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Benders' partitioning scheme applied to a new formulation of the quadratic assignment problem

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  • Mokhtar S. Bazaraa
  • Hanif D. Sherali

Abstract

In this paper we present a new formulation of the quadratic assignment problem. This is done by transforming the quadratic objective function into a linear objective function by introducing a number of new variables and constraints. The resulting problem is a 0‐1 linear integer program with a highly specialized structure. This permits the use of the partitioning scheme of Benders where only the original variables need be considered. The algorithm described thus iterates between two problems. The master problem is a pure 0‐1 integer program, and the subproblem is a transportation problem whose optimal solution is shown to be readily available from the master problem in closed form. Computational experience on problems available in the literature is provided.

Suggested Citation

  • Mokhtar S. Bazaraa & Hanif D. Sherali, 1980. "Benders' partitioning scheme applied to a new formulation of the quadratic assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(1), pages 29-41, March.
    • Handle: RePEc:wly:navlog:v:27:y:1980:i:1:p:29-41
    DOI: 10.1002/nav.3800270104
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    Cited by:

    1. Raymond G. Vickson & Elkafi Hassini & Nader Azad, 2020. "A Benders decomposition approach to product location in carousel storage systems," Annals of Operations Research, Springer, vol. 284(2), pages 623-643, January.
    2. Russ J. Vander Wiel & Nikolaos V. Sahinidis, 1996. "An exact solution approach for the time‐dependent traveling‐salesman problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 797-820, September.
    3. Hanif Sherali, 2007. "RLT: A unified approach for discrete and continuous nonconvex optimization," Annals of Operations Research, Springer, vol. 149(1), pages 185-193, February.
    4. T. G. Pradeepmon & Vinay V. Panicker & R. Sridharan, 2021. "A variable neighbourhood search enhanced estimation of distribution algorithm for quadratic assignment problems," OPSEARCH, Springer;Operational Research Society of India, vol. 58(1), pages 203-233, March.
    5. Abdelaziz, Fouad Ben & Maddah, Bacel & Flamand, Tülay & Azar, Jimmy, 2024. "Store-Wide space planning balancing impulse and convenience," European Journal of Operational Research, Elsevier, vol. 312(1), pages 211-226.

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