Suppose you are the inventory manager of a Best Buy store. You are particularly interested in finding a good inventory policy for 32” Sony Wega TV. Since the store is new, you rely on information that you obtained from other stores in the Greater Philadelphia area. Joe, the manager at Kings of Prussia says “Well buddy, I have the perfect inventory policy that I can tell you. I’ve been using it here for the last 5 years, and I haven’t had a stock out. Then you obtain from him the following information:

Demand for Wega-32 TV follows a normal distribution with average annual demand of 120, and a standard deviation of 60. Joe follows a base stock policy with base stock level of 10. The lead time for Wega-32 TV is 1 month.

(a) Do you agree with Joe in terms of not losing one customer due to stockouts?

(b) Your inventory theory knowledge tells you that the normal distribution may not be appropriate and you think that Poisson should be used instead. Using the Poisson distrubtion, what is the fill rate achieved by Joe? Compare this fill rate with your answer in part (a)

(c) Not satisfied with the fill rate achieved using the base stock policy, you decide that a (Q, r) model should provide better customer service at a lower inventory cost. Calculate the inventory policy that should be implemented to obtain a fill rate of 90%. The order cost is $35, the company use a holding cost rate of 10% per $/per year. The cost of a TV is $500. What is the backorder level, the inventory level, and the safety stock?

(d) After you implement the (Q, r) policy, you find that the lead time is variable, and you decide to model the lead time as a random variable with a mean of 1 month and a standard deviation of 1 week. Furthermore, if you have a stockout you lose the customer, which is estimated that will represent a loss of profit. The average profit for a TV is 20%. Use the stockout approach to calculate the optimal inventory policy. Make sure that the recommended inventory policy achieves a minimum service level of 90%.