Management of multi-item retail inventory systems with demand substitution

Customers for retail merchandise can often be satisfied with one of several items. When certain items are not stocked, the resulting substitutions increase the demand for other items, which increases their optimal stock levels. Defining customer service to include substitution influences how inventory is managed to maximize the total profit obtained from a retail assortment, subject to given resource constraints. in this paper, we develop a general model to capture the effects of substitution on the demands for items in an assortment. Next, we formulate a methodology for jointly optimizing the inventory levels of a set of items with potential for substitution. Specific formulas for service level and optimal inventory level are derived assuming a negative binomial distribution for total demand, which has performed particularly well in fitting retail sales data. Illustrative examples are solved to provide insights concerning the behavior of the optimal inventory policies.