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A major challenge in the initial stage of production planning for the steel industry is the material allocation problem (MAP): finding the best match of orders and materials (steel slabs and coils) with respect to an objective function that takes into account order due dates, preferences for matches, allocated weights, surplus weights of materials, and other factors. The MAP is NP-hard and is difficult to solve optimally. We apply a local search algorithm for the MAP that includes rich moves, such as ejection chain methods. Our algorithm is yielding considerable cost reduction in a real steelworks. In particular, a two-variable integer programming (TVIP) neighborhood search technique contributed to the cost reductions. TVIP defines a neighborhood space for the local search as a two-variable integer programming problem and efficiently finds a solution in the neighborhood. By using TVIP, the number of small batches of surplus material can be successfully reduced.
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