Optimal purchasing decisions for two differentiated products with demand substitutable

A purchasing decisions for two differentiated products with demand substitutable under a single period is considered in this paper, and the two differentiated products´ purchasing decision problem is formulated as a two-stage stochastic nonlinear program. The first order conditions are given by probability function. We solve the first stage of the problem to determine the optimal purchasing quantities of the two products, on the other hand, we solve the second stage problem to determine the products allocation problem when demand realized. At last, we give a numerical example for uniform demand distribution.