A coordination mechanism for supplier selection and order quantity allocation with price-sensitive demand and finite production rates

We study a supplier selection and order quantity allocation problem in a two-stage supply chain, which is composed of a set of potential suppliers and a single buyer/retailer trading one product. The demand at the buyer's stage is price-sensitive and suppliers have finite production rates. Within this framework, the optimization of the supply chain is evaluated by considering the performance of both stages and guaranteeing their profitability through a coordination mechanism based on profit-sharing. Two mixed integer nonlinear programming models are presented under different lot-sizing policies to determine the optimal set of selected suppliers, retail price, and order quantity and number of orders per order cycle for each selected supplier. The structure of the models' solutions is examined by deriving properties of the optimal supplier selection and order quantity allocation scheme. Numerical examples are also provided to illustrate the applicability of the proposed models.