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Subgradient Methods for the Service Network Design Problem

Author

Listed:
  • Judith M. Farvolden

    (Department of Industrial Engineering, University of Toronto, Toronto, Ontario, Canada M5S 1A4)

  • Warren B. Powell

    (Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey 08544)

Abstract

We present local-improvement heuristics for a Service Network Design Problem encountered in the motor carrier industry. The scheduled set of vehicle departures determines the right hand side of the capacity constraints of the shipment routing subproblem which is modeled as a multicommodity network flow problem. The heuristics, one for dropping a scheduled service and another for introducing a new service, are based upon subgradients derived from the optimal dual variables of the shipment routing subproblem. The basis of the multicommodity network flow problem is partitioned to facilitate the calculation of the dual variables, reduced costs and subgradients. These are determined in large part by additive and network operations, and only in small part by matrix multiplication. The results of our computational experimentation are presented.

Suggested Citation

  • Judith M. Farvolden & Warren B. Powell, 1994. "Subgradient Methods for the Service Network Design Problem," Transportation Science, INFORMS, vol. 28(3), pages 256-272, August.
    • Handle: RePEc:inm:ortrsc:v:28:y:1994:i:3:p:256-272
    DOI: 10.1287/trsc.28.3.256
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    Cited by:

    1. Lai, M. F. & Lo, Hong K., 2004. "Ferry service network design: optimal fleet size, routing, and scheduling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 38(4), pages 305-328, May.
    2. Alan Erera & Michael Hewitt & Martin Savelsbergh & Yang Zhang, 2013. "Improved Load Plan Design Through Integer Programming Based Local Search," Transportation Science, INFORMS, vol. 47(3), pages 412-427, August.
    3. Arnt-Gunnar Lium & Teodor Gabriel Crainic & Stein W. Wallace, 2009. "A Study of Demand Stochasticity in Service Network Design," Transportation Science, INFORMS, vol. 43(2), pages 144-157, May.
    4. Meuffels, W.J.M., 2015. "The design of road and air networks for express service providers," Other publications TiSEM d3266cb8-bc55-41be-adc7-4, Tilburg University, School of Economics and Management.
    5. Teodor Gabriel Crainic & Michel Gendreau & Judith M. Farvolden, 2000. "A Simplex-Based Tabu Search Method for Capacitated Network Design," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 223-236, August.
    6. Cassiano A. Isler & Yesid Asaff & Marin Marinov, 2020. "Designing a Geo-Strategic Railway Freight Network in Brazil Using GIS," Sustainability, MDPI, vol. 13(1), pages 1-21, December.
    7. Haiqing Song & Vernon N. Hsu & Raymond K. Cheung, 2008. "Distribution Coordination Between Suppliers and Customers with a Consolidation Center," Operations Research, INFORMS, vol. 56(5), pages 1264-1277, October.
    8. Dall'Orto, Leonardo Campo & Crainic, Teodor Gabriel & Leal, Jose Eugenio & Powell, Warren B., 2006. "The single-node dynamic service scheduling and dispatching problem," European Journal of Operational Research, Elsevier, vol. 170(1), pages 1-23, April.
    9. Antonio Frangioni, 2005. "About Lagrangian Methods in Integer Optimization," Annals of Operations Research, Springer, vol. 139(1), pages 163-193, October.
    10. Crainic, Teodor Gabriel, 2000. "Service network design in freight transportation," European Journal of Operational Research, Elsevier, vol. 122(2), pages 272-288, April.
    11. C S Sung & S H Song, 2003. "Integrated service network design for a cross-docking supply chain network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(12), pages 1283-1295, December.
    12. Mike Hewitt, 2019. "Enhanced Dynamic Discretization Discovery for the Continuous Time Load Plan Design Problem," Transportation Science, INFORMS, vol. 53(6), pages 1731-1750, November.
    13. C S Sung & W Yang, 2008. "An exact algorithm for a cross-docking supply chain network design problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 119-136, January.
    14. Herszterg, Ian & Ridouane, Yassine & Boland, Natashia & Erera, Alan & Savelsbergh, Martin, 2022. "Near real-time loadplan adjustments for less-than-truckload carriers," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1021-1034.
    15. Khaled, Abdullah A. & Jin, Mingzhou & Clarke, David B. & Hoque, Mohammad A., 2015. "Train design and routing optimization for evaluating criticality of freight railroad infrastructures," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 71-84.
    16. Crainic, Teodor Gabriel & Laporte, Gilbert, 1997. "Planning models for freight transportation," European Journal of Operational Research, Elsevier, vol. 97(3), pages 409-438, March.
    17. Wang, David Z.W. & Lo, Hong K., 2008. "Multi-fleet ferry service network design with passenger preferences for differential services," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 798-822, November.
    18. Grunert, Tore & Sebastian, Hans-Jurgen, 2000. "Planning models for long-haul operations of postal and express shipment companies," European Journal of Operational Research, Elsevier, vol. 122(2), pages 289-309, April.
    19. Louwerse, I. & Mijnarends, J. & Meuffels, I. & Huisman, D. & Fleuren, H.A., 2012. "Scheduling Movements in the Network of an Express Service Provider," Econometric Institute Research Papers EI 2012-08, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    20. Raymond K. Cheung & B. Muralidharan, 2000. "Dynamic Routing for Priority Shipments in LTL Service Networks," Transportation Science, INFORMS, vol. 34(1), pages 86-98, February.
    21. Ahmad I. Jarrah & Ellis Johnson & Lucas C. Neubert, 2009. "Large-Scale, Less-than-Truckload Service Network Design," Operations Research, INFORMS, vol. 57(3), pages 609-625, June.
    22. Xin Wang & Teodor Gabriel Crainic & Stein W. Wallace, 2019. "Stochastic Network Design for Planning Scheduled Transportation Services: The Value of Deterministic Solutions," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 153-170, February.
    23. 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.
    24. Ilfat Ghamlouche & Teodor Gabriel Crainic & Michel Gendreau, 2003. "Cycle-Based Neighbourhoods for Fixed-Charge Capacitated Multicommodity Network Design," Operations Research, INFORMS, vol. 51(4), pages 655-667, August.

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