The Thompson Supply company provides a full range of products for industrial construction. Thompson buys the product from its manufacturer and then resells the product to construction companies. Its products are readily replaceable, and so a stockout typically results in a lost sales.   Through its history, Thompson has maintained a reputation for having things in stock. It was often the first sourcing choice of its customers because they could rely on Thompson to have what was needed. The store is open 6 days per week.

One particular type of fastener experienced fairly steady demand of 27 units per day with a standard deviation of daily demand of 5 units. The lead time for delivery is 6 days.

a) Suppose Thompson uses a reorder point of 170 units. What is the implied cycle service level?

b) Thompson decides the reorder point of 170 is insufficient. They want to achieve a 98% cycle service level with this item. What should the reorder point be?

c) Thompson has another item that sells 1,200 units every week, with a standard deviation of weekly demand of 150 units. The lead time for this item is 3 days. To achieve a 98.5% cycle service level, what should the reorder point be?

d) A third item is ordered 26 times per year (i.e. it has 26 inventory cycles per year - it gets ordered every two weeks). It has a 97% cycle service level. What is the likelihood that Thompson will stockout of this item at least once over the course of the year?