Question: At a distributor of spare auto parts, the weekly demand for part XYZ is estimated to be normally distributed with mean 30 and standard deviation 10. The delivery lead time from the manufacturer of the part is six weeks. The distributor is following a (Q, R) inventory management policy to manage this part.

Assuming there are 52 weeks in a year, please answer the following questions.

1. Under the (Q, R) policy assume that the reorder point for the part is 210. Under this policy, what percentage of the order cycles will the distributor stock out of this part?
2. Assume that the distributor is willing to stock out during no more than 5% of the order cycles, and will set their reorder point accordingly. If they purchase the part from the supplier with the 6-week lead time, the unit cost of the part is $50. However they can also purchase the part from a local supplier with a lead time of one week, but then the unit cost is $55. Assuming that the fixed cost of an order is $50 (regardless of supplier used) and the annual holding cost rate is 20%, please determine which supplier they should choose. (Note: You can ignore the cost of purchasing the items to be held in safety stock since this would represent a one-time cost.)

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