Two-echelon lot-sizing with asymmetric information

We consider a two-echelon discrete lot-sizing problem with a supplier and a retailer. The retailer needs to satisfy known market demand for a given time horizon. In each time period, the retailer can order products at the supplier, which can be used to satisfy demand or be kept in inventory. Likewise, the supplier can produce in each period and keep products in inventory. A complicating factor is that the retailer has private information and the market power to enforce any order plan onto the supplier. We view this setting from the supplier's perspective, and want to minimise his production and holding costs under the constraint that the market demand must be satisfied.

The supplier uses mechanism design techniques to deal with the information asymmetry and the lack of market power. He offers the retailer a specifically constructed menu of contracts that minimises the supplier's expected costs, where each contract specifies the retailer’s order plan and a side payment to the retailer. The side payments are used as incentive to persuade the retailer to accept a contract. We propose a two-stage solution approach to determine an optimal menu, and identify cases where this approach has polynomial running time. Finally, we discuss how the solution approach can be applied to other problem settings.

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