Optimization Models for Production Planning in Metal Sheet Manufacturing

In this thesis, we address the tactical planning decision problem of ingot sizing in an aluminum sheet manufacturing facility. Ingots used for sheet manufacturing are made-to-stock, and used when necessary, to satisfy customer demands. The facility produces large ingots to exploit economies of scale in ingot casting, but customers order products frequently, and in small quantities. In this situation, the facility's current practice of dedicating an ingot to each order generates large amounts of scrap and increases processing costs. To prevent this, the facility is considering an alternate strategy of combining more than one order for production on a single ingot. When we permit multiple orders to be jointly produced from the same ingot, what standard ingot sizes should the facility produce, and which orders should be combined to minimize total scrap? We group similar orders over a long planning horizon into one product. Given the forecast demand for each product, a set of candidate ingot sizes, and a set of feasible product combinations, we need to determine the standard set of ingot sizes, and the number of times each product combination is produced on the standard ingots to minimize total scrap, while satisfying demand for all products. We formulate the ingot sizing problem as an integer program, and develop an efficient solution procedure. The solution procedure consists of dual ascent to obtain lower bounds, and two heuristics to provide good feasible solutions. We have implemented the dual ascent procedure and the heuristics, and tested them with data on actual orders received at a leading aluminum sheet manufacturing facility. Our computational results indicate that the solutions obtained by the dual ascent and heuristic procedures are within 4% of optimality on an average. For the alloy that we studied, a comparison of the proposed set of standard sizes with the current set of ingots suggests that the proposed solution could reduce total scrap by an average of 9.5%. The reduction in total scrap could result in savings of up to $100,000 annually in scrap reprocessing and ingot casting costs. To my parents and my husband 3 Acknowledgments I would like to thank my advisor, Anantaram Balakrishnan, for introducing me to this real world problem and motivating me to work on it. I very much appreciate his support and guidance for the past two years of my student life. He has been very understanding and has helped me in several aspects to …