Abstract
The Travelling Salesman Problem (TSP) has been studied extensively for over half a century, but due to its property of being at the basis of many scheduling and routing problems it still attracts the attention of many research. One variation of the standard TSP is the multi-depot travelling salesman problem (MTSP) where the salesmen can start from and return to several distinct locations. This article focusses on the MTSP with the extra restriction that each salesman should return to his home depot, known as the fixed-destination MTSP. This problem (and its variations such as the multi-depot vehicle routing problem) is usually formulated using three-index binary variables, making the problem computationally expensive to solve. Here an alternative formulation is presented using two-index binary variables through the introduction of a limited amount of continuous variables to ensure the return of the salesmen to their home depots.
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Notes
- 1.
It is possible to formulate this problem with multiple salesmen per depot as well. To avoid distraction from the main purpose of this section the problem is kept as simple as possible.
- 2.
References
Applegate, D. L., Bixby, R. E., Chvátal, V., & Cook, W. J. (2006). The traveling salesman problem: a computational study. Princeton: Princeton University Press.
Bektaş, T. (2006). The multiple traveling salesman problem: an overview of formulations and solution procedures. Omega, 34(3), 209–219.
Bektaş, T. (2012). Formulations and Benders decomposition algorithms for multidepot salesmen problems with load balancing. European Journal of Operational Research, 216(1), 83–93.
Burger, M., De Schutter, B., & Hellendoorn, J. (2012). Micro-ferry scheduling problem with time windows. In proceedings of American Control Conference (pp. 3998–4003)
Burger, M., & De Schutter, B. (2013). Energy-efficient transportation over flowing water. In proceedings of International Conference on Sensing and Control (ICNSC), pp. 226–231
Burger, M., Huiskamp, M., & Keviczky, T. (2013). Complete field coverage as a multiple harvester routing problem. In proceedings of Agriculture Control.
Desrochers, M., & Laporte, G. (1991). Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints. Operations Research Letters, 10(1), 27–36.
Golden, G., Raghavan, S., & Wasil, E. (2008). The vehicle routing problem: latest advances and new challenges. Berlin: Springer.
Kara, I., & Bektaş, T. (2006). Integer linear programming formulations of multiple salesman problems and its variations. European Journal of Operational Research, 174(3), 1449–1458.
Miller, C. E., Tucker, A. W., & Zemlin, R. A. (1960). Integer programming formulation of traveling salesman problems. Journal of the ACM, 7(4), 326–329.
Sherali, H. D., & Driscoll, P. J. (2002). On tightening the relaxations of Miller-Tucker-Zemlin formulations for asymmetric traveling salesman problems. Operations Research, 50(4), 656–669.
Toth, P., & Vigo, D. (2002). The vehicle routing problem. SIAM
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Burger, M. (2014). Exact and Compact Formulation of the Fixed-Destination Travelling Salesman Problem by Cycle Imposement Through Node Currents. In: Huisman, D., Louwerse, I., Wagelmans, A. (eds) Operations Research Proceedings 2013. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-07001-8_12
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DOI: https://doi.org/10.1007/978-3-319-07001-8_12
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