IDEAS home Printed from https://ideas.repec.org/a/taf/tprsxx/v54y2016i2p579-590.html
   My bibliography  Save this article

A mathematical model for vehicle routing problem under endogenous uncertainty

Author

Listed:
  • F. Hooshmand Khaligh
  • S.A. MirHassani

Abstract

In this study, a multistage stochastic programming (SP) model is presented for a variant of single-vehicle routing problem with stochastic demands from a dynamic viewpoint. It is assumed that the actual demand of a customer becomes known only when the customer is visited. This problem falls into the category of SP with endogenous uncertainty and hence, the scenario tree is decision-dependent. Therefore, nonanticipativity of decisions is ensured by conditional constraints making up a large portion of total constraints. Thus, a novel approach is proposed that considerably reduces the problem size without any effect on the solution space. Computational results on some test problems are reported.

Suggested Citation

  • F. Hooshmand Khaligh & S.A. MirHassani, 2016. "A mathematical model for vehicle routing problem under endogenous uncertainty," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 579-590, January.
    • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:2:p:579-590
    DOI: 10.1080/00207543.2015.1057625
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207543.2015.1057625
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00207543.2015.1057625?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. Gendreau, Michel & Laporte, Gilbert & Seguin, Rene, 1996. "Stochastic vehicle routing," European Journal of Operational Research, Elsevier, vol. 88(1), pages 3-12, January.
    2. Dror, Moshe, 1993. "Modeling vehicle routing with uncertain demands as a stochastic program: Properties of the corresponding solution," European Journal of Operational Research, Elsevier, vol. 64(3), pages 432-441, February.
    3. Novoa, Clara & Storer, Robert, 2009. "An approximate dynamic programming approach for the vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 196(2), pages 509-515, July.
    4. G. Ch. Pflug, 1990. "On-Line Optimization of Simulated Markovian Processes," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 381-395, August.
    5. Pillac, Victor & Gendreau, Michel & Guéret, Christelle & Medaglia, Andrés L., 2013. "A review of dynamic vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 225(1), pages 1-11.
    6. G. B. Dantzig & J. H. Ramser, 1959. "The Truck Dispatching Problem," Management Science, INFORMS, vol. 6(1), pages 80-91, October.
    7. Nicola Secomandi & François Margot, 2009. "Reoptimization Approaches for the Vehicle-Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 57(1), pages 214-230, February.
    8. Goodson, Justin C. & Ohlmann, Jeffrey W. & Thomas, Barrett W., 2012. "Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand," European Journal of Operational Research, Elsevier, vol. 217(2), pages 312-323.
    9. Nicola Secomandi, 2001. "A Rollout Policy for the Vehicle Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 49(5), pages 796-802, October.
    10. Walter Rei & Michel Gendreau & Patrick Soriano, 2010. "A Hybrid Monte Carlo Local Branching Algorithm for the Single Vehicle Routing Problem with Stochastic Demands," Transportation Science, INFORMS, vol. 44(1), pages 136-146, February.
    11. Wen-Huei Yang & Kamlesh Mathur & Ronald H. Ballou, 2000. "Stochastic Vehicle Routing Problem with Restocking," Transportation Science, INFORMS, vol. 34(1), pages 99-112, February.
    12. Moshe Dror & Gilbert Laporte & Pierre Trudeau, 1989. "Vehicle Routing with Stochastic Demands: Properties and Solution Frameworks," Transportation Science, INFORMS, vol. 23(3), pages 166-176, August.
    13. Gilbert Laporte & FranÇois V. Louveaux & Luc van Hamme, 2002. "An Integer L -Shaped Algorithm for the Capacitated Vehicle Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 50(3), pages 415-423, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mahmutoğulları, Özlem & Yaman, Hande, 2023. "Robust alternative fuel refueling station location problem with routing under decision-dependent flow uncertainty," European Journal of Operational Research, Elsevier, vol. 306(1), pages 173-188.
    2. Jose Escribano Macias & Nils Goldbeck & Pei-Yuan Hsu & Panagiotis Angeloudis & Washington Ochieng, 2020. "Endogenous stochastic optimisation for relief distribution assisted with unmanned aerial vehicles," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(4), pages 1089-1125, December.
    3. Abdoli, B. & Hooshmand, F. & MirHassani, S.A., 2023. "A novel stochastic programming model under endogenous uncertainty for the CCS-EOR planning problem," Applied Energy, Elsevier, vol. 338(C).
    4. Feng, Wei & Feng, Yiping & Zhang, Qi, 2021. "Multistage robust mixed-integer optimization under endogenous uncertainty," European Journal of Operational Research, Elsevier, vol. 294(2), pages 460-475.
    5. F. Hooshmand & S. A. MirHassani, 2018. "Reduction of nonanticipativity constraints in multistage stochastic programming problems with endogenous and exogenous uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 1-18, February.
    6. Nilay Noyan & Gábor Rudolf & Miguel Lejeune, 2022. "Distributionally Robust Optimization Under a Decision-Dependent Ambiguity Set with Applications to Machine Scheduling and Humanitarian Logistics," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 729-751, March.

