Robust Branch-Cut-and-Price algorithms for vehicle routing problems

Operations Research/ Computer Science Interfaces Series

Volumn 43, Issue , 2008, Pages 297-325

  Pessoa, Artur ^a   de Aragão, Marcus Poggi ^b   Uchoa, Eduardo ^a  

^a FLUMINENSE FEDERAL UNIVERSITY   (Brazil)

^b PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Branch and bound; Column generation; Cutting plane algorithms; Extended formulations

Indexed keywords

EID: 84888596674     PISSN: 1387666X     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-0-387-77778-8_14     Document Type: Article

References (39)

1. N. Achuthan, L. Caccetta, and S. Hill. Capacited vehicle routing problem: Some new cutting planes. Asia-Pacific J. of Operational Research, 15: 109-123, 1998.
2. J. Araque, L. Hall, and T. Magnanti. Capacitated trees, capacitated routing, and associated polyhedra. Technical Report OR232-90, MIT, Operations Research Center, 1990.
3. P. Augerat. Approche polyèdrale du problème de tournées de véhicles. PhD thesis, Institut National Polytechnique de Grenoble, 1995.
4. P. Augerat, J. Belenguer, E. Benavent, A. Corberán, D. Naddef, and G. Rinaldi. Computational results with a branch and cut code for the capacitated vehicle routing problem. Technical Report 949-M, Université Joseph Fourier, Grenoble, France, 1995.
5. R. Baldacci, L. Bodin, and A. Mingozzi. The multiple disposal facilities and multiple inventory locations rollon-rolloff vehicle routing problem. Computers and Operation Research, 33: 2667-2702, 2006.
6. R. Baldacci, N. Christofides, and A. Mingozzi. An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Submitted, 2007.
7. C. Barnhart, C. Hane, and P. Vance. Using branch-and-price-and-cut to solve origin-destination integer multicommodity flow problems. Operations Research, 40: 318-326, 2000.
8. C. Barnhart, E. Johnson, G. Nemhauser, M. Savelsbergh, and P. Vance. Branchand-price: Column generation for solving huge integer programs. Operations Research, 46: 316-329, 1998.
9. E. Choi and D-W Tcha. A column generation approach to the heterogeneous fleet vehicle routing problem. Computers and Operations Research, 34: 2080-2095, 2007.
10. N. Christofides and S. Eilon. An algorithm for the vehicle-dispatching problem. Operational Research Quarterly, 20: 309-318, 1969.
11. N. Christofides, A. Mingozzi, and P. Toth. Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations. Mathematical Programming, 20: 255-282, 1981.
12. G. Cornuéjols and F. Harche. Polyhedral study of the capacitated vehicle routing problem. Mathematical Programming, 60: 21-52, 1993.
13. S. Dash, R. Fukasawa, and O. Gunluk. On the generalized master knapsack polyhedron. In Proceedings of the IPCO 2007, 2007.
14. du Merle, O. Villeneuve, J. Desrosiers, and P. Hansen. Stabilized column generation. Discrete Mathematics, 194: 229-237, 1999.
15. G. Felici, C. Gentile, and G. Rinaldi. Solving large MIP models in supply chain management by branch & cut. Technical report, Istituto di Analisi dei Sistemi ed Informatica del CNR, Italy, 2000.
16. M. Fischetti, P. Toth, and D. Vigo. A branch and bound algorithm for the capacitated vehicle routing problem on directed graphs. Operations Research, 42: 846-859, 1994.
17. R. Fukasawa, H. Longo, J. Lysgaard, M. Poggi de Aragão, M. Reis, E. Uchoa, and R. F. Werneck. Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Mathematical Programming, 106: 491-511, 2006.
18. R. Fukasawa, M. Reis, M. Poggi de Aragão, and E. Uchoa. Robust branch-andcut-and-price for the capacitated vehicle routing problem. Technical Report RPEP Vol. 3 no. 8, Universidade Federal Fluminense, Engenharia de Produção, Niterói, Brazil, 2003.
