IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v45y1999i8p1156-1168.html
   My bibliography  Save this article

A Branch-First, Cut-Second Approach for Locomotive Assignment

Author

Listed:
  • Koorush Ziarati

    (École Polytechnique (Montréal) Département de Mathématiques et Génie Industriel, C.P. 6079, Succ. Centre-Ville, Montréal, Canada H3C 3A7 and GERAD)

  • François Soumis

    (École Polytechnique (Montréal) Département de Mathématiques et Génie Industriel, C.P. 6079, Succ. Centre-Ville, Montréal, Canada H3C 3A7 and GERAD)

  • Jacques Desrosiers

    (École des Hautes Études Commerciales and GERAD, 3000 chemin de la Côte-Ste-Catherine, Montréal, Canada H3T 2A7)

  • Marius M. Solomon

    (Northeastern University, College of Business Administration, Department of Management Sciences, 314 Hayden Hall, 360 Huntingdon Avenue, Boston, Massachusetts 02115 and GERAD)

Abstract

The problem of assigning locomotives to trains consists of selecting the types and number of engines that minimize the fixed and operational locomotive costs resulting from providing sufficient power to pull trains on fixed schedules. The force required to pull a train is often expressed in terms of horsepower and tonnage requirements rather than in terms of number of engines. This complicates the solution process of the integer programming formulation and usually creates a large integrality gap. Furthermore, the solution of the linearly relaxed problem is strongly fractional. To obtain integer solutions, we propose a novel branch-and-cut approach. The core of the method consists of branching decisions that define on one branch the projection of the problem on a low-dimensional subspace. There, the facets of the polyhedron describing a restricted constraint set can be easily derived. We call this approach branch-first, cut-second. We first derive facets when at most two types of engines are used. We then extend the branching rule to cases involving additional locomotive types. We have conducted computational experiments using actual data from the Canadian National railway company. Simulated test-problems involving two or more locomotive types were solved over 1-, 2-, and 3-day rolling horizons. The cuts were successful in reducing the average integrality gap by 52% for the two-type case and by 34% when more than 25 types were used. Furthermore, the branch-first, cut-second approach was instrumental in improving the best known solution for an almost 2,000-leg weekly problem involving 26 locomotive types. It reduced the number of locomotives by 11, or 1.1%, at an equivalent savings of $3,000,000 per unit. Additional tests on different weekly data produced almost identical results.

