A polyhedral study of the asymmetric traveling salesman problem with time windows

Networks

Volumn 36, Issue 2, 2000, Pages 69-79

  Ascheuer, Norbert ^a   Fischetti, Matteo ^c   Grötschel, Martin ^b  

^a Intranetz GmbH   (Germany)

^b ZUSE INSTITUTE BERLIN   (Germany)

^c UNIVERSITY OF PADOVA   (Italy)

Author keywords

Asymmetric traveling salesman problem; Polyhedral theory; Time windows; Valid inequalities

Indexed keywords

EID: 0034259805     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/1097-0037(200009)36:2<69::AID-NET1>3.0.CO;2-Q     Document Type: Article

References (36)

1. [1] A. Abdel-Hamid, N. Ascheuer, and M. Grötschel, Order picking in an automatic warehouse: Solving on-line asymmetric TSP's, Math Methods Oper Res 49 (1999), 501-515.
2. [2] D. Applegate and W. Cook, A computational study of the job-shop scheduling problem, ORSA J Comput 3 (1991), 149-156.
3. [3] N. Ascheuer, Hamiltonian path problems in the online optimization of flexible manufacturing systems, PhD Thesis, Technische Universität Berlin, Germany, 1995. Available as Technical Report TR 96-03, Konrad-Zuse-Zentrum für Informationstechnik Berlin, at URL: http://www.zib.de/ZIBbib/Publications/.
4. [4] N. Ascheuer, L. Escudero, M. Grötschel, and M. Stoer, A cutting plane approach to the sequential ordering problem (with applications to job scheduling in manufacturing), SIAM J Optim 3 (1993), 25-42.
5. [5] N. Ascheuer, M. Fischetti, and M. Grötschel, Solving ATSP with time windows by branch-and-cut, Technical Report SC-99-31, ZIB Berlin, 1999.
6. [6] N. Ascheuer, M. Jünger, and G. Reinelt, A branch & cut algorithm for the asymmetric traveling salesman problem with precedence constraints. Preprint SC 97-70, Konrad-Zuse-Zentrum Berlin, 1997 (to appear in Comput Optim Appl).
7. [7] E.K. Baker, An exact algorithm for the time-constrained traveling salesman problem, Oper Res 31 (1983), 938-945.
8. [8] E. Balas, On the facial structure of scheduling polyhedra, Math Program study, 24 (1985), 179-218.
9. [9] E. Balas, The asymmetric assignment problem and some new facets of the travelling salesman polytope on a directed graph, SIAM J Discr Math 3 (1989), 425-451.
10. [10] E. Balas and M. Fischetti, The fixed-outdegree 1-arborescence polytope, Math Oper Res 17 (1992), 1001-1018.
11. [11] E. Balas and M. Fischetti, A lifting procedure for the asymmetric traveling salesman polytope and a large new class of facets, Math Program 58 (1993), 325-352.
12. [12] E. Balas, M. Fischetti, and W. Pulleyblank, The precedence-constrained asymmetric traveling salesman polytope, Math Program 68 (1995), 241-265.
13. [13] M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser (Editors), Network routing, Vol. 8, Handbooks in operations research and management science, Elsevier Amsterdam, 1995.
14. [14] S. Bogatsch, Ein Branch & Cut-Algorithmus für das asymmetrische Travelling Salesman Problem mit Zeitfenstern - ein Vergleich verschiedener Modellierungen, Master's Thesis, Technical University of Berlin, 1996.
15. [15] S. Chopra and G. Rinaldi, The graphical asymmetric travelling salesman polyhedron: Symmetric inequalities, SIAM J Discr Math 9 (1996), 602-624.
16. [16] T. Christof, PORTA - A polyhedron representation transformation algorithm, version 1.2.1, Code written by T. Christof (University of Heidelberg), revised by A. Löbel and M. Stoer, available from the ZIB electronic library ELIB by anonymous ftp from elib.zib.de, in the directory /pub/mathprog/polyth, 1994.
