Multi-stage modeling for non-cooperative multi-echelon supply chain management problem with discount under uncertainty

The goal of supply chain management is to enhance various functions of different parts and levels of a supply chain to obtain the maximum possible profit. But this goal is not completely achievable due to the fact that there are differences between mentioned parts and levels, in their attitude towards the goals. These differences, for example pricing, stocking, and the costs related to parts and levels, will gradually result in a deduction in strength and competitiveness in system. In this study, multi-echelon supply chain has been investigated using game theory approach and considering the dependence of demand to selling price, fuzzy marketing costs, and discounts for all units. The problem has been modeled assuming that there’s no cooperation between different levels. Also, Stackelberg model assumptions have been taken into account, in which each level, with respect to market conditions, can undertake the leadership task. The aim of this problem is to determine the best decision of each player to obtain the optimal order quantity, a shortage for manufacturer and the selling price of each player, and to maximize incomes, to minimize costs and in general, to maximize possible profit for all players participating in the chain. GAMS softwares and metaheuristic algorithms have been used to solve the problem. Finally, the profit for supply chain members’ in different leadership conditions have been analyzed by generating different examples.