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Maximizing the profit per unit of time for the TSP with convex resource-dependent travelling times

Author

Listed:
  • Moshe Zofi

    (Ben-Gurion University of the Negev
    Sapir Academic College)

  • Ron Teller

    (Ben-Gurion University of the Negev)

  • Moshe Kaspi

    (Ben-Gurion University of the Negev)

Abstract

This paper introduces a new problem that is an extension of the travelling salesman problem (TSP) in which the travelling times are resource dependent and the objective is to maximize the profit per unit of time. We present an optimal solution approach comprised of three main steps: (1) calculating the optimal amount of total resource required (regardless of the selected tour); (2) constructing the tour; and (3) assigning the optimal resource to each connection between vertices using the equivalent load method. This solution approach finds the optimal solution with the same computational complexity for solving the classic TSP.

Suggested Citation

  • Moshe Zofi & Ron Teller & Moshe Kaspi, 2017. "Maximizing the profit per unit of time for the TSP with convex resource-dependent travelling times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(10), pages 1177-1182, October.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:10:d:10.1057_s41274-016-0156-5
    DOI: 10.1057/s41274-016-0156-5
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    1. Richard L. Daniels & Rakesh K. Sarin, 1989. "Technical Note—Single Machine Scheduling with Controllable Processing Times and Number of Jobs Tardy," Operations Research, INFORMS, vol. 37(6), pages 981-984, December.
    2. Van Wassenhove, Luk N. & Baker, Kenneth R., 1982. "A bicriterion approach to time/cost trade-offs in sequencing," European Journal of Operational Research, Elsevier, vol. 11(1), pages 48-54, September.
    3. Clyde L. Monma & Alexander Schrijver & Michael J. Todd & Victor K. Wei, 1990. "Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 736-748, November.
    4. Janiak, Adam & Kovalyov, Mikhail Y., 1996. "Single machine scheduling subject to deadlines and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 94(2), pages 284-291, October.
    5. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "Traveling Salesman Problems with Profits," Transportation Science, INFORMS, vol. 39(2), pages 188-205, May.
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