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Production and Service Planning II - Case Study “Macpherson Refrigeration Limited”
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MIDDLE EAST TECHNICAL UNIVERSITY
IE324 - PRODUCTION AND SERVICE OPERATIONS PLANNING II
Case Study
“Macpherson Refrigeration Limited”
June 2011, Ankara
Burcu Yüzüak
Fatoş İlbi
Onur Yılmaz
1
Table of Contents
PAGE
Table of Contents ............................................................................................................. 1
1.Introduction …………………..………………………………………………………………………………………… 2
2. Problem Statement …................................................................................................... 2
3. Performance Measures and Trade-offs ....................................................................... 3
4. Assumptions ……………………........................................................................................... 4
5. Iterative Plans …………...................................................................................................
4
5.1. Integer Programming Model ……………………………………………………………………… 5
5.2. Integer Programming Model Considering Overtime …………………………………… 6
5.3. Integer Programming Model Considering Hiring/Firing ……………………………. 7
6. Conclusion ……………………………………………………………………………………………………………… 9
7. Appendix ….……………………………………………………………………………………………………………… A-I
2
1. Introduction
In this case study, production planning of Macpherson Refrigeration Limited (RML)
for the next year is conducted. In order to provide some background information about the
company and the related production plant; there are some points to be mentioned. First of
all RML is a relatively large company with a sales of about $28.5 million and for the last ten
years they are in the business of producing consumer refrigeration. Secondly, the production
plant which this production planning is related has an increased efficiency in the last years
through process design and assembly technologies.
In this report, process and the results of this case study is presented. In the first part,
problem which is going to be studied is presented. Following that, decision criteria and
performance measures are given in order to evaluate results. Then, assumptions are made
considering the business environment and an iterative process of combining quantitative
and qualitative measures is conducted. Finally, conclusions about the report and appendix
for the further investigation are submitted as the last parts of the report.
2. Problem Statement
In this case study, the problem to be solved can be stated as developing an aggregate
plan for the following year with the given forecasts and plant capacities. In addition,
qualitative and quantitative consequences of tools used for dealing with demand
fluctuations should also be considered. The decision maker of the project who is going to
decide to implement the provided solution is Linda Metzler, Production Planning Manager of
MRL. Her objective is minimizing the cost while keeping the reputation of company at high
levels considering the future of the company. Her decision criteria and performance
measures are given in detail in the next part and environment related assumptions are
described in Assumptions (Part 4).
3
3. Performance Measures and Trade-offs
In order to compare the different aggregate plans, there should be some
performance measures in accordance with the objectives of decision maker. These measures
would be used in order to define a plan as “better” than any other plan and they are
grouped according to their relevancies in parts.
The first tool to compensate demand fluctuation is building inventory as given in the
case text. Quantitative trade-off of this tool is basically the opportunity cost of holding
inventory which is given as $8 per unit per month. In addition, keeping products for long
time intervals in inventory could lead them to hold outdated products which can be thought
both qualitative and quantitative trade-off. Considering that these aspects should have been
included in the calculation of inventory holding cost, no additional modification related to
these trade-offs are considered.
The second mentioned tool is using overtime which is considered as making some of
workers work for an additional 40 hours a week. The obvious benefit of using workers for
overtime will be that no tangible or intangible cost of firing/hiring new workers will be
considered. Quantitative trade-off using this option is additional higher monthly cost which
is $3.300; on the other hand, qualitative trade-off will be considered as decrease in the
efficiency and morale of workers. In order to reflect effects of those qualitative measures,
some assumptions and estimations will be made to change those intangible costs into
tangible costs.
The third tool is changing the number of workers, namely hiring or firing them.
Trade-offs of these options will be considered separately. First of all, considering the limited
labour market, both due to negatively affected union relations and the worsened
reputation of the firm, when firing is undertaken it will be difficult to find new workers in the
next months. In addition, morale and efficiency of remaining workers would be decreased.
With the same approach above, effects of those changes will be reflected by some additional
modifications in cost and working hour figures.
4
After making mentioned changes, all the plans are available to be compared by
looking at numerical results, because by making estimations about intangible costs they
would be reflected by more explicit costs. Those numerical results will be namely; number of
fired/hired workers, number of firing/hiring operation, total cost, average number of
workers and average inventory level.
4. Assumptions
Considering the business environment, there are some assumptions which need to be
made in order to analyze the system and solve the problem. These assumptions can be listed
as follows:
○ Forecasts of the next year are reliable and correctly represent the following
year’s situation.
○ Those reliable forecasts are reflected to the aggregate plan of the firm
correctly, in aggregate units.
