The profitable arc tour problem: Solution with a branch-and-price algorithm

Transportation Science

Volumn 39, Issue 4, 2005, Pages 539-552

  Feillet, Dominique ^a   Dejax, Pierre ^b   Gendreau, Michel ^c  

^a UNIVERSITY OF AVIGNON   (France)

^b ECOLE DES MINES DE NANTES   (France)

^c UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Arc routing problem; Bounded cycle cover; Branch and price; Column generation; Routing problem with profits

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; GRAPH THEORY; INTEGER PROGRAMMING; OPTIMIZATION; SCHEDULING; VEHICLES;

ARC-ROUTING PROBLEM; BOUNDED CYCLE COVER; BRANCH AND PRICE; COLUMN GENERATION; ROUTING PROBLEM WITH PROFITS;

PROBLEM SOLVING;

EID: 28244467964     PISSN: 00411655     EISSN: 15265447     Source Type: Journal    
DOI: 10.1287/trsc.1040.0106     Document Type: Article

References (35)

1. Ahuja, R. K., T. L. Magnanti, J. B. Orlin. 1993. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Englewood Cliffs, NJ.
2. Balas, E. 1989. The prize collecting traveling salesman problem. Networks 19(6) 621-636.
3. Barnhart, C., C. A. Hane, P. H. Vance. 2000. Using branch-and-price-and- cut to solve origin-destination integer multicommodity flow problems. Oper. Res. 48(2) 318-326.
4. Barnhart, C., E. L. Johnson, G. L. Nemhauser, M. W. P. Savelsbergh, P. H. Vance. 1998. Branch-and-price: Column generation for solving huge integer programs. Oper. Res. 46(3) 316-329.
5. Belling-Seib, K., P. Mevert, C. Muller. 1988. Network flow problems with one side constraint: A comparison of three solution methods. Comput. Oper. Res. 15(4) 381-394.
6. Boland, N. L., L. W. Clarke, G. L. Nemhauser. 2000. Asymmetric traveling salesman problem with replenishment arcs. Eur. J. Oper. Res. 123(2) 408-427.
7. Butt, S. E., D. M. Ryan. 1999. An optimal solution procedure for the multiple tour maximum collection problem using column generation. Comput. Oper. Res. 26(4) 427-441.
8. Cohen, E., N. Megiddo. 1994. Algorithms and complexity analysis for some flow problems. Algorithmica 11 320-340.
9. Deitch, R., S. P. Ladany. 2000. The one-period bus routing problem: Solved by an effective heuristic for the orienteering tour problem and improvement algorithm. Eur. J. Oper. Res. 127(1) 69-77.
10. Desaulniers, G., J. Desrosiers, I. Ioachim, M. M. Solomon, F. Soumis, D. Villeneuve. 1998a. A unified framework for deterministic time constrained vehicle routing and crew scheduling problems. C. T. Laporte, G. Laporte, eds. Fleet Management and Logistics. Kluwer Academic Publishers, Norwell, MA, 57-93.
11. Desaulniers, G., J. Lavigne, F. Soumis. 1998b. Multi-depot vehicle scheduling problems with time windows and waiting costs. Eur. J. Oper. Res. 111(3) 479-494.
12. Desrochers, M., J. Desrosiers, M. M. Solomon. 1992. A new optimization algorithm for the vehicle routing problem with time windows. Oper. Res. 40(2) 342-354.
13. Desrosiers, J., Y. Dumas, M. M. Solomon, F. Soumis. 1995. Time constrained routing and scheduling. M. Ball, T. Magnanti, C. Monma, G. Nemhauser, eds. Handbooks in OR and MS, Vol. 8. Elsevier Science Publishers B.V., Amsterdam, North-Holland.
14. Eiselt, H. A., M. Gendreau, G. Laporte. 1995. Arc routing problems. Part II: The rural postman problem. Oper. Res. 43(3) 399-414.
15. EURODECISION. 1998. LPToolKit, User's Guide and Technical Reference, 3rd ed. Eurodécision, Versailles, France.
16. Feillet, D. 2001. Problèmes de tournées avec gains: Ètude et application au transport inter-usines. Doctoral dissertation, Laboratoire Productique Logistique, École Centrale Paris.
17. Feillet, D., P. Dejax, M. Gendreau. 2002. Planification tactique de transport de marchandises interusine. J. Européen des Systèmes Automatisés 36(1) 149-168.
18. Feillet, D., P. Dejax, M. Gendreau. 2004a. Traveling salesman problems with profits. Transportation Sci. 39(4) 540-553.
19. Feillet, D., P. Dejax, M. Gendreau, C. Gueguen. 2004b. An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems. Networks. 44(3) 216-229.
20. Fischetti, M., P. Toth. 1988. An additive approach for the optimal solution of the prize-collecting travelling salesman problem. B. Golden, A. Assad, eds. Vehicle. Routing: Methods and Studies. Elsevier Science Publishers B.V., Amsterdam, North-Holland, 319-343.
21. Ford, L. R., D. R. Fulkerson. 1956. Maximum flow through a network. Canadian J. Math. 8 399-404.
22. Fortz, B., M. Labbé, F. Maffioli. 2000. Solving the two-connected network with bounded meshes problem. Oper. Res. 48(6) 866-877.
23. Garey, M. R., D. S. Johnson. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness, Vol. 50. Freeman, San Francisco, CA.
24. Gueguen, C. 1999. Méthodes de résolution exacte pour les problèmes de tournées de véhicules. Doctoral dissertation, Laboratoire Productique Logistique, École Centrale Paris.
25. Hochbaum, D. S., E. V. Olinick. 2001. The bounded cycle cover problem. INFORMS J. Comput. 13(2) 104-119.
26. ILOG. 1998. ILOG, Using the CPLEX Callable Library, 6th ed. ILOG Inc., CPLEX Division, Incline Village.
27. Kennington, J. L., V. S. S. Nair, M. H. Rahman. 1999. Optimizationbased algorithms for finding minimal cost ring covers in survivable networks. Comput. Optim. Appl, 14 219-230.
28. Labbé, M., G. Laporte, P. Soriano. 1998. Covering a graph with cycles. Comput. Oper. Res. 25(6) 499-504.
29. Laporte, G. 1997. Modeling and solving several classes of arc routing problems as traveling salesman problems. Comput. Oper. Res. 24(11) 1057-1061.
30. Mathies, S., P. Mevert. 1998. A hybrid algorithm for solving network flow problems with side constraints. Comput. Oper. Res. 25(9) 745-756.
31. Patterson, R., E. Rolland. 2003. The cardinality constrained covering traveling salesman problem. Comput. Oper. Res. 30 97-116.
32. Savelsbergh, M., M. Sol. 1998. Drive: Dynamic routing of independent vehicles. Oper. Res. 46(4) 474-490.
33. Thomassen, C. 1997. On the complexity of finding a minimum cycle cover of a graph. SIAM. J. Comput. 26(3) 675-677.
34. Vanderbeck, F. 2000. On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Oper. Res. 48(1) 111-128.
35. Yan, S. 1996. Approximating reduced costs under degeneracy in a network flow problem with side constraints. Networks 27(4) 267-278.