    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. Zhang, Junlong & Lam, William H.K. & Chen, Bi Yu, 2016. "On-time delivery probabilistic models for the vehicle routing problem with stochastic demands and time windows," European Journal of Operational Research, Elsevier, vol. 249(1), pages 144-154.
    2. Bertazzi, Luca & Secomandi, Nicola, 2018. "Faster rollout search for the vehicle routing problem with stochastic demands and restocking," European Journal of Operational Research, Elsevier, vol. 270(2), pages 487-497.
    3. 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.
    4. Majid Salavati-Khoshghalb & Michel Gendreau & Ola Jabali & Walter Rei, 2019. "A Rule-Based Recourse for the Vehicle Routing Problem with Stochastic Demands," Transportation Science, INFORMS, vol. 53(5), pages 1334-1353, September.
    5. Luo, Zhixing & Qin, Hu & Zhang, Dezhi & Lim, Andrew, 2016. "Adaptive large neighborhood search heuristics for the vehicle routing problem with stochastic demands and weight-related cost," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 85(C), pages 69-89.
    6. 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.
    7. Prasanna Balaprakash & Mauro Birattari & Thomas Stützle & Marco Dorigo, 2015. "Estimation-based metaheuristics for the single vehicle routing problem with stochastic demands and customers," Computational Optimization and Applications, Springer, vol. 61(2), pages 463-487, June.
    8. Goodson, Justin C. & Ohlmann, Jeffrey W. & Thomas, Barrett W., 2012. "Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand," European Journal of Operational Research, Elsevier, vol. 217(2), pages 312-323.
    9. Salavati-Khoshghalb, Majid & Gendreau, Michel & Jabali, Ola & Rei, Walter, 2019. "An exact algorithm to solve the vehicle routing problem with stochastic demands under an optimal restocking policy," European Journal of Operational Research, Elsevier, vol. 273(1), pages 175-189.
    10. Briseida Sarasola & Karl Doerner & Verena Schmid & Enrique Alba, 2016. "Variable neighborhood search for the stochastic and dynamic vehicle routing problem," Annals of Operations Research, Springer, vol. 236(2), pages 425-461, January.
    11. Pillac, Victor & Gendreau, Michel & Guéret, Christelle & Medaglia, Andrés L., 2013. "A review of dynamic vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 225(1), pages 1-11.
    12. Briseida Sarasola & Karl F. Doerner & Verena Schmid & Enrique Alba, 2016. "Variable neighborhood search for the stochastic and dynamic vehicle routing problem," Annals of Operations Research, Springer, vol. 236(2), pages 425-461, January.
    13. 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.
    14. Novoa, Clara & Storer, Robert, 2009. "An approximate dynamic programming approach for the vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 196(2), pages 509-515, July.
    15. Wadi Khalid Anuar & Lai Soon Lee & Hsin-Vonn Seow & Stefan Pickl, 2022. "A Multi-Depot Dynamic Vehicle Routing Problem with Stochastic Road Capacity: An MDP Model and Dynamic Policy for Post-Decision State Rollout Algorithm in Reinforcement Learning," Mathematics, MDPI, vol. 10(15), pages 1-70, July.
    16. Florent Hernandez & Michel Gendreau & Ola Jabali & Walter Rei, 2019. "A local branching matheuristic for the multi-vehicle routing problem with stochastic demands," Journal of Heuristics, Springer, vol. 25(2), pages 215-245, April.
    17. Tatarakis, A. & Minis, I., 2009. "Stochastic single vehicle routing with a predefined customer sequence and multiple depot returns," European Journal of Operational Research, Elsevier, vol. 197(2), pages 557-571, September.
    18. Walter Rei & Michel Gendreau & Patrick Soriano, 2010. "A Hybrid Monte Carlo Local Branching Algorithm for the Single Vehicle Routing Problem with Stochastic Demands," Transportation Science, INFORMS, vol. 44(1), pages 136-146, February.
    19. Nicola Secomandi & François Margot, 2009. "Reoptimization Approaches for the Vehicle-Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 57(1), pages 214-230, February.
    20. Justin C. Goodson & Jeffrey W. Ohlmann & Barrett W. Thomas, 2013. "Rollout Policies for Dynamic Solutions to the Multivehicle Routing Problem with Stochastic Demand and Duration Limits," Operations Research, INFORMS, vol. 61(1), pages 138-154, February.

    More about this item

    Statistics

    Access and download statistics

    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:taf:tprsxx:v:54:y:2016:i:2:p:579-590. 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 Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/TPRS20 .

    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.