○ Raw materials are available when they are required and acquisition of them is
not going to be a problem in future.
○ Worker-hours are directly and fully contribute to production hours.
○ There are no special allowances for training of new workers and all of the
related ones are considered in the related costs.
5. Iterative Plans
In this part, considering performance measures and objectives, problem is going to
solved through an iterative process. At each step, an additional performance measure will be
considered and its modifications will be added.
5
5.1. Integer Programming Model
Since the problem is related to the planning of a whole year, the best approach is
thought to be a plan which finds the optimal result considering the all of next twelve
months. With this notion, an integer programming model is constructed.
In the model, number of workers to hire, fire and make overtime and production plan
is considered as decision variables. Plant capacity of 13000 and worker-production capacity,
which is the total production hours that all regular and overtime workers can work, are used
as upper boundaries for production plan. Considering the on-hand inventory and the
production plan, inventory level which will be carried to next month is calculated after
making shipments. Number of workers is preserved by keeping the track of hire/fire levels
which are decision variables.
Considering the objective of minimizing total cost and not considering any qualitative
measures, this model is constructed to find the minimum total cost, which is the sum of all
inventory carrying cost, regular and overtime costs and hiring/firing costs. This described
model is developed on Microsoft Excel and solved with Excel Solver. Spreadsheet of this
model with the variables which are the results of solution is given in “Appendix 1 - Integer
Programming Model” and the summary of numerical results of this plan is given below:
Total Cost $ 6.221.180,00 Average Inventory Level 1963
Average Worker Number 191,7 Number of Hired Workers 75 Number of Fired Workers 96
Number of Overtime Workers 74 Number of Firing 3 Number of Hiring 1
Number of Overtime 2
Table 5.1: Summary of IP solution
Considering these numerical figures and being an operational research method, this
model is said to be the optimal minimum cost level when only tangible cost figures are
6
thought. Therefore, those numbers, especially total cost, can be thought as a lower bound
on this problem.
5.2. Integer Programming Model Considering Overtime
In the previous model, no quantitative performance measures are taken into
consideration, therefore in this new iterative model the only thing added to the previous
one is the efficiency of overtime workers. As mentioned in the concerns of manager, having
overtime will affect the efficiency of workers negatively. In order to show effects of this
quantitative measure, it is thought that efficiency of workers can be changed to an arbitrary
and acceptable level
It is assumed that workers doing overtime tend to work less efficiently due to the
extra 40 hours of workload. This effect is reflected as 20% decreased efficiency for the
workers who do overtime while the efficiency of the workers, who works only in regular
time, are not affected. Result of this decrease in efficiency is reflected to integer
programming model and the summary of results is given below in Table 5.2. For further
investigation, the Excel spreadsheet of this model is given in the “Appendix 2 - Integer
Programming Model Considering Overtime” with the solution results in the related cells.
Total Cost $ 6.225.880,00 Average Inventory Level 1096,7
Average Worker Number 198,2 Number of Hired Workers 129 Number of Fired Workers 149
Number of Overtime Workers 0 Number of Firing 4 Number of Hiring 2
Number of Overtime 0 Table 5.2: Summary of IP solution
7
5.3. Integer Programming Model Considering Hiring/Firing
In order to keep going on the iterative process, in this step, reducing the number of
fired workers is considered. In the integer programming model in the first step, it is found
that total number of 96 workers are fired when the average level of workers is 191,7.
Considering this high ratio, it is thought that it will negatively affect the future operations of
the company. In addition, since firing workers will decrease the moral and efficiency of
workers, total efficiency will be lowered by an arbitrary and acceptable level.
The first effect is the increasing bad reputation of company in the labor market as the
company fires more workers. First of all, it is thought that “no firing” policy would be
effective to overcome this problem. Thus, by taking an extreme measure, a new model will
limit the number of fired workers to zero. With this approach, there would be no
controversy with the Labor Union. The result of this model is given in Summary 5.3 below
and the details of the model can be found in the spreadsheet given in “Appendix 3 - Integer
Programming Model Considering Hiring/Firing (Zero Firing)”.
