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Technical Note—An Exact Algorithm for the Time-Constrained Traveling Salesman Problem

Author

Listed:
  • Edward K. Baker

    (University of Miami, Coral Gables, Florida)

Abstract

The time-constrained traveling salesman problem is a variation of the familiar traveling salesman problem that includes time window constraints on the time a particular city, or cities, may be visited. This note presents a concise formulation of the time-constrained traveling salesman problem. The model assumes that the distances of the problem are symmetrical and that the triangle inequality holds. Additionally, the model allows the salesman to wait at a city, if necessary, for a time window to open. The dual of the formulation is shown to be a disjunctive graph model, which is well known from scheduling theory. A longest path algorithm is used to obtain bounding information for subproblems in a branch and bound solution procedure. Computational results are presented for several small to moderate size problems.

Suggested Citation

  • Edward K. Baker, 1983. "Technical Note—An Exact Algorithm for the Time-Constrained Traveling Salesman Problem," Operations Research, INFORMS, vol. 31(5), pages 938-945, October.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:5:p:938-945
    DOI: 10.1287/opre.31.5.938
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    Citations

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    Cited by:

    1. Y-L Chen & L-J Hsiao & K Tang, 2003. "Time analysis for planning a path in a time-window network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 860-870, August.
    2. Rui Chen & Xinglu Liu & Lixin Miao & Peng Yang, 2020. "Electric Vehicle Tour Planning Considering Range Anxiety," Sustainability, MDPI, vol. 12(9), pages 1-17, May.
    3. Anirudh Subramanyam & Chrysanthos E. Gounaris, 2018. "A Decomposition Algorithm for the Consistent Traveling Salesman Problem with Vehicle Idling," Transportation Science, INFORMS, vol. 52(2), pages 386-401, March.
    4. Jeffrey W. Ohlmann & Barrett W. Thomas, 2007. "A Compressed-Annealing Heuristic for the Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 80-90, February.
    5. Filippo Focacci & Andrea Lodi & Michela Milano, 2002. "A Hybrid Exact Algorithm for the TSPTW," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 403-417, November.
    6. Majed G. Alharbi & Ahmed Stohy & Mohammed Elhenawy & Mahmoud Masoud & Hamiden Abd El-Wahed Khalifa, 2021. "Solving Traveling Salesman Problem with Time Windows Using Hybrid Pointer Networks with Time Features," Sustainability, MDPI, vol. 13(22), pages 1-12, November.
    7. Roberto Wolfler Calvo, 2000. "A New Heuristic for the Traveling Salesman Problem with Time Windows," Transportation Science, INFORMS, vol. 34(1), pages 113-124, February.
    8. Egon Balas & Neil Simonetti, 2001. "Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study," INFORMS Journal on Computing, INFORMS, vol. 13(1), pages 56-75, February.
    9. Ann M. Campbell & Barrett W. Thomas, 2008. "Probabilistic Traveling Salesman Problem with Deadlines," Transportation Science, INFORMS, vol. 42(1), pages 1-21, February.
    10. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti, 2012. "New State-Space Relaxations for Solving the Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 356-371, August.
    11. Sanjeeb Dash & Oktay Günlük & Andrea Lodi & Andrea Tramontani, 2012. "A Time Bucket Formulation for the Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 132-147, February.

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