The continuous assignment problem and its application to preemptive and non-preemptive scheduling with irregular cost functions

INFORMS Journal on Computing

Volumn 16, Issue 2, 2004, Pages 198-208

  Sourd, Francis ^a  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

Branch and bound; Continuous linear programming; Earliness and tardiness; Production scheduling

Indexed keywords

ALGORITHMS; INTEGRATION; JUST IN TIME PRODUCTION; LINEAR PROGRAMMING; POLYNOMIALS; SCHEDULING; SET THEORY;

BRANCH AND BOUND; CONTINOUS LINEAR PROGRAMMING; EARLINES AND TARDINESS; PRODUCTION-SCHEDULING;

PROBLEM SOLVING;

EID: 3843078491     PISSN: 10919856     EISSN: 15265528     Source Type: Journal    
DOI: 10.1287/ijoc.1030.0034     Document Type: Article

References (25)

1. Ahuja R. K., T. L. Magnanti, J. B. Orlin. 1993. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Upper Saddle River, NJ.
2. Aurenhammer F. 1987. Power diagrams: properties, algorithms, and applications. SIAM J. Comput. 16 78-96.
3. Aurenhammer F., F. Hoffmann, B. Aronov. 1998. Minkowski-type theorems and least-squares clustering. Algorithmica 20 61-76.
4. Avram F., D. Bertsimas, M. Ricard. 1995 Fluid models of sequencing problems in open queueing networks: An optimal control approach. F. Kelly, R. Williams, eds. Stochastic Networks, Vol. 71. The IMA Volumes in Mathematics and Its Applications. Springer-Verlag, New York, 199-234.
5. Bellman. R. 1953. Bottleneck problem and dynamic programming. Proc. National Acad. Sci. USA 39 947-951.
6. Bellman R. 1957. Dynamic Programming. Princeton University Press, Princeton, NJ.
7. Bertsimas D., D. Gamarnik. 1999. Asymptotically optimal algorithms for job shop scheduling and packet routing. J. Algorithms 33 296-318.
8. Bertsimas D., J. Sethuraman. 2002. From fluid relaxations to practical algorithms for job shop scheduling: The makespan objective. Math. Programming, Ser. A 92 61-102.
9. Boissonnat J. D., M. Yvinec. 2001. Algorithmic Geometry. Cambridge University Press, Cambridge, U.K.
10. Garey M. R., R. E. Tarjan, G. T. Wilfong. 1988. One-processor scheduling with symmetric earliness and tardiness penalties. Math. Oper. Res. 13 330-348.
11. Grünbaum B. 1967. Convex Polytopes. Interscience, New York.
12. Hoogeveen J. A., S. L. van de Velde. 1996. A branch-and-bound algorithm for single-machine earliness-tardiness scheduling with idle time. INFORMS J. Comput. 6 402-412.
13. Khachian L. G. 1979. A polynomial algorithm in linear programming. Soviet Math. Doklady 20 191-194.
14. Lenstra J. K., A. H. G. Rinnooy Kan, P. Brucker. 1977. Complexity of machine scheduling problems. Ann. Discrete Math. 1 343-362.
15. Luo X., D. Bertsimas. 1998. A new algorithm for state-constrained separated continuous linear programs. SIAM J. Control Optim. 37 177-210.
16. Marcus M., H. Ming. 1964. A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon, Inc., Boston, MA.
17. Minoux M. 1986. Mathematical Programming: Theory and Algorithms. Wiley & Sons, New York.
18. Philpott A. B., M. Craddock. 1995. An adaptative discretization algorithm for a class of continuous network programs. Networks 26 1-11.
19. Pullan M. C. 1996. A duality theory for separated continuous linear programs. SIAM J. Control Optim. 34 931-965.
20. Schramm R. 1980. On piecewise linear functions and piecewise linear equations. Math. Oper. Res. 5 510-522.
21. Shor N. Z. 1975. Convergence of a gradient method with space dilatation in the direction of the difference between two successive gradients. Kibernetika 11 48-53.
22. Shor N. Z. 1977. Cut-off methods with space extension in convex programming problems. Cybernetics 13 94-96.
23. Sourd F., S. Kedad-Sidhoum. 2003. The one machine problem with earliness and tardiness penalties. J. Scheduling 6. Forthcoming.
24. Vavasis S. A. 1998. Convex optimization. M. J. Atallah, ed. Algorithms and Theory of Computation Handbook, Chap. 33. CRC Press, Boca Raton, FL.
25. Weiss G. 2002. A simplex based algorithm to solve separated continuous linear programs. Math. Programming. Forthcoming.