Pricing and order quantity of substitutes in two inventory‐related markets

Abstract

We determine optimal pricing and order quantity of two substitute products in two markets, one of them is seasonal, with a decreasing market potential over time, and the other is nonseasonal. The two markets are sealed, that is, the prices in one market are irrelevant to consumers in the other market. Still, the two markets are linked through inventories and the order quantity policy. In the paper, we develop a nonlinear model, in which seasonal demand depends on time and on both products' prices, while nonseasonal demand is time‐invariant and is the function of both products' prices. Then, we provide an algorithm to compute the optimal solution. An illustrative example is given along with a sensitivity analysis. Among other results, we obtain that dynamic pricing and accounting for substitution effect lead to more profit. Also, when both ordering and holding costs are high, it is beneficial for the firm to order fewer times in large sizes.