AbstractThe multi-item lot-sizing problem considered here is concerned with finding the lot sizes over a horizon of discrete time periods to meet known future demand without incurring backlogs, such that the total cost of production and inventory holding is minimized. The capacity constraints arise because the production of each item consumes capacitated production resources at a given rate. Production is assumed to occur without set-ups. The problem is formulated as a capacitated trans-shipment problem. Use of modern, minimum-cost network flow algorithms, coupled with appropriate starting procedures, allows realistically large problem instances to be solved efficiently; thus obviating the need for specialized algorithms based on restrictive assumptions regarding cost structures.