Question

MR is a manufacturer of industrial fridges, freezers, and air conditioners. In December, the production

planner needs to submit a production plan to the plant manager for the next year. The aggregate forecast for
each quarter of next year is Q1: 14,800; Q2: 26,400; Q3: 35,000, and Q4: 19,200 units. The beginning inventory
in January is 0, and the year-end inventory in December of next year can be 0. It costs MR $24 to hold an
appliance in inventory for one quarter. Shortages are undesirable. Assume that all shortage will be backordered, and that back-order cost is $100 per unit per quarter. There are 160 permanent workers who produce
19,200 units per quarter. In busy quarters, workers can produce up to 9,600 additional units during overtime.
Regular time labour cost is $60 per unit appliance and overtime labour cost is $83 per unit. MR can hire up to
160 temporary workers for a second shift. Assume temporary workers have the same productivity and can
produce up to 19,200 units per quarter. A unit produced by temporary workers also costs $60 in labour cost.
However, there will be an extra hiring cost of $25 per unit during the first quarter of employment.


a. If permanent workers are used for the next four quarters during regular time, how many units will MR be
short at the end of the year and in which quarters?
b. Meet units short by hiring temporary workers. Use trade-off analysis to choose the minimum cost plan in
this case. (Hint: Hire approximately 78 temps for two quarters starting in Q2.)
c. Would using overtime (in addition to some temporary production) be less expensive? Use trade-off analysis
to choose the overall minimum cost plan. (Hint: Hire approximately 38 temps for two quarters starting in Q2,
supplemented with overtime.)

Answer 1

a. Using permanent workers during regular time will result in a shortage of 18,600 units at the end of the year. The shortage will occur in all four quarters. b. Hiring approximately 78 temporary workers for two quarters starting in Q2 would be the minimum cost plan to meet the units short. c. Hiring approximately 38 temporary workers for two quarters starting in Q2, supplemented with overtime, would be the overall minimum cost plan.

Step-by-step explanation:

a. To determine how many units MR will be short at the end of the year using permanent workers during regular time, we need to calculate the production and compare it to the aggregate forecast. Given that there are 160 permanent workers and they can produce 19,200 units per quarter, the total production for the year is 4 x 19,200 = 76,800 units. However, the aggregate forecast for the year is 14,800 + 26,400 + 35,000 + 19,200 = 95,400 units. Therefore, MR will be short by 95,400 - 76,800 = 18,600 units at the end of the year. This shortage will occur in all four quarters.

b. To meet the units short by hiring temporary workers, we can use trade-off analysis to choose the minimum cost plan. Hiring approximately 78 temps for two quarters starting in Q2 would be the minimum cost plan. This means that MR would hire 78 temps in Q2 and Q3. Hiring temps during these two quarters would help meet the shortage and minimize costs.

c. To determine if using overtime and temporary production would be less expensive, we can use trade-off analysis to choose the overall minimum cost plan. Hiring approximately 38 temps for two quarters starting in Q2, supplemented with overtime, would be the overall minimum cost plan. This means that MR would hire 38 temps in Q2 and Q3, and also utilize overtime during those two quarters. This plan would help meet the shortage while keeping costs lower compared to other options.