Research In Mixed-Integer Programming

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The research will focus on the theory and techniques needed to develop a robust and efficient algorithm for the general mixed integer programming problem. Topics that will be studied include efficient formulation, preprocessing, decomposition, logical testing, linear programming, constraint generation, branching and parallel processing. The project will also involve the development of a modular experimental code to test and evaluate the ideas and methodology that result from the basic research. There is tremendous demand for an efficient and robust mixed integer programming algorithm because a great variety of practical problems can be formulated in this way. But many of the larger and more difficult ones cannot be solved to (near) optimality in a reasonable amount of time by the existing methodology. Some of these large mixed integer models arise from optimization problems in the areas of logistics and manufacturing. Thus, the development of efficient methods would have a significant impact on improving the planning and operation of production and distribution processes.