Two-Echelon Lot-Sizing with Asymmetric Information and Continuous Type Space

We analyse a two-echelon discrete lot-sizing problem with a supplier and a retailer under information asymmetry. We assume that all cost parameters are time independent and that the retailer has single-dimensional continuous private information, namely either his setup cost or his holding cost. The supplier uses mechanism design to determine a menu of contracts that minimises his expected costs, where each contract specifies the retailer's procurement plan and a side payment to the retailer. There is no restriction on the number of contracts in the menu. To optimally solve this contracting problem we present a two-stage approach, based on a theoretical analysis. The first stage generates a list of procurement plans that is sufficient to solve the contracting problem to optimality. The second stage optimally assigns these plans to the retailer types and determines all side payments. The result is an optimal menu with finitely many contracts that pools retailer types. We identify cases for which the contracting problem can be solved in polynomial time and provide the corresponding algorithms. Furthermore, our analysis reveals that information asymmetry leads to atypical structures in the plans of the optimal menu, e.g., plans violating the zero-inventory property. Our solution approach and several results are directly applicable to more general problems as well.