Optimal Algorithms for the Economic Lot-Sizing Problem with Multi-supplier

This paper considers the economic lot-sizing problem with multi-supplier in which the retailer may replenish his inventory from several suppliers. Each supplier is characterized by one of two types of order cost structures: incremental quantity discount cost structure and multiple set-ups cost structure. The problem is challenging due to the mix of different cost structures. By analyzing the optimal properties, we reduce the searching range of the optimal solutions and develop several optimal algorithms to solve all cases of this multi-supplier problem.