A retailer is selling a non-perishable product over a selling season of 5 weeks. The product is sold at a price of $50 and purchased from the supplier at a price of $25. In order to determine how many units to order from the supplier, the retailer uses the (r,Q) model with r=20 and Q=80. Orders placed to the supplier are delivered immediately and incur a fixed ordering charge of $150 per order. In case of a stock- out all subsequent customers in a given week leave the store without making a purchase. The retailer estimates there is a loss of goodwill cost of $1.5 per customer who does not buy because of a stock-out. Assume that inventory holding costs are insignificant.

Demand over the 5-week selling season is given in the table below. Assume there is no inventory at the start of the first period, before the order is placed.

Period Demand

1 41

2 55

3 12

4 52

5 41

(a) Calculatethefillrate,in-stockrateandtotalprofitsoverthesellingseason.

(b) Whattheretailerdoesnotknowisthatadishonestemployeeisstealinginventoryfromthestore if there are any units left at the end of a given week: each week he steals up to 15 units, that is, if there are fewer than 15 units left, he will steal the entire leftover stock, otherwise he will steal

only 15 units. Calculate the system and physical on-hand inventory as well as inventory shrinkage at the end of the 5-week selling season. Comment on what is happening and is likely to happen in the future.