A retailer has targeted a shelf item to be out of stock only 5 percent of the time (m). Customers have come to expect this level of product availability, so much so, that when the out-of-stock percentage increases, customers seek substitutes and lost sales occur. From market research studies, the retailer has determined that when the out-of-stock probability increases to the 10 percent level (y), sales and profit drop to one-half of those at the target level. Decreasing the out-of-stock percentage from the target level seems to have little impact on sales, but it does increase inventory-carrying costs substantially. The following data have been collected on the item:
Price $5.95
Cost of item 4.25
Other expenses associated with stocking the item $0.30
Annual items sold @ 95% in-stock 880
The retailer estimates that for every one percentage point that the in-stock probability is allowed to vary from the target level, the unit cost of supplying the item decreases according to C = 1.00 - O.lO(y-m), where C is the cost per unit, y is the out-of-stock percentage, and m is the target out-of-stock percentage.