IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v245y2015i1p62-69.html
   My bibliography  Save this article

The Steiner travelling salesman problem with correlated costs

Author

Listed:
  • Letchford, Adam N.
  • Nasiri, Saeideh D.

Abstract

The Steiner Travelling Salesman Problem (STSP) is a variant of the TSP that is suitable for instances defined on road networks. We consider an extension of the STSP in which the road traversal costs are both stochastic and correlated. This happens, for example, when vehicles are prone to delays due to rush hours, road works or accidents. Following the work of Markowitz on portfolio selection, we model this problem as a bi-objective mean-variance problem. Then, we show how to approximate the efficient frontier via integer programming. We also show how to exploit certain special structures in the correlation matrices. Computational results indicate that our approach is viable for instances with up to 100 nodes. It turns out that minimum variance tours can look rather different from minimum expected cost tours.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:245:y:2015:i:1:p:62-69
    DOI: 10.1016/j.ejor.2015.02.044
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715001642
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.02.044?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. 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.
    3. Fleischmann, Bernhard, 1985. "A cutting plane procedure for the travelling salesman problem on road networks," European Journal of Operational Research, Elsevier, vol. 21(3), pages 307-317, September.
    4. Sanjay Chaudhuri & Mathias Drton & Thomas S. Richardson, 2007. "Estimation of a covariance matrix with zeros," Biometrika, Biometrika Trust, vol. 94(1), pages 199-216.
    5. Francis Sourd & Olivier Spanjaard, 2008. "A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 472-484, August.
    6. 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.
    7. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    8. 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.
    9. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    10. Astrid S. Kenyon & David P. Morton, 2003. "Stochastic Vehicle Routing with Random Travel Times," Transportation Science, INFORMS, vol. 37(1), pages 69-82, February.
    11. Warren P. Adams & Hanif D. Sherali, 1986. "A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems," Management Science, INFORMS, vol. 32(10), pages 1274-1290, October.
    12. Edward P. C. Kao, 1978. "A Preference Order Dynamic Program for a Stochastic Traveling Salesman Problem," Operations Research, INFORMS, vol. 26(6), pages 1033-1045, December.
    13. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.
    14. Letchford, Adam N. & Nasiri, Saeideh D. & Theis, Dirk Oliver, 2013. "Compact formulations of the Steiner Traveling Salesman Problem and related problems," European Journal of Operational Research, Elsevier, vol. 228(1), pages 83-92.
    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. 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.
    2. Rostami, Borzou & Chassein, André & Hopf, Michael & Frey, Davide & Buchheim, Christoph & Malucelli, Federico & Goerigk, Marc, 2018. "The quadratic shortest path problem: complexity, approximability, and solution methods," European Journal of Operational Research, Elsevier, vol. 268(2), pages 473-485.

    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. Hossein Hashemi Doulabi & Gilles Pesant & Louis-Martin Rousseau, 2020. "Vehicle Routing Problems with Synchronized Visits and Stochastic Travel and Service Times: Applications in Healthcare," Transportation Science, INFORMS, vol. 54(4), pages 1053-1072, July.
    2. Chen, Lu & Gendreau, Michel & Hà, Minh Hoàng & Langevin, André, 2016. "A robust optimization approach for the road network daily maintenance routing problem with uncertain service time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 85(C), pages 40-51.
    3. Anastasios D. Vareias & Panagiotis P. Repoussis & Panagiotis P. Repoussi, 2019. "Assessing Customer Service Reliability in Route Planning with Self-Imposed Time Windows and Stochastic Travel Times," Service Science, INFORMS, vol. 53(1), pages 256-281, February.
    4. Jiang, J. & Ng, K.M. & Teo, K.M., 2016. "Satisficing measure approach for vehicle routing problem with time windows under uncertaintyAuthor-Name: Nguyen, V.A," European Journal of Operational Research, Elsevier, vol. 248(2), pages 404-414.
    5. 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.
    6. Norlund, Ellen Karoline & Gribkovskaia, Irina & Laporte, Gilbert, 2015. "Supply vessel planning under cost, environment and robustness considerations," Omega, Elsevier, vol. 57(PB), pages 271-281.
    7. 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.
    8. Hongtao Lei & Gilbert Laporte & Bo Guo, 2012. "A generalized variable neighborhood search heuristic for the capacitated vehicle routing problem with stochastic service times," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 99-118, April.
    9. Yan, Shangyao & Lin, Jenn-Rong & Lai, Chun-Wei, 2013. "The planning and real-time adjustment of courier routing and scheduling under stochastic travel times and demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 53(C), pages 34-48.
    10. 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.
    11. 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.
    12. 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.
    13. 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).
    14. 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.
    15. Elgesem, Aurora Smith & Skogen, Eline Sophie & Wang, Xin & Fagerholt, Kjetil, 2018. "A traveling salesman problem with pickups and deliveries and stochastic travel times: An application from chemical shipping," European Journal of Operational Research, Elsevier, vol. 269(3), pages 844-859.
    16. 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.
    17. Avraham, Edison & Raviv, Tal, 2020. "The data-driven time-dependent traveling salesperson problem," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 25-40.
    18. Liu, Bingbing & Guo, Xiaolong & Yu, Yugang & Zhou, Qiang, 2019. "Minimizing the total completion time of an urban delivery problem with uncertain assembly time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 132(C), pages 163-182.
    19. 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.
    20. Mohammed Bazirha & Abdeslam Kadrani & Rachid Benmansour, 2023. "Stochastic home health care routing and scheduling problem with multiple synchronized services," Annals of Operations Research, Springer, vol. 320(2), pages 573-601, January.

    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:245:y:2015:i:1:p:62-69. 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.