Question

Manager T. C. Downs of Plum Engines, a producer of lawn mowers and leaf blowers, must develop

an aggregate plan given the forecast for engine demand shown in the table. The department has
a regular output capacity of 130 engines per month. Regular output has a cost of $60 per engine.
The beginning inventory is zero engines. Overtime has a cost of $90 per engine.
a. Develop a chase plan that matches the forecast and compute the total cost of your plan. Regular
production can be less than regular capacity.
b. Compare the costs to a level plan that uses inventory to absorb fluctuations. Inventory carrying
cost is $2 per engine per month. Backlog cost is $90 per engine per month. There should not be a
backlog in the last month.

Answer 1

Step-by-step explanation:

To develop an aggregate plan, we need to consider the forecasted demand and available capacity while minimizing costs. Let's analyze the two scenarios:

a. Chase Plan:

In a chase plan, the production is adjusted to match the forecasted demand. This means that each month's production will be equal to the demand for that month. However, the regular output can be less than regular capacity.

Using the given regular output capacity of 130 engines per month, we can match the demand as follows:

Month | Forecasted Demand | Production (Chase Plan)

-----------------------------------------

Jan | 150 | 150

Feb | 110 | 110

Mar | 120 | 120

Apr | 140 | 140

May | 160 | 160

Jun | 180 | 180

Total cost for the chase plan:

= (Regular Production Cost + Overtime Production Cost)

= (150 * $60 + 0 * $90) + (110 * $60 + 0 * $90) + (120 * $60 + 0 * $90) + (140 * $60 + 0 * $90) + (160 * $60 + 0 * $90) + (180 * $60 + 0 * $90)

= $9,000 + $6,600 + $7,200 + $8,400 + $9,600 + $10,800

= $51,600

b. Level Plan:

In a level plan, we aim to maintain a constant production rate throughout the planning horizon, using inventory to absorb fluctuations in demand. Backlog should not exist in the last month.

To calculate the optimal production rate, we need to consider the carrying cost and backlog cost. Let's calculate the production rate based on these costs:

Carrying cost = $2 per engine per month

Backlog cost = $90 per engine per month

Total cost for the level plan:

= (Carrying Cost + Backlog Cost)

= (0 * $2 + 40 * $90) + (40 * $2 + 0 * $90) + (10 * $2 + 20 * $90) + (30 * $2 + 0 * $90) + (50 * $2 + 0 * $90) + (70 * $2 + 0 * $90)

= $3,600 + $800 + $2,200 + $60 + $100 + $140

= $6,900

Therefore, the total cost for the chase plan is $51,600, and the total cost for the level plan is $6,900.