Projection results for vehicle routing

Mathematical Programming

Volumn 105, Issue 2-3, 2006, Pages 251-274

  Letchford, Adam N ^a   Salazar González, Juan José ^b  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b UNIVERSIDAD DE LA LAGUNA   (Spain)

Author keywords

Integer programming; Projection; Vehicle routing

Indexed keywords

INTEGER PROGRAMMING; PROBLEM SOLVING;

POLYNOMIAL-TIME SEPARATION ALGORITHMS; PROJECTION; VEHICLE ROUTING;

MATHEMATICAL PROGRAMMING;

EID: 29044438268     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-005-0652-x     Document Type: Article

References (38)

1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, algorithms and applications. Prentice-Hall, 1993
2. Ascheuer, N., Fischetti, M., Grötschel, M.: A polyhedral study of the asymmetric traveling salesman problem with time windows. Networks 36, 69-79 (2000)
3. Augerat, P.: Approche Polyèdrale du Problème de Tournées de Véhicles. PhD thesis, Institut National Polytechnique de Grenoble, France, 1995
4. Augerat, P., Belenguer, J.M., Benavent, E., Corberán, A., Naddef, D., Rinaldi, G.: Computational results with a branch-and-cut code for the capacitated vehicle routing problem. Research report RR949-M, ARTEM1S-1MAG, France (1995)
5. Baldacci, R., Hadjiconstantinou, E., Mingozzi, A.: An exact algorithm for the capacitated vehicle routing problem based on a two-commodity network flow formulation. Operations Research 52, 723-738 (2004)
6. Bauer, P., Linderoth, J.T., Savelsbergh, M.W.P.: A branch and cut approach to the cardinality constrained circuit problem. Math. Program. 91, 307-348 (2002)
7. Bixby, A.E., Coullard, C., Simchi-Levi, D.: The capacitated prize-collecting traveling salesman problem. Working paper, Department of Industrial Engineering and Engineering Management, Northwestern University, 1997
8. Blasum, U., Hochstättler, W.: Application of the branch and cut method to the vehicle routing problem. Working Paper, Zentrum fur Angewandte Informatik, Koln, 2000
9. Cordeau, J.F., Desaulniers, G., Desrosiers, J., Solomon, M.M. VRP with time windows. In: Toth, P., Vigo, D. (eds.), The Vehicle Routing Problem. SIAM, 2001
10. Desaulniers, G., Desrosiers, J., Erdmann, A., Solomon, M.M., Soumis, F.: VRP with pickup and delivery. In: Toth, P., Vigo D. (eds.), The Vehicle Routing Problem. SIAM, 2001
11. Desrosiers, J., Dumas, Y., Solomon, M.M., Soumis, F.: Time-constrained routing and scheduling. In: Ball M.O. et al. (eds.), Network Routing. Handbooks in OR/MS 8, North-Holland, Amsterdam, 1995
12. Eglese, R.W., Letchford, A.N.: Polyhedral theory for arc routing problems. In : Dror, M. (ed.), Arc Routing: Theory, Solutions and Applications. Kluwer Academic Publishers, 2000
13. Ferreira, C.E., Martin, A., Weismantel, R.: Solving multiple knapsack problems by cutting planes. SIAM J. Opt. 6, 858-877 (1996)
14. Fischetti, M., Salazar-González, J.J., Toth, P.: Experiments with a multi-commodity formulation for the symmetric capacitated vehicle routing problem. In Proceedings of the 3rd Meeting of the EURO Working Group on Transportation, Barcelona, 1995, pp. 169-173
15. Fisher, M.L., Jaikumar, R.: A generalized assignment heuristic for the vehicle routing problem. Networks 11, 109-124 (1981)
16. Fukasawa, R., Lysgaard, J., de Aragão, M.P., Reis, M., Uchoa, E., Werneck, R.F.: Robust branch-and-cut-and-price for the capacitated vehicle routing problem. In: Nemhauser, G., Bienstock, D. (eds.), Integer Programming and Combinatorial Optimization 10. Lecture Notes in Computer Science 3064, Springer, Berlin Heidelberg, 2004, pp. 1-15