Total Cost $ 6.778.680,00 Average Inventory Level 2230
Average Worker Number 222 Number of Hired Workers 95 Number of Fired Workers 0
Number of Overtime Workers 0 Number of Firing 0 Number of Hiring 2
Number of Overtime 0
Summary 5.3: Summary of IP solution
Considering the noteworthy increase in the total cost and being unrealistic to fire any
of the workers for the next year, another extension to this step is considered. The second
approach to this performance measure is though not to decrease the number of fired
workers to zero but to restrict that number. With this approach, it is assumed to fire at most
the 15% of the average number of workers in the company throughout the years and it is
8
found to be 30 workers. Therefore a constraint is added to the previous model to reflect this
change. In addition to limiting the number of fired workers, the effect of decrease in the
morale and efficiency of workers are included in the model. For the following months after
the first firing is occurred, efficiency of whole workers is thought to be decrease to 95 %, an
arbitrary and acceptable level. The results of this model is given in Summary 5.4 below and
the details of the model can be found in the spreadsheet given in “Appendix 4 - Integer
Programming Model Considering Hiring/Firing (Limited Firing)”
Total Cost $ 6.598.680,00 Average Inventory Level 2230
Average Worker Number 214,5 Number of Hired Workers 95 Number of Fired Workers 30
Number of Overtime Workers 0 Number of Firing 1 Number of Hiring 2
Number of Overtime 0
Summary 5.4: Summary of IP solution
If the extra $500,000 (appx. between $6.778.680 and $6.225.880) cost between the
model excluding the restrictions on number of fired workers and “no firing” model is
thought to be considerable, and then the manager may choose the model with “no firing”.
Otherwise second approach can be considered which has an extra $350,000 (appx. between
$6.598.680 and $6.225.880) cost.
Since the level of %15 is selected arbitrarily, it is thought to solve this problem with
linear programming to find its LP relaxation and to see how the total cost figure changes
when this arbitrary limit is increased. As can be seen from “Appendix 6 - Limited Hiring/Firing
- Sensitivity Analysis” it is found that increasing this limit will decrease the total cost by
$6000. This analysis could be helpful to determine the selected limit and to have a more
reliable and realistic firing worker limit.
9
6. Conclusion
The main aim of this project is retrieving a proper annual aggregate production plan
for the Macpherson Refrigeration Limited (RML). Manager pointed out her tools to
determine this scheme, which are inventory levels, worker levels and amount of overtime
that workers should do in order to meet fluctuating demands. She also mentioned that there
are some tangible and intangible costs to regard while conducting this analysis.
According to given conditions, first of all an IP model is solved without any
consideration of those intangible costs which constitutes a basis and a lower bound for
further analysis. Then the no-quantitative considerations of the manager are tried to be
reflected in calculations. First, the decreasing efficiency effect of overtimes is considered.
After that, the effects of the layoffs are considered in both further decrease in efficiency of
workers and worse off relations with the labor union, and some restrictions are added to
model in order to make a more realistic analysis for the final decision.
As a result, with given conditions and relatively assigned arbitrary values to
qualitative considerations, a final aggregate production plan for the RML is generated which
realize all efficiency and labor union relation concerns, and suggestions for the adjustments
regarding the possible different attitudes of the management are presented.
(Appendix) A - I
7. Appendix Appendix 1 - Integer Programming Model
MACPHERSON REFRIGERATION LIMITED
Integer Programming Model June 11, 2011
Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTALS
Physical Capacity 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 156000
Forecast 4400 4400 6000 8000 6600 11800 13000 11200 10800 7600 6000 5600 95400
Worker-Production Capacity 6400 6400 6400 6400 9440 9440 9480 11200 10800 7600 6000 5600 95160
Inventory 240 2240 4240 4640 3040 5880 3520 0 0 0 0 0 0 23560
Inventory capacity 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 72000
Production + Inventory 6640 8640 10640 11040 12480 15320 13000 11200 10800 7600 6000 5600
0 0 0 0 0 0 0 0 0 0 0 0 0
Production Plan 6400 6400 6400 6400 9440 9440 9480 11200 10800 7600 6000 5600 95160
Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTALS
Number of workers 160 160 160 160 160 236 236 236 236 236 190 150 140 2300
Hiring 0 0 0 0 0 76 0 0 0 0 0 0 0 76
Firing 0 0 0 0 0 0 0 0 0 0 46 40 10 96
Overtime 0 0 0 0 0 0 0 1 44 34 0 0 0 79
(Appendix) A - II
COST CALCULATIONS TOTAL COST:
$ 6.221.180,00 Hiring Costs $ 136.800,00 Layoff Costs $ 115.200,00 Inventory Costs $ 188.480,00 Regular Time Costs $ 5.520.000,00 Overtime Costs $ 260.700,00
Appendix 2 - Integer Programming Model Considering Overtime
Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTALS
Physical Capacity 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 156000
Forecast 4400 4400 6000 8000 6600 11800 13000 11200 10800 7600 6000 5600 95400
Worker-Production Capacity 5640 5640 5640 5640 10200 10800 10800 10800 10800 7600 6000 5600 95160
Inventory 240 1480 2720 2360 0 3600 2600 400 0 0 0 0 0 13160
Inventory capacity 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 72000
Production + Inventory 5880 7120 8360 8000 10200 14400 13400 11200 10800 7600 6000 5600
Production Plan 5640 5640 5640 5640 10200 10800 10800 10800 10800 7600 6000 5600 95160
Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTALS
Number of workers 160 141 141 141 141 255 270 270 270 270 190 150 140 2379
Hiring 0 0 0 0 0 114 15 0 0 0 0 0 0 129
Firing 0 19 0 0 0 0 0 0 0 0 80 40 10 149
Overtime 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(Appendix) A - III
COST CALCULATIONS TOTAL COST:
$ 6.225.880,00
Hiring Costs $ 232.200,00
Layoff Costs $ 178.800,00
Inventory Costs $ 105.280,00
Regular Time Costs $ 5.709.600,00
Overtime Costs $ -
Appendix 3 - Integer Programming Model Considering Hiring/Firing (Zero Firing)
Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTALS
Physical Capacity 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 156000
Forecast 4400 4400 6000 8000 6600 11800 13000 11200 10800 7600 6000 5600 95400
Worker-Production Capacity 6400 6400 6400 6400 9560 10200 10200 10200 10200 10200 10200 10200 106560
Inventory 240 2240 4240 4640 3040 6000 4400 1600 600 0 0 0 0 26760
Inventory capacity 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 72000
Production + Inventory 6640 8640 10640 11040 12600 16200 14600 11800 10800 7600 6000 5600
Production Plan 6400 6400 6400 6400 9560 10200 10200 10200 10200 7600 6000 5600 95160
Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTALS
Number of workers 160 160 160 160 160 239 255 255 255 255 255 255 255 2664
Hiring 0 0 0 0 0 79 16 0 0 0 0 0 0 95
Firing 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Overtime 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(Appendix) A - IV
COST CALCULATIONS TOTAL COST:
$ 6.778.680,00
Hiring Costs $ 171.000,00
Layoff Costs $ 0,00
Inventory Costs $ 214.080,00
Regular Time Costs $ 6.393.600,00
Overtime Costs $ -
Appendix 4 - Integer Programming Model Considering Hiring/Firing (Limited Firing)
Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTALS
Physical Capacity 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 13000 156000
Forecast 4400 4400 6000 8000 6600 11800 13000 11200 10800 7600 6000 5600 95400
Worker-Production Capacity 6400 6400 6400 6400 9560 10200 10200 10200 10200 8550 8550 8550 101610
Inventory 240 2240 4240 4640 3040 6000 4400 1600 600 0 0 0 0 26760
Inventory capacity 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 6000 72000
Production + Inventory 6640 8640 10640 11040 12600 16200 14600 11800 10800 7600 6000 5600
0 0 0 0 0 0 0 0 0 0 0 0 0
Production Plan 6400 6400 6400 6400 9560 10200 10200 10200 10200 7600 6000 5600 95160
Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTALS
Number of workers 160 160 160 160 160 239 255 255 255 255 225 225 225 2574
Hiring 0 0 0 0 0 79 16 0 0 0 0 0 0 95
Firing 0 0 0 0 0 0 0 0 0 0 30 0 0 30
Overtime 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(Appendix) A - V
COST CALCULATIONS TOTAL COST:
$ 6.598.680,00
Hiring Costs $ 171.000,00
Layoff Costs $ 36.000,00
Inventory Costs $ 214.080,00
Regular Time Costs $ 6.177.600,00
Overtime Costs $ -
Appendix 6 - Limited Hiring/Firing - Sensitivity Analysis
Final Shadow RHS
Allowable Allowable
Cell Name Value Price Increase Decrease
....
$J$9 Inventory Aug 600 0 6000 1E+30 5400
$K$9 Inventory Sep 0 0 6000 1E+30 6000
$L$9 Inventory Oct 0 0 6000 1E+30 6000
$M$9 Inventory Nov 0 0 6000 1E+30 6000
$N$9 Inventory Dec 0 0 6000 1E+30 6000
$P$19 Firing TOTALS 30 -6000 30 35 30
$B$18 Hiring Dec 0 0 0 0 1E+30
$B$19 Firing Dec 0 0 0 0 1E+30
$B$20 Overtime Dec 0 0 0 0 1E+30
$C$11 Production + Inventory Jan 6640 0 4400 2240 1E+30
$D$11 Production + Inventory Feb 8640 0 4400 4240 1E+30
...