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Exact Solutions for the Carrier–Vehicle Traveling Salesman Problem

Author

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  • Claudio Gambella

    (Department of Electrical, Electronic and Information Engineering, University of Bologna, 40126 Bologna, Italy; IBM Research Ireland, Dublin 15, Ireland)

  • Andrea Lodi

    (Department of Mathematical and Industrial Engineering, Polytechnique Montréal, Montréal, Québec H3T 1J4, Canada)

  • Daniele Vigo

    (Department of Electrical, Electronic and Information Engineering, University of Bologna, 40126 Bologna, Italy)

Abstract

Carrier–vehicle systems generally consist of a slow carrier (e.g., a ship) with a long operational range and a faster vehicle (e.g., an aircraft) with a limited operational range. The carrier has the role of transporting the faster vehicle and of deploying, recovering, and servicing it. The goal of the carrier–vehicle traveling salesman problem (CVTSP) is to permit the faster vehicle to visit a given collection of targets in the shortest time while using the carrier as a base for possible multiple trips. As a consequence, the carrier and vehicle should be synchronized. The visiting sequence of the targets is not given a priori. We present a mixed-integer, second-order conic programming (MISOCP) formulation for the CVTSP. Computational results are shown for the resolution of the model with commercial solvers. The MISOCP structure and the relationship to the traveling salesman problem are exploited for developing a ranking-based solution algorithm that outperforms the commercial solvers.

Suggested Citation

  • Claudio Gambella & Andrea Lodi & Daniele Vigo, 2018. "Exact Solutions for the Carrier–Vehicle Traveling Salesman Problem," Transportation Science, INFORMS, vol. 52(2), pages 320-330, March.
    • Handle: RePEc:inm:ortrsc:v:52:y:2018:i:2:p:320-330
    DOI: 10.1287/trsc.2017.0771
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    References listed on IDEAS

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    1. Brian J. Griggs & Gregory S. Parnell & Lee J. Lehmkuhl, 1997. "An Air Mission Planning Algorithm Using Decision Analysis and Mixed Integer Programming," Operations Research, INFORMS, vol. 45(5), pages 662-676, October.
    2. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    3. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    4. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
    5. Eugene L. Lawler, 1972. "A Procedure for Computing the K Best Solutions to Discrete Optimization Problems and Its Application to the Shortest Path Problem," Management Science, INFORMS, vol. 18(7), pages 401-405, March.
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    Cited by:

    1. Li, Hongqi & Chen, Jun & Wang, Feilong & Bai, Ming, 2021. "Ground-vehicle and unmanned-aerial-vehicle routing problems from two-echelon scheme perspective: A review," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1078-1095.
    2. Li, Hongqi & Wang, Haotian & Chen, Jun & Bai, Ming, 2020. "Two-echelon vehicle routing problem with time windows and mobile satellites," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 179-201.
    3. Güneş Erdoğan & E. Alper Y?ld?r?m, 2021. "Exact and Heuristic Algorithms for the Carrier–Vehicle Traveling Salesman Problem," Transportation Science, INFORMS, vol. 55(1), pages 101-121, 1-2.

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