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An Integer L-Shaped Algorithm For Time-Constrained Traveling Salesman Problem With Stochastic Travel And Service Times

Author

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  • S. Y. TENG

    (Industrial and Systems Engineering Department, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore)

  • H. L. ONG

    (Industrial and Systems Engineering Department, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore)

  • H. C. HUANG

    (Industrial and Systems Engineering Department, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore)

Abstract

The time-constrained traveling salesman problem (TCTSP) is a variant of the classical traveling salesman problem, where only a subset of the customers can be visited due to the time limit constraint. In this paper, we consider the TCTSP with stochastic travel and service times. Given the normal working hoursTand a tolerance timeΔT, the total travel and service times of a route can exceedTas long as it is withinT+ΔT, though a penalty proportional to the amount in excess ofTwill be imposed. The problem consists of optimally selecting and sequencing a subset of customers to visit in the presence of random travel and service times to maximize the expected profit while satisfying the time limit constraint. We formulate the problem as a two-stage stochastic program with recourse, and propose an integer L-shaped solution method for solving it. Computational results show that the algorithm can solve problems with moderate size to optimality within reasonable time.

Suggested Citation

  • S. Y. Teng & H. L. Ong & H. C. Huang, 2004. "An Integer L-Shaped Algorithm For Time-Constrained Traveling Salesman Problem With Stochastic Travel And Service Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 241-257.
    • Handle: RePEc:wsi:apjorx:v:21:y:2004:i:02:n:s0217595904000229
    DOI: 10.1142/S0217595904000229
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    Cited by:

    1. Verbeeck, C. & Vansteenwegen, P. & Aghezzaf, E.-H., 2016. "Solving the stochastic time-dependent orienteering problem with time windows," European Journal of Operational Research, Elsevier, vol. 255(3), pages 699-718.
    2. Shiri, Davood & Akbari, Vahid & Hassanzadeh, Ali, 2024. "The Capacitated Team Orienteering Problem: An online optimization framework with predictions of unknown accuracy," Transportation Research Part B: Methodological, Elsevier, vol. 185(C).
    3. Ann Campbell & Michel Gendreau & Barrett Thomas, 2011. "The orienteering problem with stochastic travel and service times," Annals of Operations Research, Springer, vol. 186(1), pages 61-81, June.
    4. Letchford, Adam N. & Nasiri, Saeideh D., 2015. "The Steiner travelling salesman problem with correlated costs," European Journal of Operational Research, Elsevier, vol. 245(1), pages 62-69.
    5. Li Ping Gan & Will Recker, 2013. "Stochastic Preplanned Household Activity Pattern Problem with Uncertain Activity Participation (SHAPP)," Transportation Science, INFORMS, vol. 47(3), pages 439-454, August.
    6. Evers, L. & Glorie, K.M. & van der Ster, S. & Barros, A.I. & Monsuur, H., 2012. "The Orienteering Problem under Uncertainty Stochastic Programming and Robust Optimization compared," Econometric Institute Research Papers EI 2012-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Borzou Rostami & Guy Desaulniers & Fausto Errico & Andrea Lodi, 2021. "Branch-Price-and-Cut Algorithms for the Vehicle Routing Problem with Stochastic and Correlated Travel Times," Operations Research, INFORMS, vol. 69(2), pages 436-455, March.
    8. Ann M. Campbell & Barrett W. Thomas, 2008. "Probabilistic Traveling Salesman Problem with Deadlines," Transportation Science, INFORMS, vol. 42(1), pages 1-21, February.
    9. Dolinskaya, Irina & Shi, Zhenyu (Edwin) & Smilowitz, Karen, 2018. "Adaptive orienteering problem with stochastic travel times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 1-19.

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