Stock Wars: Inventory Competition in a Two-Echelon Supply Chain with Multiple Retailers

Abstract

This paper studies the competitive and cooperative selection of inventory policies in a two-echelon supply chain with one supplier and N retailers. Stochastic demand is monitored continuously. Retailers incur inventory holding and backorder penalty costs. The supplier incurs holding costs for its inventory and backorder penalty costs for backorders at the retailers. The latter cost reflects the supplier's desire to maintain adequate availability of its product to consumers. Previous research finds the supply chain cost minimizing reorder point policies, the cooperative solution. The competitive solution is a Nash equilibrium, a set of reorder points such that no firm can deviate from the equilibrium and lower its cost. It is shown that Nash equilibria exist and a method is presented to find all of them. In some settings the cooperative solution is a Nash equilibrium; competition does not necessarily lead to supply chain inefficiency. In other settings, competition leads to costs that are substantially higher than optimal. Usually (but not always), the competitive supply chain carries too little inventory. Three cooperation strategies are discussed: change incentives, change equilibrium, and change control. A set of contracts is provided that changes the firms' incentives so that the optimal policy is a Nash equilibrium. An equilibrium change can improve performance but does not guarantee optimal performance. To change control, the firms let the supplier choose all reorder points, a key component in vendor managed inventory. That change leads to optimal supply chain performance.