Abstract
This paper presents a robust branch-cut-and-price algorithm for the Heterogeneous Fleet Vehicle Routing Problem (HFVRP), vehicles may have various capacities and fixed costs. The columns in the formulation are associated to q-routes, a relaxation of capacitated elementary routes that makes the pricing problem solvable in pseudo-polynomial time. Powerful new families of cuts are also proposed, which are expressed over a very large set of variables. Those cuts do not increase the complexity of the pricing subproblem. Experiments are reported where instances up to 75 vertices were solved to optimality, a major improvement with respect to previous algorithms.
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References
Baldacci, R., Bodin, L., Mingozzi, A.: The multiple disposal facilities and multiple inventory locations rollon-rolloff vehicle routing problem. Computers and Operation Research 33, 2667–2702 (2006)
Choi, E., Tcha, D.-W.: A column generation approach to the heterogeneous fleet vehicle routing problem. Computers and Operations Research 34, 2080–2095 (2007)
Christofides, N., Mingozzi, A., Toth, P.: Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations. Mathematical Programming 20, 255–282 (1981)
Dash, S., Fukasawa, R., Gunluk, O.: On the generalized master knapsack polyhedron. LNCS - IPCO 2007 (To appear 2007)
Gendreau, M., Laporte, G., Musaraganyi, C., Taillard, E.D.: A tabu search heuristic for the heterogeneous fleet vehicle routing problem. Computers and Operations Research 26, 1153–1173 (1999)
Golden, B., Assad, A., Levy, L., Gheysens, F.: The fleet size and mix vehicle routing problem. Computers and Operations Research 11, 49–66 (1984)
Houck, D., Picard, J., Queyranne, M., Vegamundi, R.: The travelling salesman problem as a constrained shortest path problem. Opsearch 17, 93–109 (1980)
Lysgaard, J., Letchford, A., Eglese, R.: A new branch-and-cut algorithm for the capacitated vehicle routing problem. Mathematical Programming 100, 423–445 (2004)
Ochi, L., Vianna, D., Filho, A., Drummond, L.: A parallel evolutionary algorithm for the vehicle routing problem with heterogeneous fleet. Future Generation Computer Systems 14, 285–292 (1998)
Picard, J., Queyranne, M.: The time-dependant traveling salesman problem and its application to the tardiness problem in one-machine scheduling. Operations Research 26, 86–110 (1978)
de, Aragão, M.P., Uchoa, E.: Integer program reformulation for robust branch-and-cut-and-price. In: Wolsey, L.: (ed.), Annals of Mathematical Programming in Rio, Búzios, Brazil pp. 56–61 (2003)
Renaud, J., Boctor, F.F.: A sweep-based algorithm for the fleet size and mix vehicle routing problem. European Journal of Operational Research 140, 618–628 (2002)
Taillard, E.D.: A heuristic column generation method for the heterogeneous fleet vrp. RAIRO 33, 1–14 (1999)
Uchoa, E., Fukasawa, R., Lysgaard, J., Pessoa, A., de, Aragão, M.P., Andrade, D.: Robust branch-cut-and-price for the capacitated minimum spanning tree problem over a large extended formulation. Mathematical Programming, on-line first (2007)
Wassan, N.A., Osman, I.H.: Tabu search variants for the mix fleet vehicle routing problem. Journal of the Operational Research Society 53, 768–782 (2002)
Westerlund, A., Göthe-Lundgren, M., Larsson, T.: Mathematical formulations of the heterogeneous fleet vehicle routing problem. In: ROUTE 2003, International Workshop on Vehicle Routing, pp. 1–2 (2003)
Yaman, H.: Formulations and valid inequalities for the heterogeneous vehicle routing problem. Mathematical Programming 106, 365–390 (2006)
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Pessoa, A., Poggi de Aragão, M., Uchoa, E. (2007). A Robust Branch-Cut-and-Price Algorithm for the Heterogeneous Fleet Vehicle Routing Problem. In: Demetrescu, C. (eds) Experimental Algorithms. WEA 2007. Lecture Notes in Computer Science, vol 4525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72845-0_12
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DOI: https://doi.org/10.1007/978-3-540-72845-0_12
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