The manager of a car wash received a revised price list from the vendor who supplies soap, and a promise of shorter lead time for deliveries.

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QUESTION:

The manager of a car wash received a revised price list from the vendor who supplies soap, and a promise of a shorter lead time for deliveries. Formerly the lead time was four days, but now the vendor promises a reduction of 25 percent at that time. The annual usage of soap is 4,500 gallons. The car wash is open 360 days a year. Assume that daily usage is normal and that it has a standard deviation of 2 gallons per day. The ordering cost is $ 30 and the annual carrying cost is $ 3 a gallon. The revised price list (cost per gallon) is shown in the following table:

Quantity _______________Unit Price

1–399 ……………….…………$2.00

400–799 ………….…………… 1.70

800+ …………….…….………. 1.62

a. What order quantity is optimal?

b What ROP is appropriate if the acceptable risk of a stockout is 1.5 percent?


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