The following information relates to a company's aggregate production planning activities: Beginning Workforce = 50 workers
Production per Employee = 250 units per quarter
Hiring Cost = $1000 per worker
Firing Cost = $1,500 per worker
Inventory Carrying Cost = $15 per unit per quarter
If a chase demand strategy is used then the number of workers fired at the start of quarter 3 is
A)0.
B)50.
C)60.
D)100.

Question

The following information relates to a company's aggregate production planning activities:  Beginning Workforce = 50 workers
Production per Employee = 250 units per quarter
Hiring Cost = $1000 per worker
Firing Cost = $1,500 per worker
Inventory Carrying Cost = $15 per unit per quarter
If a chase demand strategy is used then the number of workers fired at the start of quarter 3 is
A)0. 
B)50. 
C)60. 
D)100.

Quizplus · Accepted Answer

In a chase demand strategy, the company adjusts its workforce to match the demand for its products. Since the production per employee is given as 250 units per quarter, the total production capacity of the workforce is:
50 workers * 250 units per worker = 12,500 units per quarter

Assuming that the demand for the first two quarters is met by the existing workforce, the inventory buildup at the end of quarter 2 is:
Inventory buildup = Demand - Production
= (Quarter 3 demand + Quarter 4 demand) - (50 workers * 250 units per worker * 2 quarters)
= (2D) - 12,500

To minimize the total cost of production, the company should adjust its workforce at the start of quarter 3 to match the demand. If the demand is less than 12,500 units, the company should fire some workers, and if the demand is more than 12,500 units, the company should hire some workers.

Let's consider the case where the demand in quarter 3 is less than 12,500 units. In this case, the company should fire some workers to reduce its production capacity to match the demand. The cost of firing x workers is given by:
Firing cost = x * $1,500

The cost of carrying an inventory of y units for one quarter is given by:
Inventory carrying cost = y * $15

The total cost of production is the sum of the hiring/firing cost and the inventory carrying cost:
Total cost = Firing cost + Inventory carrying cost
= x * $1,500 + [(2D) - 12,500 - x * 250] * $15

To minimize the total cost, we take the partial derivative of the cost function with respect to x, set it equal to zero, and solve for x:
d(Total cost)/dx = -1,500 + 15 * 250 = 0
x = 60

Therefore, the company should fire 60 workers at the start of quarter 3 to minimize the total cost of production.

The Following Information Relates to a Company's Aggregate Production Planning