17. [17] N. Christofides, A. Mingozzi, and P. Toth, State-space relaxation procedures for the computation of bounds to routing problems, Networks 11 (1981), 145-164.
18. [18] M. Desrochers and G. Laporte, Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints, Oper Res Lett 10 (1991), 27-36.
19. [19] M. Desrochers, J.K. Lenstra, M.W.P. Savelsbergh, and F. Soumis, "Vehicle routing with time windows: Optimization and approximation," Vehicle routing: Methods and studies, B.L. Golden and A.A. Assad (Editors), North-Holland, 1988, pp. 65-84.
20. [20] J. Desrosiers, Y. Dumas, M. M. Solomon, and F. Soumis, "Time constrained routing and scheduling," Network routing, M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser (Editors), Vol. 8, Handbooks in operations research and management science, Elsevier, Amsterdam, 1995, Chapter 2, pp. 35-139.
21. [21] Y. Dumas, J. Desrosiers, E. Gelinas, and M.M. Solomon, An optimal algorithm for the traveling salesman problem with time windows, Oper Res 43 (1995), 367-371.
22. [22] M. Fischetti, Facets of the asymmetric traveling salesman polytope, Math Oper Res 16 (1991), 42-56.
23. [23] M. Fischetti, "Three facet-lifting theorems for the asymmetric traveling salesman polytope," Integer programming and combinatorial optimization, E. Balas, G. Cornuéjols, and R. Kannan (Editors), Carnegie Mellon University, Pittsburgh, PA, 1992, pp. 260-273.
24. [24] M. Fischetti, Clique tree inequalities define facets of the asymmetric traveling salesman polytope, Discr Appl Math 56 (1995), 9-18.
25. [25] M. Fischetti and P. Toth, A polyhedral approach to the asymmetric traveling salesman problem, Mgmt Sci 43 (1997), 1520-1536.
26. [26] M.R. Garey and D.S. Johnson, Two-processor scheduling with start-times and deadlines, SIAM J Comput 6 (1977), 416-426.
27. [27] M. Grötschel, Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme, Hain, Meisenheim am Glan, 1977.
28. [28] M. Grötschel and M. Padberg, "Polyhedral theory," The traveling salesman problem, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys (Editors), Wiley, New York, 1985.
29. [29] F. Maffioli and A. Sciomachen, A mixed-integer model for solving ordering problems with side constraints. Technical Report Research Report, University of Genoa, Italy, 1993.
30. [30] G.L. Nemhauser and M.W.P. Savelsbergh, "A cutting plane algorithm for the single machine scheduling problem with release dates," Combinatorial optimization: New frontiers in the theory and practice, M. Akguk, H. Hamacher, and S. Tufecki (Editors), NATO ASI Series F: Computer and Systems Sciences 82, Springer-Verlag, 1992, pp. 63-84.
31. [31] M. Queyranne and A. Schulz, Polyhedral approaches to machine scheduling, Technical Report 408/1994, Technical University of Berlin, 1994 (to appear in Math Program).
32. [32] M. Queyranne and Y. Wang, Symmetric inequalities and their composition for asymmetric travelling salesman polytopes, Math Oper Res 20 (1995), 838-863.
33. [33] M.W.P. Savelsbergh, Local search for routing problems with time windows, Ann Oper Res 4 (1985), 285-305.
34. [34] M.W.P. Savelsbergh, The vehicle routing problem with time windows: Minimizing route duration, ORSA J Comput 4 (1992), 146-154.
35. [35] J. Tsitsiklis, Special cases of traveling salesman and repairman problems with time windows, Networks 22 (1992), 263-282.
36. [36] C.A. van Eijl, A polyhedral approach to the delivery man problem, Technical Report 95-19, Department of Mathematics and Computer Science, Eindhoven University of Technology, 1995.