The surplus inventory matching problem in the process industry

We introduce a new 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 dimensions: (i) adding assignment restrictions on items that can be assigned to a knapsack, (ii) adding a new attribute (called "color" in this paper) to an item and then adding the associated "color" constraints that restrict the number of distinct colors that can be assigned to a knapsack, and (iii) considering multiple objectives for optimization. We formulate the 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-flow-based heuristic that yields solutions within 3% of optimal (or the best known feasible solution). This system has been successfully deployed and is now used daily in the mill operations.