Problem
A supplier to Chupapi stamps out parts using a press. Changing a part type requires the supplier to change a die on the press. This changeover currently takes two 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 20%.
i. Determine the optimal production batch size for the supplier.
ii. Chupapi wants the supplier to reduce its batch size by a factor of 4; that is, if the supplier currently produces Q parts per batch, Chupapi 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 (in minutes) creates a scenario in which the optimal batch size drops to ¼ of its current level?