Macpherson Refrigeration Limited Case Study

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MacPherson Refrigeration Case

Frank (Franchao) Zhu, Sida Li

Executive Summary

Linda Metzler, the newly appointed production planning manager of MacPherson Refrigeration Limited (MRL), was formulating the production plan for the year beginning on January 1. Linda has different basic tools to meet demand fluctuations, including building inventory to meet peaks, using overtime and hiring and laying off workers. Based on these different tools and trade-offs, she identified three alternatives to meet forecasted demand and Now she needs to decide which is the optimal solution to the production plan.


The decision variables:

  • No. of Workers Hired each month;
  • No. of Workers Laid Off each month;
  • No. of Overtime Worker Months

The Objective Function (and Structures):

  • Total Monthly Cost=No. of Workers Hired*Hiring Cost + No. of Workers Laid off* Layoff Cost + No. of Workers On Hand *Regular Salary per month + Overtime Worker Months*Overtime Salary per month + Ending Inventory*Carrying Cost per month.
  • Total Sum Cost=January Monthly Cost+…..+ December Monthly Cost  


  • The Labor Hiring and Layoff could be conducted immediately in the current month


  • No. of Workers Hired and Laid off each month should equal or more than 0;
  • Total production each month should equal or less than the Production Capacity;
  • Overtime Worker Months should equal or more than 0;
  • Ending Inventory should equal or more than 0;
  • No. of Workers Hired and Laid off and Overtime Worker Months should be integer;


After clarifying the Decision Variables, Objective Functions, Assumptions and Constraints, we can build a model to include all information and decision variables into one chart. To calculate the optimal production plan, we can use the Solver and put in the objective, variables, and constraints. It is important to remember when running the Solver we should choose the GRG Nonlinear because the model we set up is not LP.

Linda also has three alternatives to meet forecasted demand, we should consider whether the model we are using is appropriate for other strategies or not. Luckily, we could leverage the same model with different constraints to solve the optimal resource allocation under different strategies.

For instance,with the strategy (1) level production (i.e., produce the same number of units each month with constant workforce), we could only hire and lay off workers in the very beginning of the year.  By using alternative (2) chase demand (i.e., carry no inventory) with constant workforce using overtime only, we should make the ending inventory equals zero and the hire and lay off workers in the beginning. Considering alternative (3) chase demand by hiring and firing only but no overtime, we can adjust our hiring and laying off number but make the overtime zero.




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