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Formulations and Benders decomposition algorithms for multidepot salesmen problems with load balancing

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  • Bektaş, Tolga

Abstract

This paper describes new models and exact solution algorithms for the fixed destination multidepot salesmen problem defined on a graph with n nodes where the number of nodes each salesman is to visit is restricted to be in a predefined range. Such problems arise when the time to visit a node takes considerably longer as compared to the time of travel between nodes, in which case the number of nodes visited in a salesman’s tour is the determinant of their ‘load’. The new models are novel multicommodity flow formulations with O(n2) binary variables, which is contrary to the existing formulations for the same (and similar) problems that typically include O(n3) binary variables. The paper also describes Benders decomposition algorithms based on the new formulations for solving the problem exactly. Results of the computational experiments on instances derived from TSPLIB show that some of the proposed algorithms perform remarkably well in cases where formulations solved by a state-of-the-art optimization code fail to yield optimal solutions within reasonable computation time.

Suggested Citation

  • Bektaş, Tolga, 2012. "Formulations and Benders decomposition algorithms for multidepot salesmen problems with load balancing," European Journal of Operational Research, Elsevier, vol. 216(1), pages 83-93.
    • Handle: RePEc:eee:ejores:v:216:y:2012:i:1:p:83-93
    DOI: 10.1016/j.ejor.2011.07.020
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    Cited by:

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    2. Shoufeng Ji & Qi Sun, 2017. "Low-Carbon Planning and Design in B&R Logistics Service: A Case Study of an E-Commerce Big Data Platform in China," Sustainability, MDPI, vol. 9(11), pages 1-27, November.
    3. Bektaş, Tolga & Gouveia, Luis & Martínez-Sykora, Antonio & Salazar-González, Juan-José, 2019. "Balanced vehicle routing: Polyhedral analysis and branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 273(2), pages 452-463.
    4. Canan G. Corlu & Rocio de la Torre & Adrian Serrano-Hernandez & Angel A. Juan & Javier Faulin, 2020. "Optimizing Energy Consumption in Transportation: Literature Review, Insights, and Research Opportunities," Energies, MDPI, vol. 13(5), pages 1-33, March.
    5. Bektaş, Tolga & Gouveia, Luís & Santos, Daniel, 2019. "Revisiting the Hamiltonian p-median problem: A new formulation on directed graphs and a branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 276(1), pages 40-64.
    6. Akpinar, Sener & Elmi, Atabak & Bektaş, Tolga, 2017. "Combinatorial Benders cuts for assembly line balancing problems with setups," European Journal of Operational Research, Elsevier, vol. 259(2), pages 527-537.
    7. Gendreau, Michel & Nossack, Jenny & Pesch, Erwin, 2015. "Mathematical formulations for a 1-full-truckload pickup-and-delivery problem," European Journal of Operational Research, Elsevier, vol. 242(3), pages 1008-1016.
    8. Burger, M. & Su, Z. & De Schutter, B., 2018. "A node current-based 2-index formulation for the fixed-destination multi-depot travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 463-477.
    9. José Alejandro Cornejo-Acosta & Jesús García-Díaz & Julio César Pérez-Sansalvador & Carlos Segura, 2023. "Compact Integer Programs for Depot-Free Multiple Traveling Salesperson Problems," Mathematics, MDPI, vol. 11(13), pages 1-25, July.
    10. Ashkan Fakhri & Mehdi Ghatee, 2013. "Solution of preemptive multi-objective network design problems applying Benders decomposition method," Annals of Operations Research, Springer, vol. 210(1), pages 295-307, November.

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