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A nested partitions framework for solving large-scale multicommodity facility location problems

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Abstract

Large-scale multicommodity facility location problems are generally intractable with respect to standard mixed-integer programming (MIP) tools such as the direct application of general-purpose Branch & Cut (BC) commercial solvers i.e. CPLEX. In this paper, the authors investigate a nested partitions (NP) framework that combines meta-heuristics with MIP tools (including branch-and-cut). We also consider a variety of alternative formulations and decomposition methods for this problem class. Our results show that our NP framework is capable of efficiently producing very high quality solutions to multicommodity facility location problems. For large-scale problems in this class, this approach is significantly faster and generates better feasible solutions than either CPLEX (applied directly to the given MIP) or the iterative Lagrangian-based methods that have generally been regarded as the most effective structure-based techniques for optimization of these problems. We also briefly discuss some other large-scale MIP problem classes for which this approach is expected to be very effective.

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Wisconsin, Madison, WI, 53706, USA

    Leyuan Shi, Mehmet Bozbay & Andrew J. Miller

  2. Computer Sciences Department, University of Wisconsin, Madison, WI, 53706, USA

    Robert R. Meyer

Authors
  1. Leyuan Shi
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  2. Robert R. Meyer
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  3. Mehmet Bozbay
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  4. Andrew J. Miller
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Additional information

This work is supported partly by the National Science Foundation under grant DMI-0100220, DMI-0217924, by the Air Force of Scientific Research under grant F49620-01-1-0222, by Rockwell Automation, and by John Deere Horicon Works.

Leyuan Shi is a Professor of the Department of Industrial Engineering at University of Wisconsin-Madison. She received her Ph.D. in Applied Mathematics from Harvard University in 1992, her M.S. in Engineering from Harvard University in 1990, her M.S. in Applied Mathematics from Tsinghua University in 1985, and her B.S. in Mathematics from Nanjing Normal University in 1982. Dr. Shi has been involved in undergraduate and graduate teaching, as well as research and professional service. Dr. Shi’s research is devoted to the theory and applications of large-scale optimization algorithms, discrete event simulation and modeling and analysis of discrete dynamic systems. She has published many papers in these areas. Her work has appeared in Discrete Event Dynamic Systems, Operations Research, Management Science, IEEE Trans., and, IIE Trans. She is currently a member of the editorial board for Journal of Manufacturing & Service Operations Management, is an Associate Editor of Journal of Discrete Event Dynamic Systems, and an Associate Editor of INFORMS Journal on Computing. Dr. Shi is a member of IEEE and INFORMS.

Robert R. Meyer received a B.S. in Mathematics from Caltech and an M.S. and a Ph.D. in Computer Sciences from the University of Wisconsin-Madison. He is currently Professor of Computer Sciences at the University of Wisconsin-Madison, where he has been on the faculty since 1973. He has co-edited six volumes of optimization conference proceedings and written more than 80 articles focusing on areas such as nonlinear network optimization, parallel decomposition algorithms for large-scale optimization, genetic algorithms, and theory and applications of discrete optimization.

Mehmet Bozbay is a research assistant in the Department of Industrial Engineering at University of Wisconsin-Madison. He is currently working towards his Ph.D. degree in Industrial Engineering. He received M.S. degrees in Industrial Engineering and Computer Sciences from University of Wisconsin-Madison, and a B.S. degree in Mathematics from Beloit College. He has been dealing with real-life supply chain optimization problems for the last 4 years. He is a member of INFORMS.

Andrew J. Miller is an Assistant Professor of the Department of Industrial Engineering at the University of Wisconsin—Madison. He received his Ph.D. in Industrial Engineering from the Georgia Institute of Technology in 1999, his M.S. in Operations Research from the Georgia Institute of Technology in 1996, and his B.S. in Mathematics from Furman University in 1994. Dr. Miller has been involved in research, undergraduate and graduate teaching, and professional service, as well as in some software prototyping and development. Dr. Miller’s research focuses on theoretical and computational aspects of mixed integer programming, and on its application to areas in production planning, supply chain design, and other fields. He has published several papers in these areas, including articles in Mathematical Programming, Operations Research, and European Journal of Operations Research. He has refereed numerous articles for the journals mentioned above, as well as for Management Science, Annals of Operations Research, and others. Dr. Miller is a member of INFORMS and of the Mathematical Programming Society.

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Shi, L., Meyer, R.R., Bozbay, M. et al. A nested partitions framework for solving large-scale multicommodity facility location problems. J. Syst. Sci. Syst. Eng. 13, 158–179 (2004). https://doi.org/10.1007/s11518-006-0159-x

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