The Surplus Inventory Matching Problem in theProcess

LIMITED DISTRIBUTION NOTICE This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and speciic requests. After outside publication, requests should be lled only by reprints or legally obtained copies of the article (e.g., payment of royalties). Abstract We introduce a new integer programming problem that arises from operations planning in the process industry. This problem involves matching an order book against surplus inventory before production planning. It can be formulated by generalizing the multiple knapsack problem along three directions: (i) adding assignment restrictions on items which can be assigned to a knapsack, (ii) Adding a new attribute (called \color" in the paper) to an item and then adding the associated \color" constraints which restrict the number of distinct colors which can be assigned to a knapsack and (iii) considering multiple objectives for optimization. In this paper, we formulate this problem, provide a result regarding its complexity and report on our computational experience with solving a set of real instances based on data from the operations of a large steel plant. We then propose a network ow based heuristic which performs to within 3% of the optimum solution (or best known feasible solution). This system has been successfully deployed and is now used in the daily mill operations.