Stock Replenishment Policies in a Distributed Supply Chain with Competing Retailers

We investigate stock-replenishment problem in a distributed one-warehouse-n-retailer supply chain, in which warehouse supplying single product to n competing retailers. Each retailer intends to maximize his payoff. The profit rate per unit at retailers depends on stock available at warehouse, which replenishes his inventory from an exterior resource with ample supply. At the beginning of each period, stock at warehouse is finite, ordering strategy of each retailer has impact on other retailers. We characterize coordination solution to this distributed system with a Nash equilibrium. That is : retailers are decision makers and warehouse acts as a supervisor. When retailers replenish their stock in a Nash equilibrium, each can maximize own profit while pondering other retailers. Mathematical model for this n-retailer game is constructed. And at last, we prove that there exist only one equilibrium in this game.