Abstract
We tackle the mixed capacitated general routing problem (MCGRP) which generalizes many other routing problems. We propose an integer programming model for the MCGRP and extend some inequalities originally introduced for the capacitated arc routing problem (CARP). Identification procedures for these inequalities and for some relaxed constraints are also discussed. Finally, we describe a branch and cut algorithm including the identification procedures and present computational experiments over instances derived from the CARP.
Similar content being viewed by others
References
Belenguer, J.M., Benavent, E.: The capacitated arc routing problem: valid inequalities and facets. Comput. Optim. Appl. 10(2), 165–187 (1998)
Belenguer, J.M., Benavent, E.: A cutting plane algorithm for the capacitated arc routing problem. Comput. Oper. Res. 30(5), 705–728 (2003)
Belenguer, J.M., Benavent, E., Lacomme, P., Prins, C.: Lower and upper bounds for the mixed capacitated arc routing problem. Comput. Oper. Res. 33(12), 3363–3383 (2006)
Benavent, E., Corberán, A., Sanchis, J.M.: Linear programming based methods for solving arc routing problems. In: Dror, M. (ed.) Arc Routing: Theory, Solutions and Applications, pp. 231–275. Kluwer Academic Publishers, Dordrecht (2000)
Corberán, A., Letchford, A.N., Sanchis, J.M.: A cutting plane algorithm for the general routing problem. Math. Program. Ser. A 90(2), 291–316 (2001)
Corberán, A., Mejía, G., Sanchis, J.M.: New results on the mixed general routing problem. Oper. Res. 53(2), 363–376 (2005)
Corberán, A., Plana, I., Sanchis, J.M.: A branch& cut algorithm for the windy general routing problem and special cases. Networks 49(4), 245–257 (2007)
Corberán, A., Plana, I., Sanchis, J.M.: The windy general routing polyhedron: a global view of many known arc routing polyhedra. SIAM J. Discret. Math. 22(2), 606–628 (2008)
Corberán, A., Prins, C.: Recent results on arc routing problems: an annotated bibliography. Networks 56(1), 50–69 (2010)
Corberán, A., Romero, A., Sanchis, J.M.: The mixed general routing polyhedron. Math. Program. Ser. A 96(1), 103–137 (2003)
Corberán, A., Sanchis, J.M.: The general routing problem polyhedron: facets from the RPP and GTSP polyhedra. Eur. J. Oper. Res. 108(3), 538–550 (1998)
Dror, M. (ed.) Arc Routing: Theory, Solutions and Applications. Kluwer Academic Publishers, Dordrecht (2000)
Fischetti, M., Glover, F., Lodi, A.: The feasibility pump. Math. Program. 104(1), 91–104 (2005)
Fischetti, M., Salazar, J.J., Toth, P.: A branch-and-cut algorithm for the symmetric generalized traveling salesman problem. Oper. Res. 45(3), 378–394 (1997)
Golden, B.L., Dearmon, J.S., Baker, E.K.: Computational experiments with algorithms for a class of routing problems. Comput. Oper. Res. 10(1), 47–59 (1983)
Golden B.L., Raghavan, S., Wasil, E.A. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges (Operations Research/Computer Science Interfaces Series). Springer, Berlin (2008)
Gouveia, L., Mourão, M.C., Pinto, L.S.: Lower bounds for the mixed capacitated arc routing problem. Comput. Oper. Res. 37(4), 692–699 (2010)
Gutiérrez, J.C.A., Soler, D., Hervás, A.: The capacitated general routing problem on mixed graphs. Revista Investigacion Operacional 23(1), 15–26 (2002)
Lenstra, J.K., Rinnooy Kan, A.H.G.: On general routing problems. Networks 6(3), 273–280 (1976)
Letchford, A.N.: New inequalities for the general routing problem. Eur. J. Oper. Res. 96(2), 317–322 (1997)
Letchford, A.N.: The general routing polyhedron: a unifying framework. Eur. J. Oper. Res. 112(1), 122–133 (1999)
Orloff, C.S.: A fundamental problem in vehicle routing. Networks 4(1), 35–64 (1974)
Padberg, M.W., Rao, M.R.: Odd minimum cut-sets and b-matchings. Math. Oper. Res. 7(1), 67–80 (1982)
Pandit, R., Muralidharan, B.: A capacitated general routing problem on mixed networks. Comput. Oper. Res. 22(5), 465–478 (1995)
Pearn, W.L., Assad, A., Golden, B.L.: Transforming arc routing into node routing problems. Comput. Oper. Res. 14(4), 285–288 (1987)
Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Tech. J. 36, 1389–1401 (1957)
Prins, C., Bouchenoua, S.: A memetic algorithm solving the VRP, the CARP and general routing problems with nodes, edges and arcs. In: Hart, W.E., Krasnogor, N., Smith, J.E. (eds.) Recent Advances in Memetic Algorithms, pp. 65–85. Springer, Berlin (2005)
Santos, L., Coutinho-Rodrigues, J., Current, J.R.: An improved heuristic for the capacitated arc routing problem. Comput. Oper. Res. 36(9), 2632–2637 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bosco, A., Laganà, D., Musmanno, R. et al. Modeling and solving the mixed capacitated general routing problem. Optim Lett 7, 1451–1469 (2013). https://doi.org/10.1007/s11590-012-0552-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-012-0552-y