Coordination of Pricing and Order Quantity for Two Replaceable and Seasonal Products

Document Type : Original Article


1 Department of Industrial and System Engineering, Tabriat Modares University, Iran

2 Group for Research in Decision Analysis (GERAD), HEC Montreal University, Canada

3 Department of Industrial Engineering, University of Kurdistan, Kurdistan, Iran


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.