A supplier to Toyota stamps out parts using a press. Changing a part type requir

Question

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 two hours. The supplier estimates that each hour spent on the changeover costs $200. Demand for parts is 1,000 per month. Each part costs the supplier $100, and the supplier incurs an annual holding cost of 25%.

Determine the optimal production batch size for the supplier.

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?)

Explanation / Answer

Annual demand = 12*1000 = 12000

Fixed setup cost, S = 2*200 = $ 400

Holding cost, H = 100*25% = $ 25

Optimal production batch size, Q = SQRT(2DS/H)

= SQRT(2*12000*400/25)

= 620

Target batch size as per Toyota requirement = Q/4 = 620/4 = 155

In the equation of EOQ, we see that Batch size (Q) is directly proportional to square root of setup cost.

Therefore, if Q is reduced by a factor of 4, then setup cost should reduce by a factor of 16

Target setup cost = 400/16 = $ 25

Each hour of setup costs $ 200

Therefore, target setup time = 25/200 = 0.125 hours or 7.5 minutes

Therefore, supplier should achieve a setup time of 7.5 minutes so that optimal batch size drops to 1/4th of its current level.

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