Optimal inventory policies for substitutable commodities with stochastic demand

In this article the authors consider a stochastic model for two products which have a single-period inventory structure and which can be used as substitutes for each other should the need arise. Substitution will occur with probability one, but at perhaps a different revenue level. The authors prove that the expected profit function is concave allowing them to find optimal stocking levels for the two products. They compare optimum inventory levels for the case of single substitution with that where there is no substitution. It is demonstrated for the case of single substitution that total optimum order quantities can actually increase or decrease with the substitution revenue.