Joint Pricing and Inventory Control for Seasonal and Substitutable Goods Mentioning the Symmetrical and Asymmetrical Substitution

Nowadays many well-known firms may produce similar products at different prices in order to remain in the competitive environment. The price differences may cause substitution condition which motivates the customers to substitute the similar cheaper product with an expensive one leading to an environment which is known as “customer-based price driven substitution”. This research proposes a new mathematical model towards a joint pricing and inventory control for seasonal and substitutable goods in a competitive market over a finite time planning horizon.  It is assumed that the two substitute goods belong to two different rival firms. The objective is to determine the optimal price, order quantity and the number of periods for one product in the presence of symmetrical and asymmetrical substitutions such that the total profit of the related firm is maximized. Firs tit is showed that total profit is a concave function of price which leads us to a unique optimal solution. To provide the optimal solution a simple algorithm is developed. Finally, in order to evaluate the performance of proposed algorithm a numerical example is presented.