IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v64y2016i1p186-200.html
   My bibliography  Save this article

Routing Optimization Under Uncertainty

Author

Listed:
  • Patrick Jaillet

    (Department of Electrical Engineering and Computer Science, Laboratory for Information and Decision Systems, Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Jin Qi

    (Department of Industrial Engineering and Logistics Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Melvyn Sim

    (Department of Decision Sciences, NUS Business School, National University of Singapore, Singapore 119077)

Abstract

We consider a class of routing optimization problems under uncertainty in which all decisions are made before the uncertainty is realized. The objective is to obtain optimal routing solutions that would, as much as possible, adhere to a set of specified requirements after the uncertainty is realized. These problems include finding an optimal routing solution to meet the soft time window requirements at a subset of nodes when the travel time is uncertain, and sending multiple capacitated vehicles to different nodes to meet the customers’ uncertain demands. We introduce a precise mathematical framework for defining and solving such routing problems. In particular, we propose a new decision criterion, called the Requirements Violation (RV) Index , which quantifies the risk associated with the violation of requirements taking into account both the frequency of violations and their magnitudes whenever they occur. The criterion can handle instances when probability distributions are known, and ambiguity when distributions are partially characterized through descriptive statistics such as moments. We develop practically efficient algorithms involving Benders decomposition to find the exact optimal routing solution in which the RV Index criterion is minimized, and we give numerical results from several computational studies that show the attractive performance of the solutions.

Suggested Citation

  • Patrick Jaillet & Jin Qi & Melvyn Sim, 2016. "Routing Optimization Under Uncertainty," Operations Research, INFORMS, vol. 64(1), pages 186-200, February.
  • Handle: RePEc:inm:oropre:v:64:y:2016:i:1:p:186-200
    DOI: 10.1287/opre.2015.1462
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2015.1462
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.2015.1462?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
    ---><---

