Mixed Integer Programming Approaches to Production Planning Problems

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While the application of operations research has aided manufacturing companies to cut costs and improve efficiency, fundamental problems in production and supply chain planning remain challenging to solve. These problems involve the interaction of factors such as external demands, internal bill-of-material structure, production capacities, holding costs, and setup times. Most systems implementing Manufacturing Resources Planning (MRP II) and related methods solve only rough approximations of these problems. The resulting plans are not as efficient and cost-effective as may be possible, and they also often do not accurately account for basic restrictions such as production capacity. This project will develop basic mixed integer programming (MIP) methods that can solve such problems. This project aims to develop fundamental results to strengthen the MIP formulations of these problems so as to improve branch-and-cut algorithms designed to solve them. In addition, the project will incorporate these into MIP-based heuristics in order to optimize the performance on large practical problems. The theoretical results and heuristics developed will apply not only to broad families of production planning problems, but also to supply chain planning problems incorporating transportation and distribution as well as production decisions. Moreover, the results of this project will be incorporated into classes in the University of Wisconsin curriculum. This will expose students to the possibilities of, and challenges involved in, using MIP methods to solve these kinds of problems. This research will allow new kinds of industrial problems to be solved efficiently. The successful completion of the goals of this project will make it possible to consider implementing these ideas in planning systems for many practical situations in manufacturing and supply chain enterprises. It will also contribute to general industrial engineering/operations research methodology, particularly to solving problems in the field of mixed integer programming that occur in a wide variety of engineering applications. Finally, this project will add breadth and depth to the curriculum of the University of Wisconsin, and it will contribute to the professional development of the research assistant who will be supported through it.