Reference no: EM132099242

A retailer has targeted a shelf item to be out of stock only 5% of the time (m = 0.05). Customers have come to expect this level of product availability such 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% level (y), profit (per unit) drops to 1/2 of that 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 $8.95/unit Cost of item $4.50 Other expenses associated with stocking the item $0.3 Annual items sold @95% in-stock 880 The retailer estimates that for every 1% 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 - 0.10(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. How much variability from the target stocking percentage should the retailer allow?