Optimal Ordering Decisions for Multiple Substitutable Products with Stochastic Demands

Abstract

This paper deals with a single period stochastic inventory problem with multiple products some (or all) of which can be substituted if one is out of stock. ‘Given the cross substitution probabilities of these products, the problem is to find the optimal order quantity of each item which will maximize the expected profit per period. Since the objective function representing the one period expected profit is extremely difficult to analyze in the general case of n products, we propose a heuristic rule which is based on the exact solution for the two product case whose solution is known. The effectiveness of the heuristic is compared with the results of a simulation-optimization study which can generate the optimal solution. A detailed example using exponential demand for three products illustrates the results.