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.

This paper deals with the coordination of pricing and order quantity decisions for two seasonal and substitutable goods in one firm. We assume that the customers are price sensitive and they are willing to buy the cheaper products, which is known as one way and customers-based price driven substitution. First, a mathematical model is developed for one firm, which contains two replaceable products considering seasonality. The model aims to maximize the profit by determining optimal dynamic prices, order quantities and the number of periods for both of the products. Then, we show that the objective function is strictly concave of price and has a unique maximum solution. Next, an exact algorithm based on the Karush Kuhn Tucker (KKT) conditions is presented to determine the optimal decisions. Finally, a numerical example accompanied by sensitivity analysis on key parameters is developed to illustrate the efficiency of solution procedure and the algorithm.