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Online Routing Problems: Value of Advanced Information as Improved Competitive Ratios

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  • Patrick Jaillet

    (Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Michael R. Wagner

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

We consider online versions of the traveling salesman problem (TSP) and traveling repairman problem (TRP) where instances are not known in advance. Cities (points) to be visited are revealed over time, while the server is en route serving previously released requests. These problems are known in the literature as the online TSP (TRP, respectively). The corresponding offline problems are the TSP (TRP) with release dates, problems where each point has to be visited at or after a given release date. In the current literature, the assumption is that a request becomes known at the time of its release date. In this paper we introduce the notion of a request’s disclosure date , the time when a city’s location and release date are revealed to the server. In a variety of disclosure date scenarios and metric spaces, we give new online algorithms and quantify the value of this advanced information in the form of improved competitive ratios. We also provide a general result on polynomial-time online algorithms for the online TSP.

Suggested Citation

  • Patrick Jaillet & Michael R. Wagner, 2006. "Online Routing Problems: Value of Advanced Information as Improved Competitive Ratios," Transportation Science, INFORMS, vol. 40(2), pages 200-210, May.
    • Handle: RePEc:inm:ortrsc:v:40:y:2006:i:2:p:200-210
    DOI: 10.1287/trsc.1060.0147
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    References listed on IDEAS

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    Cited by:

    1. Srour, F.J. & Agatz, N.A.H. & Oppen, J., 2014. "Strategies for Handling Temporal Uncertainty in Pickup and Delivery Problems with Time Windows," ERIM Report Series Research in Management ERS-2014-015-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Akbari, Vahid & Shiri, Davood, 2021. "Weighted online minimum latency problem with edge uncertainty," European Journal of Operational Research, Elsevier, vol. 295(1), pages 51-65.
    3. Dunke, Fabian & Nickel, Stefan, 2016. "A general modeling approach to online optimization with lookahead," Omega, Elsevier, vol. 63(C), pages 134-153.
    4. Dunke, Fabian & Heckmann, Iris & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2018. "Time traps in supply chains: Is optimal still good enough?," European Journal of Operational Research, Elsevier, vol. 264(3), pages 813-829.
    5. Berbeglia, Gerardo & Cordeau, Jean-François & Laporte, Gilbert, 2010. "Dynamic pickup and delivery problems," European Journal of Operational Research, Elsevier, vol. 202(1), pages 8-15, April.
    6. Srour, F.J. & Zuidwijk, R.A., 2008. "How Much is Location Information Worth? A Competitive Analysis of the Online Traveling Salesman Problem with Two Disclosure Dates," ERIM Report Series Research in Management ERS-2008-075-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Wohlgemuth, Sascha & Oloruntoba, Richard & Clausen, Uwe, 2012. "Dynamic vehicle routing with anticipation in disaster relief," Socio-Economic Planning Sciences, Elsevier, vol. 46(4), pages 261-271.
    8. Douglas G. Macharet & Armando Alves Neto & Vila F. Camara Neto & Mario F. M. Campos, 2018. "Dynamic region visit routing problem for vehicles with minimum turning radius," Journal of Heuristics, Springer, vol. 24(1), pages 83-109, February.
    9. Xingang Wen & Yinfeng Xu & Huili Zhang, 2015. "Online traveling salesman problem with deadlines and service flexibility," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 545-562, October.
    10. Fabian Dunke & Stefan Nickel, 2021. "Exact distributional analysis of online algorithms with lookahead," 4OR, Springer, vol. 19(2), pages 199-233, June.
    11. Zhang, Huili & Tong, Weitian & Xu, Yinfeng & Lin, Guohui, 2015. "The Steiner Traveling Salesman Problem with online edge blockages," European Journal of Operational Research, Elsevier, vol. 243(1), pages 30-40.
    12. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    13. Zolfagharinia, Hossein & Haughton, Michael, 2014. "The benefit of advance load information for truckload carriers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 70(C), pages 34-54.
    14. Fan, Tijun & Pan, Qianlan & Pan, Fei & Zhou, Wei & Chen, Jingyi, 2020. "Intelligent logistics integration of internal and external transportation with separation mode," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 133(C).
    15. Florian Dandl & Michael Hyland & Klaus Bogenberger & Hani S. Mahmassani, 2019. "Evaluating the impact of spatio-temporal demand forecast aggregation on the operational performance of shared autonomous mobility fleets," Transportation, Springer, vol. 46(6), pages 1975-1996, December.
    16. Rob A. Zuidwijk & Albert W. Veenstra, 2015. "The Value of Information in Container Transport," Transportation Science, INFORMS, vol. 49(3), pages 675-685, August.
    17. Zhang, Huili & Tong, Weitian & Lin, Guohui & Xu, Yinfeng, 2019. "Online minimum latency problem with edge uncertainty," European Journal of Operational Research, Elsevier, vol. 273(2), pages 418-429.
    18. Davood Shiri & Hakan Tozan, 2022. "Online routing and searching on graphs with blocked edges," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1039-1059, September.
    19. Patrick Jaillet & Michael R. Wagner, 2008. "Generalized Online Routing: New Competitive Ratios, Resource Augmentation, and Asymptotic Analyses," Operations Research, INFORMS, vol. 56(3), pages 745-757, June.
    20. F. Jordan Srour & Niels Agatz & Johan Oppen, 2018. "Strategies for Handling Temporal Uncertainty in Pickup and Delivery Problems with Time Windows," Transportation Science, INFORMS, vol. 52(1), pages 3-19, January.
    21. Fabian Dunke & Stefan Nickel, 2021. "Online optimization with gradual look-ahead," Operational Research, Springer, vol. 21(4), pages 2489-2523, December.
    22. Mengyuan Gou & Haiyan Yu, 2023. "Online Delivery Problem for Hybrid Truck–Drone System with Independent and Truck-Carried Drones," Sustainability, MDPI, vol. 15(2), pages 1-15, January.
    23. Melih Çelik & Özlem Ergun & Pınar Keskinocak, 2015. "The Post-Disaster Debris Clearance Problem Under Incomplete Information," Operations Research, INFORMS, vol. 63(1), pages 65-85, February.
    24. Zolfagharinia, Hossein & Haughton, Michael A., 2017. "Operational flexibility in the truckload trucking industry," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 437-460.
    25. Albert Einstein Fernandes Muritiba & Tibérius O. Bonates & Stênio Oliveira Da Silva & Manuel Iori, 2021. "Branch-and-Cut and Iterated Local Search for the Weighted k -Traveling Repairman Problem: An Application to the Maintenance of Speed Cameras," Transportation Science, INFORMS, vol. 55(1), pages 139-159, 1-2.

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