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Compact formulations of the Steiner Traveling Salesman Problem and related problems

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  • Letchford, Adam N.
  • Nasiri, Saeideh D.
  • Theis, Dirk Oliver

Abstract

The Steiner Traveling Salesman Problem (STSP) is a variant of the TSP that is particularly suitable when routing on real-life road networks. The standard integer programming formulations of both the TSP and STSP have an exponential number of constraints. On the other hand, several compact formulations of the TSP, i.e., formulations of polynomial size, are known. In this paper, we adapt some of them to the STSP, and compare them both theoretically and computationally. It turns out that, just by putting the best of the formulations into the CPLEX branch-and-bound solver, one can solve instances with over 200 nodes. We also briefly discuss the adaptation of our formulations to some related problems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:228:y:2013:i:1:p:83-92
    DOI: 10.1016/j.ejor.2013.01.044
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    Cited by:

    1. HILL, Alessandro & VOß, Stefan, 2014. "Optimal capacitated ring trees," Working Papers 2014012, University of Antwerp, Faculty of Business and Economics.
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    5. Briant, Olivier & Cambazard, Hadrien & Cattaruzza, Diego & Catusse, Nicolas & Ladier, Anne-Laure & Ogier, Maxime, 2020. "An efficient and general approach for the joint order batching and picker routing problem," European Journal of Operational Research, Elsevier, vol. 285(2), pages 497-512.
    6. Yang, Fei & Dai, Ying & Ma, Zu-Jun, 2020. "A cooperative rich vehicle routing problem in the last-mile logistics industry in rural areas," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    7. Paolo Gianessi & Laurent Alfandari & Lucas Létocart & Roberto Wolfler Calvo, 2016. "The Multicommodity-Ring Location Routing Problem," Transportation Science, INFORMS, vol. 50(2), pages 541-558, May.
    8. André Scholz, 2016. "An Exact Solution Approach to the Single-Picker Routing Problem in Warehouses with an Arbitrary Block Layout," FEMM Working Papers 160006, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    9. Raeesi, Ramin & Zografos, Konstantinos G., 2019. "The multi-objective Steiner pollution-routing problem on congested urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 457-485.
    10. Rodríguez-Pereira, Jessica & Fernández, Elena & Laporte, Gilbert & Benavent, Enrique & Martínez-Sykora, Antonio, 2019. "The Steiner Traveling Salesman Problem and its extensions," European Journal of Operational Research, Elsevier, vol. 278(2), pages 615-628.
    11. 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.
    12. Zhang, Huili & Tong, Weitian & Xu, Yinfeng & Lin, Guohui, 2015. "The Steiner Traveling Salesman Problem with online edge blockages," European Journal of Operational Research, Elsevier, vol. 243(1), pages 30-40.
    13. Scholz, André & Schubert, Daniel & Wäscher, Gerhard, 2017. "Order picking with multiple pickers and due dates – Simultaneous solution of Order Batching, Batch Assignment and Sequencing, and Picker Routing Problems," European Journal of Operational Research, Elsevier, vol. 263(2), pages 461-478.
    14. Su, Yixuan & Zhu, Xi & Yuan, Jinlong & Teo, Kok Lay & Li, Meixia & Li, Chunfa, 2023. "An extensible multi-block layout warehouse routing optimization model," European Journal of Operational Research, Elsevier, vol. 305(1), pages 222-239.
    15. Yann Ruberg & André Scholz, 2016. "A Mathematical Programming Formulation for the Single-Picker Routing Problem in a Multi-Block Layout," FEMM Working Papers 160002, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    16. Valle, Cristiano Arbex & Beasley, John E. & da Cunha, Alexandre Salles, 2017. "Optimally solving the joint order batching and picker routing problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 817-834.
    17. Scholz, André & Henn, Sebastian & Stuhlmann, Meike & Wäscher, Gerhard, 2016. "A new mathematical programming formulation for the Single-Picker Routing Problem," European Journal of Operational Research, Elsevier, vol. 253(1), pages 68-84.
    18. Jiang, Jie & Dai, Ying & Yang, Fei & Ma, Zujun, 2024. "A multi-visit flexible-docking vehicle routing problem with drones for simultaneous pickup and delivery services," European Journal of Operational Research, Elsevier, vol. 312(1), pages 125-137.
    19. André Scholz & Daniel Schubert & Gerhard Wäscher, 2016. "Order picking with multiple pickers and due dates – Simultaneous solution of order batching, batch assignment and sequencing, and picker routing problems," FEMM Working Papers 160005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    20. Lu, Wenrong & McFarlane, Duncan & Giannikas, Vaggelis & Zhang, Quan, 2016. "An algorithm for dynamic order-picking in warehouse operations," European Journal of Operational Research, Elsevier, vol. 248(1), pages 107-122.
    21. Alessandro Hill & Stefan Voß, 2016. "Optimal capacitated ring trees," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(2), pages 137-166, May.
    22. John S. F. Lyons & Peter C. Bell & Mehmet A. Begen, 2018. "Solving the Whistler-Blackcomb Mega Day Challenge," Interfaces, INFORMS, vol. 48(4), pages 323-339, August.
    23. Sebastian Henn & André Scholz & Meike Stuhlmann & Gerhard Wäscher, 2015. "A New Mathematical Programming Formulation for the Single-Picker Routing Problem in a Single-Block Layout," FEMM Working Papers 150005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.

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