Abstract: Companies often order products from multiple suppliers. Combining these orders from different suppliers into joint shipments can have environmental and economic benefits. Based on a case company, we formulate the problem of determining in which periods orders for multiple products should be placed to minimize the sum of the order and inventory costs. However, we limit the number of periods in which shipment, and vary the number of periods to measure its impact. We call this problem the Bi-Objective Lot Sizing Problem with Shipment Minimization (BLSPSM). This problem combines an overarching problem, namely the determination of shipment periods, with subproblems for each product, namely the determination of order periods and order quantities. We introduce dynamic programming heuristics for the BLSPSM, which utilize the bi-level nature of the problem, and which we call bi-level dynamic programming. We show that these heuristics outperform existing methods for a special case of our problem (the Coordinated Uncapacitated Lot Sizing Problem) and finds efficient frontiers very close to the best ones for all instances in our test
