Scenario 3: Parts-R-Us

A supplier to Toyota 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%.

1)Determine the optimal production batch size for the supplier.

2)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 1⁄4 of its current level? 

1.)

Given:

Annual demand = 12*1000 = 12000

Fixed setup cost, S = 2*250 = $500

Holding cost, H = 100*20% = $20

Formula:

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

Solution:

Q = SQRT(2*12000*500/20)

Q = 774.59 (rounded off to whole number)

Answer:

Q = 775 

2.)

Target batch size as per Toyota requirement = Q/4 = 775/4 = 193.75

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 as shown below:

Target setup cost = 500/16 = $31.25

Given that each hour the setup costs = $250

Solution:

Therefore, target setup time = 31.25 / 250

Target setup time = 0.125 hours (convert to minutes, multiply by 60)

Target setup time = 7.5 minutes

Answer:

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

Step-by-step explanation

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