Production and Service Planning II - Case Study “Macpherson Refrigeration Limited”

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

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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).

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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.

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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.

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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

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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



Number of Overtime 0 Table 5.2: Summary of IP solution

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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)”.


Average Worker Number 222 Number of Hired Workers 95 Number of Fired Workers 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

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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)”





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.

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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


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



Forecast 4400 4400 6000 8000 6600 11800 13000 11200 10800 7600 6000 5600 95400


Inventory 240 1480 2720 2360 0 3600 2600 400 0 0 0 0 0 13160



Production Plan 5640 5640 5640 5640 10200 10800 10800 10800 10800 7600 6000 5600 95160



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


$ 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)



Forecast 4400 4400 6000 8000 6600 11800 13000 11200 10800 7600 6000 5600 95400


Inventory 240 2240 4240 4640 3040 6000 4400 1600 600 0 0 0 0 26760



Production Plan 6400 6400 6400 6400 9560 10200 10200 10200 10200 7600 6000 5600 95160



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


$ 6.778.680,00


Layoff Costs $ 0,00



Overtime Costs $ -

Appendix 4 - Integer Programming Model Considering Hiring/Firing (Limited Firing)



Forecast 4400 4400 6000 8000 6600 11800 13000 11200 10800 7600 6000 5600 95400


Inventory 240 2240 4240 4640 3040 6000 4400 1600 600 0 0 0 0 26760



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



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


$ 6.598.680,00


Layoff Costs $ 36.000,00



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

...

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Production and Service Planning II - Case Study “Macpherson Refrigeration Limited”