Two-echelon supply chain model with demand dependent on price, promotional effort and service level in crisp and fuzzy environments

Abstract

This article explores a supply chain model consisting of a single manufacturer and two competing retailers in the same market. The manufacturer, as a Stackelberg leader specifies a wholesale price and bears servicing costs of the products. Then, both the retailers advertise the products and sell them to the customers. So, the demand of the products is influenced by selling price, service level and also promotional effort. On the basis of this gaming structure, two mathematical models have been formed-crisp model, where each member of the chain exactly knows all the cost parameters and fuzzy model where those cost parameters are considered as fuzzy numbers. Optimal strategies for the manufacturer and the retailers are determined and some numerical examples have been given. Finally, how little perturbations of parameters affect the profits of the chain members have been determined. The fuzzy model is specially applicable in practical situations where different costs can not be known precisely.