Forecast demand 300 500 400 100 200 300
Work days 22 19 21 21 22 20
Work hour at 8 per day 176 152 168 168 176 160
Three aggregate plans are proposed.
Plan I. Vary the work-force size to accommodate demand.
Plan II. Maintain a constant work-force of 20, and use overtime and idle times to meet demand.
Plan III. Maintain a constant workforce of 20 and build inventory or incur a stock out cost. The firm
must begin January with the 50-unit inventory on hand.
Compare the costs of the three plans.
Solution:
We must first determine what the production requirements are as adjusted to include a safety stock of
20 per cent of next months forecast. Beginning with a January inventory of 50, each subsequent month’s
inventory reflects the difference between the forecast demand and the production requirement of the
previous month.
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Production Planning and Productivity Management
January February March April May June
Forecast demand 300 500 400 100 200 300
Work days 22 19 21 21 22 20
Work hour at 8 per day 176 152 168 168 176 160
Plan I (Vary workforce size)
Jan Feb Mar Apr May June Total
(in Rs.)
Production Required 310 540 380 40 220 320
Production hrs. Required 3100 5400 3800 400 2200 3200
Available Hrs./worker 176 152 168 168 176 160
No. of worker Required 18 36 23 3 13 20
No. of worker Hired – 18 – – 10 7
Hiring Cost 5400 – 3000 2100 10.500
No. of workers laid-off 2 – 13 20 – –
Lay off cost 800 – 5200 8000 – – 14,000
Plan II (Use overtime and idle time) (based on constant 20-work force)
Jan Feb Mar April May June Total
(in Rs.)
Production Required 310 540 380 40 220 320
Production hrs. Required 3100 5400 3800 400 2200 3200
Available Hrs./worker 176 152 168 168 176 160
Total Available Hrs. 3520 3040 3360 3360 3520 320
O.T. hrs. Required 2360 440 – 0
O.T. Premium – 7080 1320 – – 0 8,400
Idle hours 420 – – 2960 1320 0
Idle Time Cost 2520 – – 17,760 7920 0 28,200
Operation Management
113
Plan III (Used inventory and stockouts on a constant 20 - worker force)
Jan Feb Mar April May June Total
(in Rs.)
Production Required 310 540 380 40 220 320
Cumulative 310 850 1230 1270 1490 1810
Requirement
Available Hours 3520 3040 3360 3360 3520 3200
Unit produced 352 304 336 336 352 320
Cumulative Production 352 656 992 1328 1680 2000
Units Short — 194 238 — — —
Shortage cost — 3880 4760 — — —
Excess units 42 — — 58 190 190 8,640
Inventory Cost 84 — — 116 380 380 960
Note that Plan III assumes that a stockout cost is incurred if safety stock is not maintained at prescribe
level of 20% of forecast. The firm is in effect managing the safety stock level to yield a specified degree
of production by absorbing the cost of carrying the safety stock as a policy decision.
Summary:
Plan I - 10,500 (Hiring) + 14,000 (Layoff) = Rs.24,500
Plan II - 8,400 (OT) + 28,200 (IT) = Rs. 36,600
Plan III - 8,640 (Stockout) + 960 (Inventory) = Rs. 9,600
Thus, Plan III is the preferred plan.
Problem: 19
X Garment Products produces garment. While planning for next year production following demand
(quarterwise) pattern was noticed.
Quarter I II III IV
Demand 7000 10000 9000 10000
At present it is running in single shift operation having rate of production 80 units. As and when
required X.G.P. runs a second shift by hiring extra workers, in which the production is only 60 units.
The extra workers, once hired, must be kept for any period equal to a quarter or its’ multiples. There
is also a provision for giving over time to the workers, which is limited to 25% of the regular hours.
However, the O.T. provision is only for the quarters where the production is run in a single shift. The
productivity during O.T. is 20% more than that during regular time. The O.T. wages are quite attractive,
being at a premium of 50% over the normal wages, which are Rs. 150 per day. X.G.P pays the same
wages to all its workers including the temporary ones hired for the second shift. In each shift 20
workers are required.
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Production Planning and Productivity Management
The cost of change over from a single shift working to double shift working is Rs.30000, and that from
a double shift to a single shift working is only Rs.20000 These change over costs are onetime costs,
incurred only at the time the shift working changes are made.
