MacPherson Refrigeration Guidelines
Set up an optimization model that clearly shows the decision variables, how they
affect the number of workers on hand, regular and overtime production, and ending
inventory, as well as the various costs incurred each month. Explicitly state the
constraints that must be satisfied, and the overall objective. You may find it convenient
to express the units in thousands of appliances and costs in thousands of dollars. Note that
overtime is measured in number of worker months.
a. Determine optimal hiring and firing of workers, regular time and overtime production
and inventory decisions, month to month over the given planning period. (Answer:
Minimum total cost = $6,221,160)
b. Consider the three strategies that Linda has identified: stable production (i.e., produce
same number of units each month), chase demand (i.e., carry no inventory in any
month) with overtime only (without hiring/firing, except perhaps in January), and
chase demand by hiring and firing only (without using overtime). Each strategy is a
plausible practical alternative, but imposes additional constraints on the optimization
model in part a. Modify your optimization model to capture these additional
requirements imposed by each of the three strategies and solve. Compare your
optimal solutions and total costs with those provided in Exhibits 1 – 3 of the case. In
some cases you may be able to get a lower than Linda’s solutions.
c. Plot on one line chart the demand forecast and total monthly production under each of
the four strategies in parts a and b above. Comment on how each attempts to match
supply with demand.
d. Tabulate and graph on one stacked chart the annual costs of regular time, overtime,
hiring, layoffs, and inventory stocking across the four strategies in parts a and b.
Comment on how the four strategies differ along these cost dimensions.
e. Comment on how a purely quantitative, cost based model in part a above may fail to
capture some important qualitative aspects of managing this operation in the real
world. Suggest a modification of the quantitative optimization model that would take
into account these qualitative aspects to yield a more practical solution.