A Gilmore-Gomory construction of integer programming value functions |
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| Institution: | 1. Rice University, Department of Computational and Applied Mathematics, United States of America;2. Tsinghua University, Department of Industrial Engineering, China;3. The University of Texas MD Anderson Cancer Center, Department of Radiation Oncology, United States of America |
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| Abstract: | In this paper, we analyze how sequentially introducing decision variables into an integer program (IP) affects the value function and its level sets. We use a Gilmore-Gomory approach to find parametrized IP value functions over a restricted set of variables. We introduce the notion of maximal connected subsets of level sets - volumes in which changes to the constraint right-hand side have no effect on the value function - and relate these structures to IP value functions and optimal solutions. |
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| Keywords: | Value function Level set Parametrized optimization |
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