Competitive and Cooperative Inventory Management in a Two-Echelon Supply Chain With Lost Sales

This paper studies inventory management in a two echelon supply chain with stochastic demand and lost sales. The optimal policy is evaluated and compared with the competitive solution, the outcome of a game between a supplier and a retailer in which each firm attempts to maximize its own profit. It is shown that supply chain profit in the competitive solution is always less than the optimal profit. However, the magnitude of the competition penalty is sometimes a trifle, sometimes enormous. Several contracts are considered to align the firms’ incentives so that they choose supply chain optimal actions. These contracts contain one or more of the following elements: a retailer holding cost subsidy (which acts like a buy-back/return policy), a lost sales transfer payment (which acts like a revenue sharing contract) and inventory holding cost sharing. With the latter each firm incurs a fixed fraction of the total supply chain holding cost. It is found that the retailer holding cost subsidy is generally not sufficient to coordinate the supply chain. The most effective contract combines a lost sales transfer payment with inventory holding cost sharing: it always coordinates the supply chain, both players are always better o¤ and it is simple to evaluate