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Dynamic Programming for the Minimum Tour Duration Problem

Author

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  • Christian Tilk

    (Johannes Gutenberg-Universitaet Mainz, Germany)

  • Stefan Irnich

    (Johannes Gutenberg-Universitaet Mainz, Germany)

Abstract

The minimum tour duration problem (MTDP) is the variant of the traveling salesman problem with time windows, which consists of finding a time window-feasible Hamiltonian path minimizing the tour duration. We present a new effective dynamic programming (DP)-based approach for the MTDP. When solving the traveling salesman problem with time windows with DP, two independent resources are propagated along partial paths, one for costs and one for earliest arrival times. For dealing with tour duration minimization, we provide a new DP formulation with three resources for which effective dominance and bounding procedures are applicable. This is a non-trivial task because in the MTDP at least two resources depend on each other in a non-additive and non-linear way. In particular, we define consistent resource extension functions (REF) so that dominance is straightforward using componentwise comparison for the respective resource vectors. Moreover, one of the main advantages of the new REF definition is that the DP can be reversed consistently such that the forward DP or any of its relaxations provides bounds for the backward DP, and vice versa. Computational test confirm the effectiveness of the proposed approach.

Suggested Citation

  • Christian Tilk & Stefan Irnich, 2014. "Dynamic Programming for the Minimum Tour Duration Problem," Working Papers 1408, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 04 Aug 2014.
    • Handle: RePEc:jgu:wpaper:1408
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    References listed on IDEAS

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    1. Michel Gendreau & Alain Hertz & Gilbert Laporte & Mihnea Stan, 1998. "A Generalized Insertion Heuristic for the Traveling Salesman Problem with Time Windows," Operations Research, INFORMS, vol. 46(3), pages 330-335, June.
    2. Asvin Goel, 2009. "Vehicle Scheduling and Routing with Drivers' Working Hours," Transportation Science, INFORMS, vol. 43(1), pages 17-26, February.
    3. 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.
    4. Eric Prescott-Gagnon & Guy Desaulniers & Michael Drexl & Louis-Martin Rousseau, 2010. "European Driver Rules in Vehicle Routing with Time Windows," Transportation Science, INFORMS, vol. 44(4), pages 455-473, November.
    5. Aristide Mingozzi & Lucio Bianco & Salvatore Ricciardelli, 1997. "Dynamic Programming Strategies for the Traveling Salesman Problem with Time Window and Precedence Constraints," Operations Research, INFORMS, vol. 45(3), pages 365-377, June.
    6. E. Balas, 1999. "New classes of efficiently solvable generalized Traveling Salesman Problems," Annals of Operations Research, Springer, vol. 86(0), pages 529-558, January.
    7. Stefan Irnich & Guy Desaulniers, 2005. "Shortest Path Problems with Resource Constraints," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 33-65, Springer.
    8. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    9. Yvan Dumas & Jacques Desrosiers & Eric Gelinas & Marius M. Solomon, 1995. "An Optimal Algorithm for the Traveling Salesman Problem with Time Windows," Operations Research, INFORMS, vol. 43(2), pages 367-371, April.
    10. 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.
    11. Jean-Yves Potvin & Samy Bengio, 1996. "The Vehicle Routing Problem with Time Windows Part II: Genetic Search," INFORMS Journal on Computing, INFORMS, vol. 8(2), pages 165-172, May.
    12. 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.
    13. Martin W. P. Savelsbergh, 1992. "The Vehicle Routing Problem with Time Windows: Minimizing Route Duration," INFORMS Journal on Computing, INFORMS, vol. 4(2), pages 146-154, May.
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