Two improved formulations for the minimum latency problem

Applied Mathematical Modelling

Volumn 37, Issue 4, 2013, Pages 2257-2266

  Angel Bello, Francisco ^a   Alvarez, Ada ^b   García, Irma ^c  

^a SCHOOL OF ENGINEERING AND SCIENCES   (Mexico)

^b UNIVERSIDAD AUTÓNOMA DE NUEVO LEÓN   (Mexico)

^c UNIVERSIDAD AUTÓNOMA DE COAHUILA   (Mexico)

Author keywords

Computational evaluation; Deliveryman problem; Directed minimum latency problem; Integer formulations; Repairman problem

Indexed keywords

COMPUTATIONAL EVALUATION; DELIVERYMAN PROBLEM; INTEGER FORMULATIONS; LATENCY PROBLEM; REPAIRMAN PROBLEM;

COMPUTER SIMULATION; MATHEMATICAL MODELS;

TRAVELING SALESMAN PROBLEM;

EID: 84870249964     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2012.05.026     Document Type: Article

References (23)

1. Conway R., Maxwell W., Miller L. Theory of Scheduling 1967, Addison-Wesley.
2. Rinnooy Kan A. Machine Scheduling Problems 1976, Martinus Nijhoff, The Hague.
3. Picard J., Queyranne M. The time-dependent traveling salesman problem and its application to the tardiness problem in one-machine scheduling. Oper. Res. 1978, 26(1):86-110.
4. A. Blum, P. Chalasani, D. Coppersmith, B. Pulleyblank, P. Raghavan, M. Sudan, The minimum latency problem, in: Proceedings of the 26th ACM Symposium on Theory of Computing (STOC), 1994, pp. 163-171.
5. Simchi-Levi D., Berman O. Minimizing the total flow time of n jobs on a network. IIE Trans. 1991, 23(3):236-244.
6. G. Ausiello, S. Leonardi, A. Marchetti-Spaccamela, On salesmen, repairmen, spiders and other traveling agents, in: Proceedings of the Italian Conference on Algorithms and Complexity, 2000, pp. 1-16.
7. Sahni S., Gonzalez T. P-complete approximation problems. J. Assoc. Comput. Mach. 1976, 23:555-565.
8. R. Sitters, The minimum latency problem is NP-hard for weighted trees, in: Proceedings of the 9th Conference on Integer Programming and Combinatorial Optimization, 2002, pp. 230-239.
9. Goemans M., Kleinberg J. An improved approximation ratio for the minimum latency problem. Math. Program. 1998, 82:111-124.
10. A. Archer, D. P. Williamson, Faster approximation algorithms for the minimum latency problem, in: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, 2003, pp. 88-96.
11. Archer A., Levin A., Williamson D.P. A faster, better approximation algorithm for the minimum latency problem. SIAM J. Comput. 2008, 37:1472-1498.
12. S. Arora, G. Karakostas, Approximation schemes for minimum latency problem, in: Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, Atlanta, 1993, pp. 688-693.
13. B. Chaudhuri, S. Godfrey, S. Rao, K. Talwar, Paths, trees, and minimum latency tours, in: Proceedings of the 44th IEEE Symposium on Foundations of Computer Science (FOCS), 2003.
14. V. Nagarajan, R. Ravi, The directed minimum latency problem, in: A. Goel et al. (Eds.), APPROX and RANDOM 2008, LNCS, vol. 5171, Springer-Verlag, 2008, pp. 193-206.
15. Z. Friggstad, M. Salavatipour, Z. Svitkina, Asymmetric traveling salesman path and directed latency problems. In Proceedings of the 21st ACM-SIAM Symposium on Discrete Algorithms, 2010, pp. 419-428.
16. Lucena A. Time-dependent traveling salesman problem-the deliveryman case. Networks 1990, 20:753-763.
17. Fischetti M., Laporte G., Martello S. The delivery man problem and cumulative matroids. Oper. Res. 1993, 41(6):1055-1064.
18. Wu BY., Huang Z.-N., Zhan F.-J. Exact algorithms for the minimum latency problem. Inform. Process. Lett. 2004, 92(6):303-309.
19. Méndez-Díaz I., Zabala P., Lucena A. A new formulation for the traveling deliveryman problem. Discrete Appl. Math. 2008, 156:3223-3237.
20. C. Eijl, A polyhedral approach to the delivery man problem, Memorandum COSOR 95-19, Eindhoven University of Technology, 1995.
21. J. Sarubbi, H. Luna, G. Miranda, Minimum latency problem as a shortest path problem with side constraints, in: Book of Extended Abstracts of the XIV Latin Ibero-American Congress on Operations Research (CLAIO 2008), 2008.
22. Gouveia L., Voss A. A classification of formulations for the (time-dependent) travelling salesman problem. Eur. J. Oper. Res. 1995, 83:69-82.
23. Desrochers M., Laporte G. Improvements and extensions to the Miller-Tucker-Zemlin sub-tour elimination constraints. Oper. Res. Lett. 1991, 10:27-36.