OzDe Distributing, located on Kuhl Road in Erie, Pennsylvania, manages the inventory at all of the retail stores it delivers to. One of the decisions that is made at each of the 21 stores is how much inventory should be in the store on the shelf (where the consumer can see it) and how much should be placed in the back room (where the consumer cannot see it). Allocating too little shelf space for a particular product can cause frequent “stockouts,” resulting in opportunity loss when the consumer finds the shelf empty and requiring frequent replenishment. Allocating too much shelf space for a particular product will inevitably cause the shelf space for other products to be smaller (there is only so much shelf space), and then that product may experience more frequent stock-outs. 

OzDe makes deliveries and manages shelf space every day. With 21 stores to which to deliver goods and manage inventory, OzDe visits three stores each day. On each visit, OzDe records whether or not a stock-out (the shelf is empty) has occurred and tries to adjust the space allocation of the product (i.e., if a stockout has occurred for a particular product, OzDe allocates more shelf space). 

Discussion Questions 

1. What type of random variable is the number of stock-outs per year? Explain. What is the range of outcomes for this random variable per product? 

2. What type of random variable is the time between stockouts? Explain. What is the range of outcomes for this random variable per product? 

3. When OzDe allocates more shelf space for a particular product, what happens to both the number of stock-outs per year and the time between stock-outs for that particular product?