The cost accounting section has worked out the inventory holding cost for the products which comes
to Rs.30 per unit per month. A quarter is of three months and every month consists of approximately
25 working days.
X.G.P.’s back ordering costs in it are quite heavy, at Rs. 100 per unit per month. An order once delayed
can only be accepted in the next quarter or one next to it, i.e. multiple of a quarter.
There is an initial inventory of 1000 units, which is the amount of safety stock that is required to be
kept at all times.
Compute and compare the aggregate production plans which provide for:
1. Production at a continuous rate of 9000 units per quarter.
2. Running a single-shift for the first half of the year and a double shift for the second
half of the year. (Wherever possible, use OT to the maximum)
Solution:
(i) Aggregate Plan-I (Constant rate of production)
In single shift possible unit/quarter=80 units/day × 75day/quarter=6000 units /quarter
Which is not sufficient to reach constant 9000 units/quarter
So OT option may be explored
= (25 ÷100 × 75 day/quarter) × (120/100) × 80 units/day = 1800 units/quarter.
By inclusion of OT option it was not possible to reach 9000 unit/quarter.
Introducing 2nd shift operation:
The production per quarter = 60 units /day × 75days/quarter = 4500units/quarter
As per given condition as 2nd shift operation is put in force option of O.T. to be discarded.
Thus total production possible in double-shift = 6000+4500 units/quarter.
The relevant cost of 9000 unit per quarter. Regular time wages = 20 × 2 × 150 × 75 = Rs.4,50,000 Cost of
change over from single shift to double shift = Rs.30,000/-
Operation Management
115
Cost of inventory carrying
Quarter 1 2 3 4
Opening (inventory) 1000 3000 2000 2000
Production–(units) 9000 9000 9000 9000
Demand–(units) 7000 10000 9000 10000
End inventory–(units) 3000 2000 2000 1000
Average inventory (units) 2000 2500 2000 1500
Cost of carrying inventory (Rs) 30×3×2000 30×3×2500 30×3×2000 30×3×1500
=1,80,000 =2,25,000 =1,80,000 = 1,35,000
The total relevant costs over the entire planing
= Regular time wage for year + O.T. + Costs of changeover + inventory cost + Backlog costs
= Rs.4,50,000×4 + 0 + Rs.30,000 + Rs. 1,80,000 + Rs.2,25,000 + Rs. 1,80,000 + Rs. 1,35,000 + 0
= Rs.25,50,000
Aggregate Plan 2 (Single shift for quarter I & II, double shift for quarter III and IV, O.T. to be used to
maximum)
Production Plan
Quarter 1 2 3 4
Regular time production 6000 6000 10500 10500
O.T. 2400 2400 – –
Quarter-I
Production 8400
Opening invetory 1000
9400 units
Demand 7000
Inventory at the end of quarter 2400 units
Average inventory at the end of quarter = (1000 + 2400) ÷2 = 1700 units.
Quarter-II
Production 8400
Opening invetory 2400
10800 units
Demand 10000
Inventory at the end of quarter 800 units
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Production Planning and Productivity Management
[Here the stock is lower than safety stock] Average inventory
= (2400 + 800) ÷ 2 = 1600 units
Quarter-III
Now the safety stock has to be made up to the 1000 units, i.e. 200 units (1000-800) are demanded over
9000 unit demanded.
Production 8400
Beginning invetory 2400
10800 units
Demand 10000
Inventory at the end of quarter 800 units
Average inventory = (800 + 1300) ÷ 2 = 1050 units.
Quarter -IV
Production 8400
Initial invetory 2400
10800 units
Demand 10000
Quarter End inventory 1300 units
Average inventory = (1300+1800) ÷ 2 = 1550 units.
The relevant costs for aggregate plan-2 Regular time wages
= 2 single shift + 2 double shift
= 2,25,000×2+4,50,000×2 = Rs. 13,50,000
Overtime wages for 1st 2 quarters = 225000 × (25/100) × (150/100) × 2
= Rs. 168750
Inventory carrying cost = 3 × 30× (1700+ 1600+ 1050+1550)
= Rs. 5,31,000
Change over cost = Rs. 30000
Total relevant cost = Rs.(13,50,000+1,68,750 + 5,31,000 + 30,000)
= Rs. 20,79,750
The aggregate plan-2 is less costly.
