Safety stock

The Acheson Supply Company provides a full range of products for industrial construction. Acheson 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 sale. Through its history, Acheson has maintained a reputation for having things in stock. It was often the first sourcing choice of its customers because they could rely on Acheson 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 Acheson uses a reorder point of 170 units. What is the implied cycle service level?
b) Acheson 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) Acheson 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 has a demand of 120 units per day with a standard deviation of 10 units. The lead time is also uncertain: it averages 9 days, with a standard deviation of 0.5 days. To achieve a 96% service level, what should the reorder point be?
e) A fourth 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 Acheson will stockout of this item at least once over the course of the year? (Do you remember your basic probability theory?)
f) Acheson actually maintains 4 warehouses across the state. Acheson is considering consolidating the four into a single warehouse. Suppose Acheson has a part that has a demand of 180 units per day with a standard deviation of 25 units per day. This occurs at each of the four warehouses. Also suppose that lead time is 7 days at all four warehouses, and that each maintains a 92% cycle service level.
i) What is the total safety stock at all four warehouses?
ii) If Acheson maintains the same total safety stock at the single, consolidated warehouse as it did at the four separate ones, what would the new cycle service level be?
iii) What should the safety stock be at the consolidated warehouse to achieve the same 92% cycle service level as before?

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