19. M. T. Godinho, L. Gouveia, and T. Magnanti. Combined route capacity and path length models for unit demand vehicle routing problems. In Proceedings of the INOC, volume 1, pages 8-15, Lisbon, 2005.
20. B. Golden, A. Assad, L. Levy, and F. Gheysens. The fleet size and mix vehicle routing problem. Computers and Operations Research, 11: 49-66, 1984.
21. L. Hall and T. Magnanti. A polyhedral intersection theorem for capacitated spanning trees. Mathematics of Operations Research, 17, 1992.
22. D. Houck, J. Picard, M. Queyranne, and R. Vegamundi. The travelling salesman problem as a constrained shortest path problem. Opsearch, 17: 93-109, 1980.
23. S. Irnich and D. Villeneuve. The shortest path problem with resource constraints and k-cycle elimination for k ≥ 3. INFORMS Journal on Computing, 18: 391-406, 2006.
24. M. Jepsen, S. Spoorendonk, B. Petersen, and D. Pisinger. A non-robust branchand-cut-and-price for the vehicle routing problem with time windows. Technical Report 06/03, University of Copenhagen, 2006.
25. B. Kallehauge, N. Boland, and O. Madsen. Path inequalities for the vehicle routing problem with time windows. Technical report, Technical University of Denmark, 2005.
26. D. Kim, C. Barnhart, K. Ware, and G. Reinhardt. Multimodal express package delivery: A service network design application. Transportation Science, 33: 391-407, 1999.
27. N. Kohl, J. Desrosiers, O. Madsen, M. Solomon, and F. Soumis. 2-Path cuts for the vehicle routing problem with time windows. Transportation Science, 33: 101-116, 1999.
28. A. Letchford, R. Eglese, and J. Lysgaard. Multistars, partial multistars and the capacitated vehicle routing problem. Mathematical Programming, 94: 21-40, 2002.
29. A. Letchford, J. Lysgaard, and R. Eglese. A branch-and-cut algorithm for the capacitated open vehicle routing problem. Journal of the Operational Research Society, 2007.
30. A. Letchford and J-J. Salazar. Projection results for vehicle routing. Mathematical Programming, 105: 251-274, 2006.
31. J. Lysgaard. Reachability cuts for the vehicle routing problem with time windows. European Journal of Operational Research, 175: 210-233, 2006.
32. J. Lysgaard, A. Letchford, and R. Eglese. A new branch-and-cut algorithm for the capacitated vehicle routing problem. Mathematical Programming, 100: 423-445, 2004.
33. D. Naddef and G. Rinaldi. Branch-and-cut algorithms for the capacitated VRP. In P. Toth and D. Vigo, editors, The Vehicle Routing Problem, chapter 3, pages 53-84. SIAM, 2002.
34. J. Picard and M. Queyranne. The time-dependant traveling salesman problem and its application to the tardiness problem in one-machine scheduling. Operations Research, 26: 86-110, 1978.
35. M. Poggi de Aragão and E. Uchoa. Integer program reformulation for robust branch-and-cut-and-price. In L. Wolsey, editor, Annals of Mathematical Programming in Rio, pages 56-61, Búzios, Brazil, 2003.
36. E. Uchoa, R. Fukasawa, J. Lysgaard, A. Pessoa, M. Poggi de Aragão, and D. Andrade. Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Mathematical Programming, on-line first, 2007.
37. J. Van den Akker, C. Hurkens, and M. Savelsbergh. Time-indexed formulation for machine scheduling problems: column generation. INFORMS J. on Computing, 12: 111-124, 2000.
38. F. Vanderbeck. Lot-sizing with start-up times. Management Science, 44: 1409-1425, 1998.
39. H. Yaman. Formulations and valid inequalities for the heterogeneous vehicle routing problem. Mathematical Programming, 106: 365-390, 2006.