Suggested Citation

  • Koorush Ziarati & François Soumis & Jacques Desrosiers & Marius M. Solomon, 1999. "A Branch-First, Cut-Second Approach for Locomotive Assignment," Management Science, INFORMS, vol. 45(8), pages 1156-1168, August.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:8:p:1156-1168
    DOI: 10.1287/mnsc.45.8.1156
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.45.8.1156
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.45.8.1156?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. Julien Bramel & David Simchi-Levi, 1996. "Probabilistic Analyses and Practical Algorithms for the Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 44(3), pages 501-509, June.
    2. Martin Desrochers & Jacques Desrosiers & Marius Solomon, 1992. "A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 40(2), pages 342-354, April.
    3. Michel Gamache & François Soumis & Daniel Villeneuve & Jacques Desrosiers & Éric Gélinas, 1998. "The Preferential Bidding System at Air Canada," Transportation Science, INFORMS, vol. 32(3), pages 246-255, August.
    4. Vanderbeck, F. & Wolsey, L. A., 1996. "An exact algorithm for IP column generation," LIDAM Reprints CORE 1242, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Niklas Kohl & Jacques Desrosiers & Oli B. G. Madsen & Marius M. Solomon & François Soumis, 1999. "2-Path Cuts for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 33(1), pages 101-116, February.
    6. Jean-François Cordeau & Paolo Toth & Daniele Vigo, 1998. "A Survey of Optimization Models for Train Routing and Scheduling," Transportation Science, INFORMS, vol. 32(4), pages 380-404, November.
    7. Ziarati, Koorush & Soumis, Francois & Desrosiers, Jacques & Gelinas, Sylvie & Saintonge, Andre, 1997. "Locomotive assignment with heterogeneous consists at CN North America," European Journal of Operational Research, Elsevier, vol. 97(2), pages 281-292, March.
    8. Matteo Fischetti & Paolo Toth, 1989. "An Additive Bounding Procedure for Combinatorial Optimization Problems," Operations Research, INFORMS, vol. 37(2), pages 319-328, April.
    9. Celso C. Ribeiro & François Soumis, 1994. "A Column Generation Approach to the Multiple-Depot Vehicle Scheduling Problem," Operations Research, INFORMS, vol. 42(1), pages 41-52, February.
    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. Belgacem Bouzaiene-Ayari & Clark Cheng & Sourav Das & Ricardo Fiorillo & Warren B. Powell, 2016. "From Single Commodity to Multiattribute Models for Locomotive Optimization: A Comparison of Optimal Integer Programming and Approximate Dynamic Programming," Transportation Science, INFORMS, vol. 50(2), pages 366-389, May.
    2. Agostinho Agra & Marielle Christiansen & Alexandrino Delgado, 2013. "Mixed Integer Formulations for a Short Sea Fuel Oil Distribution Problem," Transportation Science, INFORMS, vol. 47(1), pages 108-124, February.
    3. Petr KOZLOV & Elena TIMUKHINA & Nikolay TUSHIN, 2018. "Coordination Of Locomotives Turnover And Servicing Modes," Transport Problems, Silesian University of Technology, Faculty of Transport, vol. 13(1), pages 19-26, March.
    4. Philimon Nyamugure & Siphosenkosi Dube Swene & Edward T. Chiyaka & Farikayi K. Mutasa, 2014. "Train Schedule Optimization: A Case Study of the National Railways of Zimbabwe," International Journal of Management Sciences, Research Academy of Social Sciences, vol. 3(1), pages 1-20.
    5. Rouillon, Stéphane & Desaulniers, Guy & Soumis, François, 2006. "An extended branch-and-bound method for locomotive assignment," Transportation Research Part B: Methodological, Elsevier, vol. 40(5), pages 404-423, June.
    6. Lin, Zhiyuan & Kwan, Raymond S.K., 2016. "A branch-and-price approach for solving the train unit scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 97-120.
    7. Camilo Ortiz-Astorquiza & Jean-François Cordeau & Emma Frejinger, 2021. "The Locomotive Assignment Problem with Distributed Power at the Canadian National Railway Company," Transportation Science, INFORMS, vol. 55(2), pages 510-531, March.
    8. Petr KOZLOV & Sergey VAKULENKO & Nikolay TUSHIN & Elena TIMUKHINA, 2017. "Model To Calculate The Optimal Mode Of Train Locomotives Turnover," Transport Problems, Silesian University of Technology, Faculty of Transport, vol. 12(3), pages 125-133, September.
    9. Piu, F. & Prem Kumar, V. & Bierlaire, M. & Speranza, M.G., 2015. "Introducing a preliminary consists selection in the locomotive assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 217-237.
    10. Balachandran Vaidyanathan & Ravindra K. Ahuja & James B. Orlin, 2008. "The Locomotive Routing Problem," Transportation Science, INFORMS, vol. 42(4), pages 492-507, November.
    11. Gao, Yuan & Schmidt, Marie & Yang, Lixing & Gao, Ziyou, 2020. "A branch-and-price approach for trip sequence planning of high-speed train units," Omega, Elsevier, vol. 92(C).
    12. Vaidyanathan, Balachandran & Ahuja, Ravindra K. & Liu, Jian & Shughart, Larry A., 2008. "Real-life locomotive planning: New formulations and computational results," Transportation Research Part B: Methodological, Elsevier, vol. 42(2), pages 147-168, February.
    13. Warren B. Powell & Belgacem Bouzaiene-Ayari & Coleman Lawrence & Clark Cheng & Sourav Das & Ricardo Fiorillo, 2014. "Locomotive Planning at Norfolk Southern: An Optimizing Simulator Using Approximate Dynamic Programming," Interfaces, INFORMS, vol. 44(6), pages 567-578, December.
    14. Armin Fügenschuh & Henning Homfeld & Andreas Huck & Alexander Martin & Zhi Yuan, 2008. "Scheduling Locomotives and Car Transfers in Freight Transport," Transportation Science, INFORMS, vol. 42(4), pages 478-491, November.
    15. Zhiyuan Lin & Raymond S. K. Kwan, 2016. "Local convex hulls for a special class of integer multicommodity flow problems," Computational Optimization and Applications, Springer, vol. 64(3), pages 881-919, July.
    16. Prashant Premkumar & P. N. Ram Kumar, 2022. "Locomotive assignment problem: integrating the strategic, tactical and operational level aspects," Annals of Operations Research, Springer, vol. 315(2), pages 867-898, August.
    17. Ravindra K. Ahuja & Jian Liu & James B. Orlin & Dushyant Sharma & Larry A. Shughart, 2005. "Solving Real-Life Locomotive-Scheduling Problems," Transportation Science, INFORMS, vol. 39(4), pages 503-517, November.
    18. Prashant Premkumar & P. N. Ram Kumar, 2019. "Literature Review of Locomotive Assignment Problem from Service Operations Perspective: The Case of Indian Railways," IIM Kozhikode Society & Management Review, , vol. 8(1), pages 74-86, January.
    19. Danial Davarnia & Jean-Philippe P. Richard & Ece Içyüz-Ay & Bijan Taslimi, 2019. "Network Models with Unsplittable Node Flows with Application to Unit Train Scheduling," Operations Research, INFORMS, vol. 67(4), pages 1053-1068, July.
    20. Xu, Xiaoming & Li, Chung-Lun & Xu, Zhou, 2018. "Integrated train timetabling and locomotive assignment," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 573-593.
    21. Chung, Ji-Won & Oh, Seog-Moon & Choi, In-Chan, 2009. "A hybrid genetic algorithm for train sequencing in the Korean railway," Omega, Elsevier, vol. 37(3), pages 555-565, June.

