A campus bookstore sells the Palm m505 handheld for $399. The wholesale price is $250 per unit. The store estimates that weekly demand averages 0.5 unit and has a Poisson distribution. The bookstore's annual inventory holding cost is 20 percent of the cost of inventory. Assume orders are made weekly and the lead time to receive an order from the distributor is four weeks.
a. What base stock level minimizes inventory while achieving a 99 percent in-stock probability?
b. Suppose the base stock level is S 4. What is the average pipeline inventory?
c. Suppose the base stock level is S 5. What is the average inventory held at the end of the week in the store?
d. Suppose the base stock level is S 6. What is the probability a stockout occurs during a week (i.e., some customer is back-ordered)?
e. Suppose the base stock level is S 6. What is the probability the store is out of stock (i.e., has no inventory) at the end of a week?
f. Suppose the base stock level is S 6. What is the probability the store has one or more units of inventory at the end of a week? The bookstore is concerned that it is incurring excessive ordering costs by ordering weekly. For parts g and h, suppose the bookstore now submits orders every two weeks. The demand forecast remains the same and the lead time is still four weeks.
g. What base stock level yields at least a 99 percent in-stock probability while minimizing inventory?
h. What is the average pipeline stock?