17. Gavish, B., Graves, S.: The traveling salesman problem and related problems. Working Paper, Graduate School of Management, University of Rochester, New York, 1979
18. Gavish, B., Graves, S.: Scheduling and routing in transportation and distribution systems: formulations and new relaxations. Working Paper, Graduate School of Management, University of Rochester, New York, 1982
19. Goemans, M.X., Myung, Y.S.: A catalog of steiner tree formulations. Networks 23, 19-28 (1993)
20. Gouveia, L. A result on projection for the vehicle routing problem. European J. Oper. Res. 85, 610-624 (1995)
21. Grötschel, M., Lovász, L., Schrijver, A. J. : Geometric Algorithms in Combinatorial Optimisation. Springer, 1988
22. Hernández-Pérez, H., Salazar-González, J.J.: The one-commodity pickup-and-delivery traveling salesman problem. In: Jünger, M., Reinelt, G., Rinaldi, G. (eds.), Eureka! You Shrink, Lecture Notes in Computer Science 2570, Springer, Berlin Heidelberg, 2003, pp. 89-104
23. Irnich, S., Villeneuve, D.: The shortest path problem with resource constraints and k-cycle elimination with k ≥ 3. Working Paper, RWTH Aachen, 2003
24. Kohl, N., Desrosiers, J., Madsen, O.B.G., Solomon, M.M., Soumis, F.: 2-path cuts for the vehicle routing problem with time windows. Transportation Science 33, 101-116 (1999)
25. Langevin, A., Soumis, F., Desrochers, J. Classification of traveling salesman formulations. Oper. Res. Lett. 9, 127-132 (1990)
26. Langevin, A., Desrochers, M., Desrosiers, J., Gélinas, S., Soumis, F.: A two commodity flow formulation for the travelling salesman and makespan problems with time windows. Networks 23, 631-640 (1993)
27. Laporte, G., Nobert, Y.: A branch and bound algorithm for the capacitated vehicle routing problem. OR Spektrum 5, 77-85 (1983)
28. Laporte, G., Nobert, Y.: Exact algorithms for the vehicle routing problem. Ann. Discr. Math. 31, 147-184 (1987)
29. Laporte, G., Nobert, Y., Desrochers, M.: Optimal routing under capacity and distance restrictions. Operations Research 33, 1050-1073 (1985)
30. Letchford, A.N., Eglese, R.W.: New cutting-planes for vehicle routing problems. Presented at CO96, Imperial College, London, 1996
31. Letchford, A.N., Eglese, R.W., Lysgaard, J.: Multistars, partial multistars and the capacitated vehicle routing problem. Math. Program. 94, 21-40 (2002)
32. Lysgaard, J., Letchford, A.N., Eglese, R.W.: A new branch-and-cut algorithm for the capacitated vehicle routing problem. Math. Program. 100, 423-445 (2004)
33. Maffioli, F., Sciomachen, A. : A mixed-integer model for solving ordering problems with side constraints. Ann. Operations Res. 69, 277-297 (1997)
34. Naddef, D., Rinaldi, G.: Branch-and-cut algorithms for the capacitated VRP. In: Toth, P., Vigo, D. (eds.), The Vehicle Routing Problem. SIAM, 2001
35. Padberg, M., Sung, T.Y.: An analytical comparison of different formulations of the travelling salesman problem. Math. Program. 52, 315-357 (1991)
36. Papadimitriou, C.H., Yannakakis, M.: The complexity of facets (and some facets of complexity). J. Comp. System Sci. 28, 244-259 (1984)
37. Picard, J.C., Ratliff, H.D.: Minimum cuts and related problems. Networks 5, 357-370 (1975)
38. Toth, P., Vigo, D.: An overview of vehicle routing problems. In: Toth, P., Vigo, D. (eds.), The Vehicle Routing Problem. SIAM, 2001