    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. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    2. Jans, Raf, 2010. "Classification of Dantzig-Wolfe reformulations for binary mixed integer programming problems," European Journal of Operational Research, Elsevier, vol. 204(2), pages 251-254, July.
    3. Stefan Irnich & Guy Desaulniers & Jacques Desrosiers & Ahmed Hadjar, 2010. "Path-Reduced Costs for Eliminating Arcs in Routing and Scheduling," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 297-313, May.
    4. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    5. Omid Shahvari & Rasaratnam Logendran & Madjid Tavana, 2022. "An efficient model-based branch-and-price algorithm for unrelated-parallel machine batching and scheduling problems," Journal of Scheduling, Springer, vol. 25(5), pages 589-621, October.
    6. Baldacci, Roberto & Mingozzi, Aristide & Roberti, Roberto, 2012. "Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints," European Journal of Operational Research, Elsevier, vol. 218(1), pages 1-6.
    7. Timo Gschwind & Stefan Irnich, 2012. "Effective Handling of Dynamic Time Windows and Synchronization with Precedences for Exact Vehicle Routing," Working Papers 1211, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    8. Timo Gschwind & Stefan Irnich & Simon Emde & Christian Tilk, 2018. "Branch-Cut-and-Price for the Scheduling Deliveries with Time Windows in a Direct Shipping Network," Working Papers 1805, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    9. Sana Jawarneh & Salwani Abdullah, 2015. "Sequential Insertion Heuristic with Adaptive Bee Colony Optimisation Algorithm for Vehicle Routing Problem with Time Windows," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-23, July.
    10. Müller, Juliane, 2010. "Approximative solutions to the bicriterion Vehicle Routing Problem with Time Windows," European Journal of Operational Research, Elsevier, vol. 202(1), pages 223-231, April.
    11. Jonathan F. Bard & George Kontoravdis & Gang Yu, 2002. "A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 36(2), pages 250-269, May.
    12. Ahmed Hadjar & Odile Marcotte & François Soumis, 2006. "A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem," Operations Research, INFORMS, vol. 54(1), pages 130-149, February.
    13. Theodore Athanasopoulos & Ioannis Minis, 2013. "Efficient techniques for the multi-period vehicle routing problem with time windows within a branch and price framework," Annals of Operations Research, Springer, vol. 206(1), pages 1-22, July.
    14. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
    15. Mirela Stojković & François Soumis & Jacques Desrosiers, 1998. "The Operational Airline Crew Scheduling Problem," Transportation Science, INFORMS, vol. 32(3), pages 232-245, August.
    16. Vis, Iris F.A., 2006. "Survey of research in the design and control of automated guided vehicle systems," European Journal of Operational Research, Elsevier, vol. 170(3), pages 677-709, May.
    17. Keng Hoo Chuah & Jon C. Yingling, 2005. "Routing for a Just-in-Time Supply Pickup and Delivery System," Transportation Science, INFORMS, vol. 39(3), pages 328-339, August.
    18. Russell Bent & Pascal Van Hentenryck, 2004. "A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 38(4), pages 515-530, November.
    19. Dayarian, Iman & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2015. "A column generation approach for a multi-attribute vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 888-906.
    20. Timo Gschwind & Stefan Irnich & Christian Tilk & Simon Emde, 2020. "Branch-cut-and-price for scheduling deliveries with time windows in a direct shipping network," Journal of Scheduling, Springer, vol. 23(3), pages 363-377, June.

    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:ormnsc:v:45:y:1999:i:8:p:1156-1168. 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.