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Computational Experience with an M-Salesman Traveling Salesman Algorithm

Author

Listed:
  • Joseph A. Svestka

    (The Cleveland Trust Company, Cleveland, Ohio)

  • Vaughn E. Huckfeldt

    (Western Interstate Commission on Higher Education (WICHE), Boulder, Colorado)

Abstract

A formulation of the traveling salesman problem with more than one salesman is offered. The particular formulation has computational advantages over other formulations. Experience is obtained with an exact branch and bound algorithm employing both upper and lower bounds (mean run time for 55 city problems is one minute). Due to the special formulation, certain subtours may satisfy the constraints, thus reducing the search. A very good initial tour and upper bound are employed. The determination of these as well as the pathology of the formulation and the algorithm are discussed. No increase in computation time over the one-salesman case is experienced.

Suggested Citation

  • Joseph A. Svestka & Vaughn E. Huckfeldt, 1973. "Computational Experience with an M-Salesman Traveling Salesman Algorithm," Management Science, INFORMS, vol. 19(7), pages 790-799, March.
    • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:7:p:790-799
    DOI: 10.1287/mnsc.19.7.790
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    Cited by:

    1. Yuan, Shuai & Skinner, Bradley & Huang, Shoudong & Liu, Dikai, 2013. "A new crossover approach for solving the multiple travelling salesmen problem using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 228(1), pages 72-82.
    2. Julia Rieck & Jürgen Zimmermann & Matthias Glagow, 2007. "Tourenplanung mittelständischer Speditionsunternehmen in Stückgutkooperationen: Modellierung und heuristische Lösungsverfahren," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 17(4), pages 365-388, January.
    3. Chen, Lijian & Chiang, Wen-Chyuan & Russell, Robert & Chen, Jun & Sun, Dengfeng, 2018. "The probabilistic vehicle routing problem with service guarantees," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 149-164.
    4. He, Pengfei & Hao, Jin-Kao, 2023. "Memetic search for the minmax multiple traveling salesman problem with single and multiple depots," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1055-1070.
    5. Bektas, Tolga, 2006. "The multiple traveling salesman problem: an overview of formulations and solution procedures," Omega, Elsevier, vol. 34(3), pages 209-219, June.
    6. Qu, Hong & Yi, Zhang & Tang, HuaJin, 2007. "A columnar competitive model for solving multi-traveling salesman problem," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 1009-1019.
    7. Bismark Singh & Lena Oberfichtner & Sergey Ivliev, 2023. "Heuristics for a cash-collection routing problem with a cluster-first route-second approach," Annals of Operations Research, Springer, vol. 322(1), pages 413-440, March.
    8. Luo, Zhixing & Qin, Hu & Lim, Andrew, 2014. "Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints," European Journal of Operational Research, Elsevier, vol. 234(1), pages 49-60.
    9. Bräysy, Olli & Dullaert, Wout & Nakari, Pentti, 2009. "The potential of optimization in communal routing problems: case studies from Finland," Journal of Transport Geography, Elsevier, vol. 17(6), pages 484-490.
    10. José Alejandro Cornejo-Acosta & Jesús García-Díaz & Julio César Pérez-Sansalvador & Carlos Segura, 2023. "Compact Integer Programs for Depot-Free Multiple Traveling Salesperson Problems," Mathematics, MDPI, vol. 11(13), pages 1-25, July.
    11. Kara, Imdat & Bektas, Tolga, 2006. "Integer linear programming formulations of multiple salesman problems and its variations," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1449-1458, November.

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