Problem 1. Weekly demand for paper towels at a Target store is normally distributed, with a mean of 1,000 and a standard deviation of 300. The supplier takes two weeks to supply a Target order, which is for a batch size of 5,000. Target is aiming for a fill rate of 99 percent and monitors its inventory continuously. How much safety inventory of paper towels should Target carry? What should its ROP be?
Problem 2. Weekly demand for gaming consoles at Liverpool, a Mexican department store chain, is normally distributed with a mean of 1,000 and a standard deviation of 400. The replenishment lead time from the supplier is four weeks. Liverpool is targeting a CSL of 95 percent and uses a periodic review policy under which it reorders consoles every eight weeks. What is the average order size? How much safety inventory of consoles should Liverpool carry? What should its order up to level be? How much safety inventory would be required if Liverpool switched to a continuous review policy?
Problem 3. Demand for fasteners at W.W. Grainger is 20,000 boxes per month. The holding cost at Grainger is 20 percent per year. Each order incurs a fixed cost of $400. The supplier offers an all unit discount pricing scheme with a price of $5 per box for orders under 30,000 and a price of $4.90 for all orders of 30,000 or more. How many boxes should Grainger order per replenishment?
Problem 4. Demand for phones at Amazon is 5,000 per month. The hold¬ing cost at Amazon is 25 percent and the company incurs a fixed cost of $500 for each order placed. The supplier offers a marginal unit quantity discount with a price of $200 per phone for the first 10,000 phones in an order, a price of $195 for the next 10,000 phones in the order, and a price of $190 for the quantity above 20,000 in the order. How many phones should Amazon order per replenishment?
Problem 5. The Orange company has introduced a new music device called the J-Pod. The J-Pod is sold through Good Buy, a major electronics retailer. Good Buy has estimated that demand for the J-Pod will depend on the final retail price p according to the demand curve
Demand D = 2,000,000 - 2,000p
The production cost for Orange is $100 per J-Pod.
a. What wholesale price should Orange charge for the J-Pod? At this wholesale price, what retail price should Good Buy set? What are the profits for Orange and Good Buy at equilibrium?
b. If Orange decides to discount the wholesale price by $40, how much of a discount should Good Buy offer to cus¬tomers if it wants to maximize its own profits? What frac¬tion of the discount offered by Orange does Good Buy pass along to the customer?