The traveling salesman problem with pickup and delivery: Polyhedral results and a branch-and-cut algorithm

Mathematical Programming

Volumn 121, Issue 2, 2010, Pages 269-305

  Dumitrescu, Irina ^a   Ropke, Stefan ^b   Cordeau, Jean Francois ^b   Laporte, Gilbert ^b  

^a UNIVERSITY OF SYDNEY   (Australia)

^b HEC MONTRÉAL   (Canada)

Author keywords

Branch and cut algorithm; Pickup and delivery; Polyhedral results; Precedence relationships; Separation procedures; Traveling salesman problem; Valid inequalities

Indexed keywords

COMBINATORIAL OPTIMIZATION; INTEGER PROGRAMMING;

BRANCH-AND-CUT ALGORITHMS; PICKUP AND DELIVERY; POLYHEDRAL RESULTS; PRECEDENCE RELATIONSHIPS; VALID INEQUALITY;

TRAVELING SALESMAN PROBLEM;

EID: 73849117170     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-008-0234-9     Document Type: Article

References (23)

1. Ascheuer, N., Jünger, M., Reinelt, G.: A branch&cut algorithm for the asymmetric traveling salesman problem with precedence constraints. Comput. Optim. Appl. 17, 61-84 (2000)
2. Balas, E., Fischetti, M., Pulleyblank,W.R.: The precedence-constrained asymmetric traveling salesman polytope. Math. Program. 68, 241-265 (1995)
3. Christof, T., Löbel, A.: Porta -a polyhedron representation and transformation algorithm. http://www. iwr.uni-heidelberg.de/groups/comopt/ software/PORTA/index.html. ZIB, Konrad-Zuse-Zentrum für Informationstechnik Berlin.
4. Cordeau, J.-F.: A branch-and-cut algorithm for the dial-a-ride problem. Oper. Res. 54, 573-586 (2006)
5. Cordeau, J.-F., Laporte, G., Ropke, S.: Recent models and algorithms for one-to-one pickup and delivery problems. In: Golden, B.L., Raghavan, S., Wasil, E.A. (eds.) The Vehicle Routing Problem, Latest Advances and Challenges. Springer, Boston (2008) (forthcoming)
6. Dumitrescu, I.: Polyhedral results for the pickup and delivery travelling salesman problem. Technical Report CIRRELT-2008-07, Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (2008). http://www.crt.umontreal.ca/~irina/CRTdumitrescu.pdf.
7. Fiala Timlin, M.T., Pulleyblank, W.R.: Precedence constrained routing and helicopter scheduling: Heuristic design. Interfaces 22(3), 100-111 (1992)
8. Gendreau, M., Hertz, A., Laporte, G.: The traveling salesman problem with backhauls. Comp. Oper. Res. 23, 501-508 (1996)
9. Healy, P., Moll, R.: A new extension of local search applied to the dial-a-ride problem. Eur. J. Oper. Res. 83, 83-104 (1995)
10. Hernández-Pérez, H., Salazar-González, J.-J.: A branch-and-cut algorithm for a traveling salesman problem with pickup and delivery. Discrete Appl. Math. 145, 126-139 (2004)
11. Irnich, S., Desaulniers, G. : Shortest path problems with resource constraints. In: Desaulniers, G., Desrosiers, J., Solomon, M.M. (eds.) Column Generation, pp. 33-65. Springer, Boston (2005)
12. Kalantari, B., Hill, A.V., Arora, S.R.: An algorithm for the traveling salesman problem with pickup and delivery customers. Eur. J. Oper. Res. 22, 377-386 (1985)
13. Lu, Q., Dessouky, M.: An exact algorithm for themultiple vehicle pickup and delivery problem. Transportation Sci. 38, 503-514 (2004)
14. Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, Chichester (1988)
15. Reinelt, G.: TSPLIB -a traveling salesman problem library. ORSA J. Comput. 3, 376-384 (1991)
16. Renaud, J., Boctor, F.F., Laporte, G.: Pertubation heuristics for the pickup and delivery traveling salesman problem. Comp. Oper. Res. 29, 1129-1141 (2002)
17. Renaud, J., Boctor, F.F., Ouenniche, J.: A heuristic for the pickup and delivery traveling salesman problem. Comp. Oper. Res. 27, 905-916 (2000)
18. Ropke, S., Cordeau, J.-F., Laporte, G.: Models and branch-and-cut algorithms for pickup and delivery problems with time windows. Networks 49, 258-272 (2007)
19. Ropke, S., Pisinger, D.: An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Sci. 40, 455-472 (2006)
20. Ruland, K.S.: Polyhedral Solution to the Pickup and Delivery Problem. PhD thesis, Sever Institute of Washington University (1994)
21. Ruland, K.S., Rodin, E.Y.: The pickup and delivery problem: Faces and branch-and-cut algorithm. Comp. Math. Appl. 33, 1-13 (1997)
22. Savelsbergh, M.W.P.: An efficient implementation of local search algorithms for constrained routing problems. Euro. J. Oper. Res. 47, 75-85 (1990)
23. Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: CP-98 (Fourth International Conference on Principles and Practice of Constraint Programming), pp. 417-431. Lecture Notes in Computer Science, vol. 1520. Springer, Berlin (1998)