Question 10: A supplier to Toyota stamps out parts using a press. Changing a par

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 $500. Demand for parts is 1,000 per month. Each part costs the supplier $200, 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 2; that is, if the
supplier currently produces Q parts per batch, Toyota would like them to produce Q/2
parts per batch. What should the supplier do in order to make this amount optimal for
him? (In other words, what setup time creates a scenario in which the optimal batch
size drops to 1/2 of its current level?)

Explanation / Answer

a.) Setup cost, S = $500*4 = $2000 ($500 per hr for 4 hr long setup) Demand, D = 1000 per month = 12000 per year Cost of part, C = $200 Holding cost = I*C = $200*0.25 = $50 per year Optimum batch size is given by... Q* = sqrt(2DS/IC) = sqrt(2*12000*200/50) = 309.84 = 310 (approxx.) b.) For half batch size the setup cost must be 1/4th (because of the root) So if we want half the batch size setup cost must be $100 i.e. Setup time = 2 hrs

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