Question: Question 10:

A supplier to Toyota stamps out parts using a press. Changing a part type requires the supplier to change the die on the press. This changeover currently takes four hours. The supplier estimates that each hour spent on the changeover costs $250. Demand for parts is 1,000 per month. Each part costs the supplier $100, and the supplier incurs an annual holding cost of 25%.

a. Determine the optimal production batch size for the supplier.

b. Toyota wants the supplier to reduce its batch size by a factor of 4; that is, if the supplier currently produces Q parts per batch, Toyota would like them to produce Q/4 parts per batch. What should the supplier do in order to achieve this result? (In other words, what setup time creates a scenario in which the optimal batch size drops to ¼ of its current level?)

Note that the supplier cannot alter demand or his holding cost. Therefore, Toyota is asking him to cut his setup cost so that the smaller order is optimal for him.