Designing multi-period supply contracts in a two-echelon supply chain with asymmetric information

We study a two-echelon supply chain consisting of a supplier and a retailer, where the supplier uses a simple and easily implementable incentive scheme - making a side payment - to influence the retailer’s ordering plan. The supplier makes a take-it-or-leave-it offer to the retailer in the form of a menu of contracts, each consisting of a procurement plan plus a side payment. The retailer, who possesses private information about customer demand and his cost parameters, either accepts one of the contracts or imposes his own optimal plan. We formulate the supplier’s problem of designing optimal contracts with the realistic assumption that the retailer’s outside option depends on his private information. Taking into account the retailer’s reaction to the proposed offer, the supplier faces a nested (bi-level) optimization problem, which we transform into a single-level mixed integer programming formulation. In our analysis, we use a network interpretation for the set of incentive constraints and show some properties of optimal contracts. This enables us to considerably reduce the number of incentive constraints and to find optimal values of the side payment quantities. Our findings regarding the possible behavior of the opportunistic retailer deviate from those of previous studies as a result of considering more realistic assumptions.