    References listed on IDEAS

    as
    1. Häme, Lauri & Hakula, Harri, 2013. "Dynamic journeying under uncertainty," European Journal of Operational Research, Elsevier, vol. 225(3), pages 455-471.
    2. David B. Brown & Enrico De Giorgi & Melvyn Sim, 2012. "Aspirational Preferences and Their Representation by Risk Measures," Management Science, INFORMS, vol. 58(11), pages 2095-2113, November.
    3. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    4. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    5. R A Russell & T L Urban, 2008. "Vehicle routing with soft time windows and Erlang travel times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1220-1228, September.
    6. Chrysanthos E. Gounaris & Wolfram Wiesemann & Christodoulos A. Floudas, 2013. "The Robust Capacitated Vehicle Routing Problem Under Demand Uncertainty," Operations Research, INFORMS, vol. 61(3), pages 677-693, June.
    7. 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.
    8. C Lee & K Lee & S Park, 2012. "Robust vehicle routing problem with deadlines and travel time/demand uncertainty," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(9), pages 1294-1306, September.
    9. R. Montemanni & J. Barta & M. Mastrolilli & L. M. Gambardella, 2007. "The Robust Traveling Salesman Problem with Interval Data," Transportation Science, INFORMS, vol. 41(3), pages 366-381, August.
    10. G Laporte, 2010. "A concise guide to the Traveling Salesman Problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 35-40, January.
    11. Dimitris J. Bertsimas & David Simchi-Levi, 1996. "A New Generation of Vehicle Routing Research: Robust Algorithms, Addressing Uncertainty," Operations Research, INFORMS, vol. 44(2), pages 286-304, April.
    12. Ann M. Campbell & Barrett W. Thomas, 2008. "Probabilistic Traveling Salesman Problem with Deadlines," Transportation Science, INFORMS, vol. 42(1), pages 1-21, February.
    13. Dimitris J. Bertsimas, 1992. "A Vehicle Routing Problem with Stochastic Demand," Operations Research, INFORMS, vol. 40(3), pages 574-585, June.
    14. Shao-Wei Lam & Tsan Sheng Ng & Melvyn Sim & Jin-Hwa Song, 2013. "Multiple Objectives Satisficing Under Uncertainty," Operations Research, INFORMS, vol. 61(1), pages 214-227, February.
    15. David B. Brown & Melvyn Sim, 2009. "Satisficing Measures for Analysis of Risky Positions," Management Science, INFORMS, vol. 55(1), pages 71-84, January.
    16. Li, Xiangyong & Tian, Peng & Leung, Stephen C.H., 2010. "Vehicle routing problems with time windows and stochastic travel and service times: Models and algorithm," International Journal of Production Economics, Elsevier, vol. 125(1), pages 137-145, May.
    17. Taş, D. & Gendreau, M. & Dellaert, N. & van Woensel, T. & de Kok, A.G., 2014. "Vehicle routing with soft time windows and stochastic travel times: A column generation and branch-and-price solution approach," European Journal of Operational Research, Elsevier, vol. 236(3), pages 789-799.
    18. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    19. Nie, Yu (Marco) & Wu, Xing, 2009. "Shortest path problem considering on-time arrival probability," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 597-613, July.
    20. Nicholas G. Hall & Daniel Zhuoyu Long & Jin Qi & Melvyn Sim, 2015. "Managing Underperformance Risk in Project Portfolio Selection," Operations Research, INFORMS, vol. 63(3), pages 660-675, June.
    21. Chang, Tsung-Sheng & Wan, Yat-wah & OOI, Wei Tsang, 2009. "A stochastic dynamic traveling salesman problem with hard time windows," European Journal of Operational Research, Elsevier, vol. 198(3), pages 748-759, November.
    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. Yossiri Adulyasak & Patrick Jaillet, 2016. "Models and Algorithms for Stochastic and Robust Vehicle Routing with Deadlines," Transportation Science, INFORMS, vol. 50(2), pages 608-626, May.
    2. Ji, Chenlu & Mandania, Rupal & Liu, Jiyin & Liret, Anne, 2022. "Scheduling on-site service deliveries to minimise the risk of missing appointment times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    3. Axel Parmentier, 2019. "Algorithms for non-linear and stochastic resource constrained shortest path," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 281-317, April.
    4. Jorge Oyola & Halvard Arntzen & David L. Woodruff, 2017. "The stochastic vehicle routing problem, a literature review, Part II: solution methods," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 349-388, December.
    5. F. Errico & G. Desaulniers & M. Gendreau & W. Rei & L.-M. Rousseau, 2018. "The vehicle routing problem with hard time windows and stochastic service times," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 223-251, September.
    6. Errico, F. & Desaulniers, G. & Gendreau, M. & Rei, W. & Rousseau, L.-M., 2016. "A priori optimization with recourse for the vehicle routing problem with hard time windows and stochastic service times," European Journal of Operational Research, Elsevier, vol. 249(1), pages 55-66.
    7. Zhang, Yu & Tang, Jiafu, 2018. "Itinerary planning with time budget for risk-averse travelers," European Journal of Operational Research, Elsevier, vol. 267(1), pages 288-303.
    8. Enrico Bartolini & Dominik Goeke & Michael Schneider & Mengdie Ye, 2021. "The Robust Traveling Salesman Problem with Time Windows Under Knapsack-Constrained Travel Time Uncertainty," Transportation Science, INFORMS, vol. 55(2), pages 371-394, March.
    9. Antonio J. Conejo & Nicholas G. Hall & Daniel Zhuoyu Long & Runhao Zhang, 2021. "Robust Capacity Planning for Project Management," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1533-1550, October.
    10. Shubhechyya Ghosal & Wolfram Wiesemann, 2020. "The Distributionally Robust Chance-Constrained Vehicle Routing Problem," Operations Research, INFORMS, vol. 68(3), pages 716-732, May.
    11. Minglong Zhou & Melvyn Sim & Shao‐Wei Lam, 2022. "Advance admission scheduling via resource satisficing," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 4002-4020, November.
    12. Yu Zhang & Zhenzhen Zhang & Andrew Lim & Melvyn Sim, 2021. "Robust Data-Driven Vehicle Routing with Time Windows," Operations Research, INFORMS, vol. 69(2), pages 469-485, March.
    13. Vincent Tsz Fai Chow & Zheng Cui & Daniel Zhuoyu Long, 2022. "Target-Oriented Distributionally Robust Optimization and Its Applications to Surgery Allocation," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2058-2072, July.
    14. Jonathan De La Vega & Pedro Munari & Reinaldo Morabito, 2019. "Robust optimization for the vehicle routing problem with multiple deliverymen," 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. 27(4), pages 905-936, December.
    15. Ehmke, Jan Fabian & Campbell, Ann Melissa & Urban, Timothy L., 2015. "Ensuring service levels in routing problems with time windows and stochastic travel times," European Journal of Operational Research, Elsevier, vol. 240(2), pages 539-550.
    16. Vidal, Thibaut & Laporte, Gilbert & Matl, Piotr, 2020. "A concise guide to existing and emerging vehicle routing problem variants," European Journal of Operational Research, Elsevier, vol. 286(2), pages 401-416.
    17. Mojtaba Rajabi-Bahaabadi & Afshin Shariat-Mohaymany & Mohsen Babaei & Daniele Vigo, 2021. "Reliable vehicle routing problem in stochastic networks with correlated travel times," Operational Research, Springer, vol. 21(1), pages 299-330, March.
    18. 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.
    19. 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.
    20. Jinil Han & Chungmok Lee & Sungsoo Park, 2014. "A Robust Scenario Approach for the Vehicle Routing Problem with Uncertain Travel Times," Transportation Science, INFORMS, vol. 48(3), pages 373-390, August.

    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:inm:oropre:v:64:y:2016:i:1:p:186-200. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.