Operation Management
117
Problem: 20
Machines A and B are both capable of manufacturing a product. They compare as follows:
Machine A Machine B
Investment Rs. 50,000/– Rs. 80,000/–
Interest on capital invested 15% per annum 15% per annum
Hourly charges (Wages + Power) Rs. 10/– Rs. 8/–
No. of pieces produced per hour 5 8
Annual operating hours 2,000 2,000
(i) Which machine will have the lower cost per unit of output, if run for the whole year?
(ii) If only 4000 pieces are to be produced in a year, which machine would have the lower cost per
piece?
(iii) Will your answer to (i) above vary if you informed that 12.5% of the output of machine B gets
rejected at the inspection stage. If so, what would be the new solution?
Solution:
Data Machine A Machine B
Annual interest charges Rs. 50,000 ×
100
15
Rs. 80,000 ×
100
15
= Rs.7,500/– = Rs. 12,000/–
Annual operating charges Rs. 10×2,000 Rs. 8 × 2,000
= Rs. 20,000 = Rs. 16,000
Total annual charge 7,500 + 20,000 12,000 + 16,000
= Rs. 27,500 = Rs. 28,000
Annual production (units) 5 ×2,000 = 10,000 nos 8 ×2,000 = 16,000 nos
for 2000 hours
Cost per unit = 10,000
27,500
= Rs2.75 = 16,000
28,000
= Rs1.75
Machine ‘B’ gives the lower cost per unit if run for the whole year (for 2000 hours),
(ii) If only 4000 pieces are to be produced in an year:
118
Production Planning and Productivity Management
Data Machine A Machine B
Operating hours required for
8
4,000
=500hrs.
8
4,000
=500hrs.
Operating charges Rs. 10×500= Rs. 5,000/– Rs.8 × 500 =Rs.4,000/–
Interest charges Rs. 7,500/– Rs. 12,000/–
Total annual charges Rs.(5000 + 7500) Rs.(4000 + 12000 )
= Rs. 12,500 = Rs. 16,000
Cost per unit = Rs.3.125/– = Rs. 4/–
Machine ‘A’ gives lower cost per unit.
(iii) If 12.5% of output of Machine B is rejected, net annual production
from Machine B = 16,000 x
(100-12.5)
100
= 16,000 x
87.5
100
=14,000
Cost per unit =
28,000
14,000 = Rs. 2/-
Even though, unit cost of production on Machine B increases from Rs. 1.75 to Rs. 2.0, still machine B
continues to be cheaper, if used for 2000 hours in the year.
Problem:21
Methods P and Q are both capable of manufacturing a product. They compare as follows
Data Method P Method Q
Fixture – cost Rs. 24,000/– Rs. 16,000/–
– life 6 months 4 months
Tooling – cost Rs. 2,500/– Rs. 4,800/–
– life 300 pieces 500 pieces
Processing time per piece 6mts 4 mts
The annual requirement is 1500 nos. Operating cost per hour of the process is Rs. 128 for both processes.
Material cost is same in each case.
Which method would you choose for production during a period of one year?
Solution:
Data Method P Method Q
Cost of manufacture per year
Fixture cost Rs. 24,000 x 2 = Rs. 48,000/–
= Rs. 48,000/– Rs. 16,000x3
Operation Management
119
(2 nos of fixtures are required per year in method P and 3 nos required in method Q)
Tooling cost = 2,560×
300
Rs.1,500
= 4,800×
300
Rs.1,500
= 2560 x5 = 4800 x 3
= Rs.12,800 = Rs.14,400
Operating hours to produce 1500 nos.
1500 6
60
×
=150hrs.
1500 4
60
×
=100hrs.
Operating cost per year Rs. 128x150 Rs. 128x100
= Rs. 19,200/– = Rs. 12,800/–
Total manufacturing cost per year Rs. 48,000 /– Rs. 48,000 /–
Rs. 12,800 /– Rs. 14,400 /–
Rs. 19,200 /– Rs. 12,800 /–
Rs. 80,000 /– Rs. 75,200 /–
Since method Q is cheaper than method P, method ‘Q’ is the choice for production during the whole
one year/period.
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