Optimal Multi-Products Dynamic Pricing and Inventory Policies for Coordinating Production and Marketing under Fuzzy Environment: Fuzzy Expansion Methods


1 Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamc Azad University, Qazvin, P.O.Box 3419759811, Iran.

2 Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, P.O.Box 3419759811, Iran.

3 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, P.O.Box 14515/775 , Iran.


This paper investigates the optimal multi-products dynamic pricing and inventory policies over a multi-period planning horizon with deteriorating products and a fuzzy demand function. The objective is maximization of the discount profit. A dynamic programming model is presented to determine retail price and replenishment quantities. Also, due to the existence of uncertainties in the parameter values such as cost, deterioration rate, and the optimal strategies in general, it cannot be obtained with high feasibility. So, the concept of fuzzy set theory can be applied to cope whit this issue. Since the presented model is a fuzzy partial differential equation, three novel fuzzy expansion methods including Jacobi polynomials, airfoil polynomials, and fuzzy collocation methods are proposed for solving this problem. Finally, this paper carries out various computational experiments to assess the proposed model and solution approaches.