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A note on the separation of subtour elimination constraints in elementary shortest path problems

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  • Drexl, Michael

Abstract

This note proposes an alternative procedure for identifying violated subtour elimination constraints (SECs) in branch-and-cut algorithms for elementary shortest path problems. The procedure is also applicable to other routing problems, such as variants of travelling salesman or shortest Hamiltonian path problems, on directed graphs. The proposed procedure is based on computing the strong components of the support graph. The procedure possesses a better worst-case time complexity than the standard way of separating SECs, which uses maximum flow algorithms, and is easier to implement.

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  • Drexl, Michael, 2013. "A note on the separation of subtour elimination constraints in elementary shortest path problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 595-598.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:3:p:595-598
    DOI: 10.1016/j.ejor.2013.03.009
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    1. Matteo Fischetti & Paolo Toth, 1997. "A Polyhedral Approach to the Asymmetric Traveling Salesman Problem," Management Science, INFORMS, vol. 43(11), pages 1520-1536, November.
    2. Vansteenwegen, Pieter & Souffriau, Wouter & Oudheusden, Dirk Van, 2011. "The orienteering problem: A survey," European Journal of Operational Research, Elsevier, vol. 209(1), pages 1-10, February.
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    Cited by:

    1. Taccari, Leonardo, 2016. "Integer programming formulations for the elementary shortest path problem," European Journal of Operational Research, Elsevier, vol. 252(1), pages 122-130.
    2. Lera-Romero, Gonzalo & Miranda-Bront, Juan José, 2021. "A branch and cut algorithm for the time-dependent profitable tour problem with resource constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 879-896.
    3. Tamke, Felix & Buscher, Udo, 2021. "A branch-and-cut algorithm for the vehicle routing problem with drones," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 174-203.
    4. Skålnes, Jørgen & Andersson, Henrik & Desaulniers, Guy & Stålhane, Magnus, 2022. "An improved formulation for the inventory routing problem with time-varying demands," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1189-1201.
    5. Rafael Castro Andrade & Rommel Dias Saraiva, 2020. "MTZ-primal-dual model, cutting-plane, and combinatorial branch-and-bound for shortest paths avoiding negative cycles," Annals of Operations Research, Springer, vol. 286(1), pages 147-172, March.

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