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Stronger multi-commodity flow formulations of the (capacitated) sequential ordering problem

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  • Letchford, Adam N.
  • Salazar-González, Juan-José

Abstract

The sequential ordering problem (SOP) is the generalisation of the asymmetric travelling salesman problem in which there are precedence relations between pairs of nodes. Hernández & Salazar introduced a multi-commodity flow (MCF) formulation for a generalisation of the SOP in which the vehicle has a limited capacity. We strengthen this MCF formulation by fixing variables and adding valid equations. We then use polyhedral projection, together with some known results on flows, cuts and metrics, to derive new families of strong valid inequalities for both problems. Finally, we give computational results, which show that our findings yield good lower bounds in practice.

Suggested Citation

  • Letchford, Adam N. & Salazar-González, Juan-José, 2016. "Stronger multi-commodity flow formulations of the (capacitated) sequential ordering problem," European Journal of Operational Research, Elsevier, vol. 251(1), pages 74-84.
    • Handle: RePEc:eee:ejores:v:251:y:2016:i:1:p:74-84
    DOI: 10.1016/j.ejor.2015.11.001
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    References listed on IDEAS

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    1. Gouveia, Luis, 1995. "A result on projection for the vehicle routing ptoblem," European Journal of Operational Research, Elsevier, vol. 85(3), pages 610-624, September.
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    4. Vicky Mak & Andreas Ernst, 2007. "New cutting-planes for the time- and/or precedence-constrained ATSP and directed VRP," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 69-98, August.
    5. Escudero, L. F., 1988. "An inexact algorithm for the sequential ordering problem," European Journal of Operational Research, Elsevier, vol. 37(2), pages 236-249, November.
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    Cited by:

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    2. Margarita P. Castro & Andre A. Cire & J. Christopher Beck, 2020. "An MDD-Based Lagrangian Approach to the Multicommodity Pickup-and-Delivery TSP," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 263-278, April.
    3. Aziez, Imadeddine & Côté, Jean-François & Coelho, Leandro C., 2020. "Exact algorithms for the multi-pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 284(3), pages 906-919.
    4. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.
    5. Salii, Yaroslav, 2019. "Revisiting dynamic programming for precedence-constrained traveling salesman problem and its time-dependent generalization," European Journal of Operational Research, Elsevier, vol. 272(1), pages 32-42.
    6. Naccache, Salma & Côté, Jean-François & Coelho, Leandro C., 2018. "The multi-pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 269(1), pages 353-362.

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