Pre-emptive scheduling problems with controllable processing times

Journal of Scheduling

Volumn 8, Issue 3, 2005, Pages 233-253

  Shakhlevich, Natalia V ^a   Strusevich, Vitaly A ^b  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITY OF GREENWICH   (United Kingdom)

Author keywords

Bicriteria problems; Controllable processing times; Greedy algorithms; Parallel machine scheduling; Polymatroids; Single machine scheduling

Indexed keywords

ALGORITHMS; FUNCTIONS; MATHEMATICAL MODELS; PROBLEM SOLVING;

BICRITERIA PROBLEMS; CONTROLLABLE PROCESSING TIMES; PARALLEL MACHINE SCHEDULING; POLYMATROIDS; SINGLE MACHINE SCHEDULING;

SCHEDULING;

EID: 24144441172     PISSN: 10946136     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10951-005-6813-1     Document Type: Conference Paper

References (32)

1. Aho, A. V., J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, London, 1974.
2. Balas, E. and E. Zemel, "An algorithm for large zero-one knapsack problems," Oper. Res., 28, 1130-1154 (1980).
3. Brucker, P., Scheduling Algorithms, Springer, Berlin, 2001.
4. Chase, R. B., N. J. Acquilano, and F. R. Jacobs, Production and Operations Management: Manufacturing and Services, Irwin McGraw-Hill, 1998.
5. Cheng, T. C. E. and A. Janiak, "Resource optimal control in some single machine scheduling problems," IEEE Trans. Automat. Control, 39, 1243-1246 (1994).
6. Cheng, T. C. E., A. Janiak, and M. Kovalyov, "Bicriterion single machine scheduling with resource dependent processing times," SIAM J. Optim., 8, 617-630 (1998).
7. Cheng, T. C. E., A. Janiak, and M. Kovalyov, "Single machine batch scheduling with resource dependent setup and processing times," Eur. J. Oper. Res., 135, 177-183 (2001).
8. Edmonds, J., "Submodular functions, matroids, and certain polyhedra," in: R. Guy, H. Hanani, N. Sauer, and J. Schonheim (eds.), Combinatorial Structures and their Applications, Gordon and Breach, New York, 1970.
9. Frank, A. and E. Tardos, "Generalized polymatroids and submodular flows," Math. Program., 42, 489-563 (1988).
10. Gordon, V. S. and V. S. Tanaev, "Due dates in single-stage deterministic scheduling," in Optimization of Systems of Collecting, Transfer and Processing of Analogous and Discrete Data in Local Information Computing Systems, Institute of Engineering Cybernetics, Minsk, Belarus, 1973, pp. 54-58 (in Russian).
11. Hoogeveen H. and G. J. Woeginger, "Some comments on sequencing with controllable processing times," Computing, 68, 181-192 (2002).
12. Horn, W A., "Some simple scheduling algorithms," Naval Res. Logist. Quart., 21, 177-185 (1974).
13. Janiak, A, "Minimization of the makespan in two-machine problem under given resource constraints," Eur. J. Oper. Res., 107, 325-337 (1998).
14. Janiak, A. and M. Y. Kovalyov, "Single machine scheduling subject to deadlines and resource dependent processing times," Eur. J. Oper. Res., 94, 284-291 (1996).
15. Janiak, A., M. Y. Kovalyov, W. Kubiak, and F. Werner, "Positive half-products and scheduling with controllable processing times," Eur. J. Oper. Res., 165, 416-422 (2005).
16. Lawler, E. L., J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys, "Sequencing and scheduling: Algorithms and complexity," in S. C. Graves, A. H. G. Rinnooy Kan and P. H. Zipkin (eds.), Handbooks in Operations Research and Management Science, Vol. 4, Logistics of Production and Inventory, North-Holland, Amsterdam, 1993, pp. 445-522.
17. Lenstra, J. K., A. H. G. Rinnooy Kan, and P. Brucker, "Complexity of machine scheduling problems," Ann. Discrete Math., 1, 343-362 (1977).
18. Leung, J. Y.-T., V. K. M. Yu, and W.-D. Wei, "Minimizing the weighted number of tardy task units," Discrete Appl. Math., 51, 307-316 (1994).
19. McNaughton, R., "Scheduling with deadlines and loss functions," Manage. Sci., 59, 1-12 (1959).
20. Nemhauser, G. L. and L. A. Wolsey, Integer and Combinatorial Optimization, John Wiley & Sons, 1988.
21. Nowicki, E. and S. Zdrzalka, "Scheduling jobs with controllable processing times as an optimal-control problem," Int. J. Contr., 39, 839-848 (1984).
22. Nowiki, E., and S. Zdrzalka, "A survey of results for sequencing problems with controllable processing times," Discrete Appl. Math., 26, 271-287 (1990).
23. Nowicki, E. and S. Zdrzalka, "A bicriterion approach to pre-emptive scheduling of parallel machines with controllable job processing times," Discrete Appl. Math., 63, 271-287 (1995).
24. Schrijver, A., Combinatorial Optimization: Polyhedra and Efficiency, Springer, Berlin, 2003.
25. Shih W.-K., J. W. S. Liu, and J.-Y. Chung, "Fast algorithms for scheduling imprecise computations," in Proceedings of the 10th Real-time Systems Symposium, Santa-Monica, 1989, pp. 12-19.
26. Shih W.-K., J. W. S. Liu, and J.-Y. Chung, "Algorithms for scheduling imprecise computations with timing constraints," SIAM J. Comput., 20, 537-552 (1991).
27. Tanaev, V. S., V. S. Gordon and Y. M. Shafransky, Scheduling Theory. Single-Stage Systems, Kluwer Academic Publishers, Dordrecht, 1994.
28. T'kindt V., and J.-C. Billaut, Multicriteria Scheduling: Theory, Models and Algorithms, Springer, Berlin, 2002.
29. Van Wassenhove, L. N., and K. R. Baker, "A bicriterion approach to time/cost tradeoffs in sequencing," Eur. J. Oper. Res., 11, 48-54 (1982).
30. Vickson, R. G. "Choosing the job sequence and processing times to minimize total processing plus flow cost on a single machine," Oper. Res., 28, 1155-1167 (1980).
31. Waller, D. L., Operations Management: A Supply Chain Approach, International Thomson Publishing, London, 1999.
32. Wan, G., B. P. C. Yen, and C. L. Li, "Single machine scheduling to minimize total compression plus weighted flow cost is NP-hard," Information Processing Letters, 79, 273-280 (2001).