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An exact solution approach for the time‐dependent traveling‐salesman problem

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  • Russ J. Vander Wiel
  • Nikolaos V. Sahinidis

Abstract

We present an algorithm for solving the time‐dependent traveling‐salesman problem (TDTSP), a generalization of the classical traveling salesman problem in which the cost of travel between two cities depends on the distance between the cities and the position of the transition in the tour. The algorithm is derived by applying Benders decomposition to a mixed‐integer linear programming formulation for the problem. We identify trivial TDTSPs for which a standard implementation of the algorithm requires an exponential number of iterations to converge. This motivates the development of an efficient, network‐flow‐based method for finding Pareto‐optimal dual solutions of a highly degenerate subproblem. Preliminary computational experience demonstrates that the use of these Pareto‐optimal solutions has a dramatic impact on the performance of the algorithm. © 1996 John Wiley & Sons, Inc.

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  • 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.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:6:p:797-820
    DOI: 10.1002/(SICI)1520-6750(199609)43:63.0.CO;2-#
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    References listed on IDEAS

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    1. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    2. Russ J. Vander Wiel & Nikolaos V. Sahinidis, 1995. "Heuristic Bounds and Test Problem Generation for the Time-Dependent Traveling Salesman Problem," Transportation Science, INFORMS, vol. 29(2), pages 167-183, May.
    3. 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.
    4. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    5. Matteo Fischetti & Gilbert Laporte & Silvano Martello, 1993. "The Delivery Man Problem and Cumulative Matroids," Operations Research, INFORMS, vol. 41(6), pages 1055-1064, December.
    6. Jean-Claude Picard & Maurice Queyranne, 1978. "The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling," Operations Research, INFORMS, vol. 26(1), pages 86-110, February.
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    Cited by:

    1. Przemysław Kowalik & Grzegorz Sobecki & Piotr Bawoł & Paweł Muzolf, 2023. "A Flow-Based Formulation of the Travelling Salesman Problem with Penalties on Nodes," Sustainability, MDPI, vol. 15(5), pages 1-28, February.
    2. Cacchiani, Valentina & Contreras-Bolton, Carlos & Toth, Paolo, 2020. "Models and algorithms for the Traveling Salesman Problem with Time-dependent Service times," European Journal of Operational Research, Elsevier, vol. 283(3), pages 825-843.
    3. Jean-François Cordeau & Goran Stojković & François Soumis & Jacques Desrosiers, 2001. "Benders Decomposition for Simultaneous Aircraft Routing and Crew Scheduling," Transportation Science, INFORMS, vol. 35(4), pages 375-388, November.
    4. Richa Agarwal & Özlem Ergun, 2008. "Ship Scheduling and Network Design for Cargo Routing in Liner Shipping," Transportation Science, INFORMS, vol. 42(2), pages 175-196, May.
    5. Roberto Roberti & Aristide Mingozzi, 2014. "Dynamic ng-Path Relaxation for the Delivery Man Problem," Transportation Science, INFORMS, vol. 48(3), pages 413-424, August.
    6. Ivana Semanjski & Sidharta Gautama, 2024. "Sustainable Time-Dependent Cheapest Path Problem with Integrated Collaborative Stakeholders’ Perspectives," Sustainability, MDPI, vol. 16(9), pages 1-19, April.

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