IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v309y2023i1p271-285.html
   My bibliography  Save this article

A bi-criteria moving-target travelling salesman problem under uncertainty

Author

Listed:
  • Maskooki, Alaleh
  • Kallio, Markku

Abstract

This article concerns a variant of moving target travelling salesman problem where the number and locations of targets vary with time and realizations of random trajectories. Managerial objectives are to maximize the number of visits to different targets and to minimize the total travel distance. Employing a linear value function for finding supported Pareto-efficient solutions, we develop a two-stage stochastic programming model. We propose an iterative randomized dynamic programming (RDP) algorithm which converges to a global optimum with probability one. Each iteration in RDP involves a randomized backward and forward recursion stage as well as options for improving any given schedule: swaps of targets and optimization of timing for visits. An integer linear programming (ILP) model is developed and solved by a standard ILP solver to evaluate the performance of RDP on instances of real data for scheduling an environmental surveillance boat to visit ships navigating in the Baltic Sea. Due to a huge number of binary variables, the ILP model in practice becomes intractable. For small to medium size data sets, the Pareto-efficiency of solutions found by RDP and ILP solver are equal within a reasonable tolerance; however, RDP is significantly faster and able to deal with large-scale problems in practice.

Suggested Citation

  • Maskooki, Alaleh & Kallio, Markku, 2023. "A bi-criteria moving-target travelling salesman problem under uncertainty," European Journal of Operational Research, Elsevier, vol. 309(1), pages 271-285.
    • Handle: RePEc:eee:ejores:v:309:y:2023:i:1:p:271-285
    DOI: 10.1016/j.ejor.2023.01.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221723000097
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.01.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gilbert Laporte & François Louveaux & Hélène Mercure, 1992. "The Vehicle Routing Problem with Stochastic Travel Times," Transportation Science, INFORMS, vol. 26(3), pages 161-170, August.
    2. Anke Stieber & Armin Fügenschuh, 2022. "Dealing with time in the multiple traveling salespersons problem with moving targets," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(3), pages 991-1017, September.
    3. Dimitris J. Bertsimas & Garrett van Ryzin, 1991. "A Stochastic and Dynamic Vehicle Routing Problem in the Euclidean Plane," Operations Research, INFORMS, vol. 39(4), pages 601-615, August.
    4. Bertsimas, Dimitris & Van Ryzin, Garrett., 1991. "A stochastic and dynamic vehicle routing problem in the Euclidean plane," Working papers 3286-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. Alejandro Toriello & William B. Haskell & Michael Poremba, 2014. "A Dynamic Traveling Salesman Problem with Stochastic Arc Costs," Operations Research, INFORMS, vol. 62(5), pages 1107-1125, October.
    6. Stein W. Wallace, 2000. "Decision Making Under Uncertainty: Is Sensitivity Analysis of Any Use?," Operations Research, INFORMS, vol. 48(1), pages 20-25, February.
    7. Chryssi Malandraki & Mark S. Daskin, 1992. "Time Dependent Vehicle Routing Problems: Formulations, Properties and Heuristic Algorithms," Transportation Science, INFORMS, vol. 26(3), pages 185-200, August.
    8. Patrick Jaillet, 1988. "A Priori Solution of a Traveling Salesman Problem in Which a Random Subset of the Customers Are Visited," Operations Research, INFORMS, vol. 36(6), pages 929-936, December.
    9. George B. Dantzig, 1955. "Linear Programming under Uncertainty," Management Science, INFORMS, vol. 1(3-4), pages 197-206, 04-07.
    10. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    11. Donati, Alberto V. & Montemanni, Roberto & Casagrande, Norman & Rizzoli, Andrea E. & Gambardella, Luca M., 2008. "Time dependent vehicle routing problem with a multi ant colony system," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1174-1191, March.
    12. Jean-Claude Picard & Maurice Queyranne, 1978. "The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling," Operations Research, INFORMS, vol. 26(1), pages 86-110, February.
    13. Andrzej Ruszczynski & Robert J. Vanderbei, 2003. "Frontiers of Stochastically Nondominated Portfolios," Econometrica, Econometric Society, vol. 71(4), pages 1287-1297, July.
    14. Biju Thapalia & Stein Wallace & Michal Kaut & Teodor Crainic, 2012. "Single source single-commodity stochastic network design," Computational Management Science, Springer, vol. 9(1), pages 139-160, February.
    15. Patrizia Beraldi & Gianpaolo Ghiani & Roberto Musmanno & Francesca Vocaturo, 2010. "Efficient Neighborhood Search For The Probabilistic Multi-Vehicle Pickup And Delivery Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(03), pages 301-314.
    16. Archetti, C. & Feillet, D. & Mor, A. & Speranza, M.G., 2020. "Dynamic traveling salesman problem with stochastic release dates," European Journal of Operational Research, Elsevier, vol. 280(3), pages 832-844.
    17. Furini, Fabio & Persiani, Carlo Alfredo & Toth, Paolo, 2016. "The Time Dependent Traveling Salesman Planning Problem in Controlled Airspace," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 38-55.
    18. Zhang, Shu & Ohlmann, Jeffrey W. & Thomas, Barrett W., 2014. "A priori orienteering with time windows and stochastic wait times at customers," European Journal of Operational Research, Elsevier, vol. 239(1), pages 70-79.
    19. Bruce L. Golden & Larry Levy & Rakesh Vohra, 1987. "The orienteering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 307-318, June.
    20. Dimitris J. Bertsimas, 1992. "A Vehicle Routing Problem with Stochastic Demand," Operations Research, INFORMS, vol. 40(3), pages 574-585, June.
    21. Malandraki, Chryssi & Dial, Robert B., 1996. "A restricted dynamic programming heuristic algorithm for the time dependent traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 90(1), pages 45-55, April.
    22. Michael Hassoun & Shraga Shoval & Eran Simchon & Liron Yedidsion, 2020. "The single line moving target traveling salesman problem with release times," Annals of Operations Research, Springer, vol. 289(2), pages 449-458, June.
    23. Francesca Maggioni & Michal Kaut & Luca Bertazzi, 2009. "Stochastic optimization models for a single-sink transportation problem," Computational Management Science, Springer, vol. 6(2), pages 251-267, May.
    24. Zhang, Guowei & Jia, Ning & Zhu, Ning & Adulyasak, Yossiri & Ma, Shoufeng, 2023. "Robust drone selective routing in humanitarian transportation network assessment," European Journal of Operational Research, Elsevier, vol. 305(1), pages 400-428.
    25. Florio, Alexandre M. & Hartl, Richard F. & Minner, Stefan, 2020. "Optimal a priori tour and restocking policy for the single-vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 285(1), pages 172-182.
    26. Maskooki, Alaleh & Deb, Kalyanmoy & Kallio, Markku, 2022. "A customized genetic algorithm for bi-objective routing in a dynamic network," European Journal of Operational Research, Elsevier, vol. 297(2), pages 615-629.
    27. Jorge Oyola & Halvard Arntzen & David L. Woodruff, 2018. "The stochastic vehicle routing problem, a literature review, part I: models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 193-221, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Maskooki, Alaleh & Deb, Kalyanmoy & Kallio, Markku, 2022. "A customized genetic algorithm for bi-objective routing in a dynamic network," European Journal of Operational Research, Elsevier, vol. 297(2), pages 615-629.
    2. Alejandro Toriello & William B. Haskell & Michael Poremba, 2014. "A Dynamic Traveling Salesman Problem with Stochastic Arc Costs," Operations Research, INFORMS, vol. 62(5), pages 1107-1125, October.
    3. Said Dabia & Stefan Ropke & Tom van Woensel & Ton De Kok, 2013. "Branch and Price for the Time-Dependent Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 47(3), pages 380-396, August.
    4. Van Woensel, T. & Kerbache, L. & Peremans, H. & Vandaele, N., 2008. "Vehicle routing with dynamic travel times: A queueing approach," European Journal of Operational Research, Elsevier, vol. 186(3), pages 990-1007, May.
    5. Zhang, Jian & Woensel, Tom Van, 2023. "Dynamic vehicle routing with random requests: A literature review," International Journal of Production Economics, Elsevier, vol. 256(C).
    6. Soumia Ichoua & Michel Gendreau & Jean-Yves Potvin, 2006. "Exploiting Knowledge About Future Demands for Real-Time Vehicle Dispatching," Transportation Science, INFORMS, vol. 40(2), pages 211-225, May.
    7. Jean-François Cordeau & Gianpaolo Ghiani & Emanuela Guerriero, 2014. "Analysis and Branch-and-Cut Algorithm for the Time-Dependent Travelling Salesman Problem," Transportation Science, INFORMS, vol. 48(1), pages 46-58, February.
    8. Tao Zhang & W. Art Chaovalitwongse & Yuejie Zhang, 2014. "Integrated Ant Colony and Tabu Search approach for time dependent vehicle routing problems with simultaneous pickup and delivery," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 288-309, July.
    9. Malmborg, Charles J., 1996. "A genetic algorithm for service level based vehicle scheduling," European Journal of Operational Research, Elsevier, vol. 93(1), pages 121-134, August.
    10. Mathias A. Klapp & Alan L. Erera & Alejandro Toriello, 2018. "The One-Dimensional Dynamic Dispatch Waves Problem," Transportation Science, INFORMS, vol. 52(2), pages 402-415, March.
    11. Barrett W. Thomas & Chelsea C. White, 2004. "Anticipatory Route Selection," Transportation Science, INFORMS, vol. 38(4), pages 473-487, November.
    12. Jian Yang & Patrick Jaillet & Hani Mahmassani, 2004. "Real-Time Multivehicle Truckload Pickup and Delivery Problems," Transportation Science, INFORMS, vol. 38(2), pages 135-148, May.
    13. 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.
    14. Russell W. Bent & Pascal Van Hentenryck, 2004. "Scenario-Based Planning for Partially Dynamic Vehicle Routing with Stochastic Customers," Operations Research, INFORMS, vol. 52(6), pages 977-987, December.
    15. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.
    16. Furini, Fabio & Persiani, Carlo Alfredo & Toth, Paolo, 2016. "The Time Dependent Traveling Salesman Planning Problem in Controlled Airspace," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 38-55.
    17. Roberto Tadei & Guido Perboli & Francesca Perfetti, 2017. "The multi-path Traveling Salesman Problem with stochastic travel costs," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 3-23, March.
    18. Cristián E. Cortés & Doris Sáez & Alfredo Núñez & Diego Muñoz-Carpintero, 2009. "Hybrid Adaptive Predictive Control for a Dynamic Pickup and Delivery Problem," Transportation Science, INFORMS, vol. 43(1), pages 27-42, February.
    19. Papastavrou, Jason D., 1996. "A stochastic and dynamic routing policy using branching processes with state dependent immigration," European Journal of Operational Research, Elsevier, vol. 95(1), pages 167-177, November.
    20. Andres Figliozzi, Miguel, 2012. "The time dependent vehicle routing problem with time windows: Benchmark problems, an efficient solution algorithm, and solution characteristics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(3), pages 616-636.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:309:y:2023:i:1:p:271-285. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.