On minimizing average weighted completion time: A PTAS for the job shop problem with release dates

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2906, Issue , 2003, Pages 319-328

  Fishkin, Aleksei V ^a   Jansen, Klaus ^a   Mastrolilli, Monaldo ^b  

^a UNIVERSITY OF KIEL   (Germany)

^b DALLE MOLLE INSTITUTE FOR ARTIFICIAL INTELLIGENCE IDSIA   (Switzerland)

Author keywords

Approximation; Job shop; PTAS; Scheduling

Indexed keywords

OPTIMIZATION; POLYNOMIAL APPROXIMATION; SCHEDULING;

APPROXIMATION; JOB SHOP; JOB SHOP PROBLEM; JOB SHOP SCHEDULING PROBLEMS; NON-PREEMPTIVE; POLYNOMIAL TIME APPROXIMATION SCHEMES; PTAS; WEIGHTED COMPLETION TIME;

JOB SHOP SCHEDULING;

EID: 35248816899     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24587-2_34     Document Type: Article

References (29)

1. F. Afrati, E. Bampis, C. Chekuri, D. Karger, C. Kenyon, S. Khanna, I. Millis, M. Queyranne, M. Skutella, C. Stein, and M. Sviridenko. Approximation schemes for minimizing average weighted completion time with release dates. In Proceedings 40th IEEE Symposium on Foundations of Computer Science, pages 32-43, 1999.
2. F. Afrati, E. Bampis, A. V. Fishkin, K. Jansen, and C. Kenyon. Scheduling to minimize the average completion time of dedicated tasks. In Proceedings 20th Conference on Foundations of Software Technology and Theoretical Computer Science, LNCS 1974, Springer Verlag, pages 454-464, 2000.
3. F. Afrati and I. Milis. Designing PTASs for MIN-SUM scheduling problems. In Proceedings 13th International Symposium on Fundamentals of Computation Theory, LNCS 2138, pages 432-444. Springer Verlag, 2001.
4. S. Chakrabarti, C. A. Phillips, A. S. Schulz, D. B. Shmoys, C. Stein, and J. Wein. Improved scheduling algorithms for minsum criteria. In Proceedings 23rd International Colloquium on Automata, Languages and Programming, LNCS 1099, pages 646-657. Springer Verlag, 1996.
5. C. Chekuri. Approximation algorithms for scheduling problems. PhD thesis, Department of Computer Science, Stanford University, 1998.
6. C. Chekuri and S. Khanna. A PTAS for minimizing weighted completion time on uniformly related machines. In Proceedings 28th International Colloquium on Automata, Languages and Programming, LNCS 2076, pages 848-861. Springer Verlag, 2001.
7. C. Chekuri, R. Motwani, B. Natarajan, and C. Stein. Approximation techniques for average completion time scheduling. In Proceedings of 8th Annual ACM-SIAM Symposium on discrete Algorithms, pages 609-618, 1997.
8. B. Chen, C. N. Potts, and G. J. Woeginger. Handbook of combinatorial optimization (D.-Z. Du and P. M. Paradalos eds.), chapter A review of machine scheduling: complexity, algorithms and approximability, pages 21-169. Kluwer, 1998.
9. A. V. Fishkin, K. Jansen, and M. Mastrolilli. Grouping techniques for scheduling problems: Simpler and faster. In Proceedings 9th Annual European Symposium, LNCS 2161, pages 206-217, Arhus, 2001. Springer Verlag.
10. A. V. Fishkin, K. Jansen, and L. Porkolab. On minimizing average weighted completion time of multiprocessor tasks with release dates. In Proceedings 28th International Colloquium on Automata, Languages and Programming, LNCS 2076, pages 875-886, Crete, 2001. Springer Verlag.
11. M. R. Garey and D. S. Johnson. Computers and intractability: A guide to the theory of NP-completeness. Freeman, San Francisco, CA, 1979.
12. M. R. Garey, D. S. Johnson, and R. Sethi. The complexity of flowshop and jobshop scheduling. Mathematics of Operation Research, 1:117-129, 1976.
13. L. A. Goldberg, M. Paterson, A. Srinivasan, and E. Sweedyk. Better approximation • guarantees for job-shop scheduling. In Proceedings 8th Symposium on Discrete Algorithms, pages 599-608, 1997.
14. T. Gonzales and S. Sahni. Flowshop and jobshop schedules: Complexity and approximation. Operations Research, 26:36-52, 1978.
15. R. L. Graham, E. L. Lawler, J. K. Lenstra, and A. H. G. Rinnooy Kan. Optimization and approximation in deterministic scheduling: A survey. Annals of Discrete Mathematics, 287-326, 1979.
16. L. A. Hall, A. S. Schulz, D. B. Shmoys, and J. Wein. Scheduling to minimize average time: Off-line and on-line algorithm. Mathematics of Operation Research, pages 513-544, 1997.
17. H. Hoogeveen, P. Schuurman, and G. Weoginger. Non-approximability results for scheduling problems with minsum criteria. In Proceedings 6th Conference on Integer Programming and Combinatorial Optimization, LNCS 1412, pages 353-366. Springer Verlag, 1998.
18. K. Jansen, R. Solis-Oba, and M. Sviridenko. Makespan minimization in job shops: A polynomial time approximation scheme. In Proceedings 31st Annual ACM Symposium on Theory of Computing, pages 394-399, Atlanta, 1999. To appear in SIAM Journal on Discrete Mathematics.
19. E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys. Logistics of Production and Inventory, volume 4 of Handbooks in Operation Research and Management Science, chapter Sequencing and scheduling: Algorithms and complexity, pages 445-522. North-Holland, Amsterdam, 1993.
20. M. Queyranne and M. Sviridenko. New and improved algorithms for minsum shop scheduling. In Proceedings 11th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 871-878, 2000.
21. A. S. Schulz. Poly topes and scheduling. PhD thesis, Technical University of Berlin, Germany, 1996.
22. P. Schuurman and G. J. Woeginger, Polynomial time approximation algorithms for machine scheduling: Ten open problems. Journal of Scheduling, 2: 203-213, 1999.
23. P. Schuurman and G. J. Woeginger. Polynomial time approximation algorithms for machine scheduling: Ten open problems. Journal of Scheduling, 2:203-213, 2000.
24. P. Schuurman and G. J. Woeginger. Approximation schemes - a tutorial. To appear in the book Lectures on Scheduling, edited by R. H. Moehring, C. N. Potts, A. S. Schulz, G. J. Woeginger and L. A. Wolsey., 2002.
25. D. B. Shmoys. Using linear programming in the design and analysis of approximation algorithms: Two illustrative examples. In Proceedings 1st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, LNCS 1444, pages 15-32. Springer Verlag, 1998.
26. D. B. Shmoys, C. Stein, and J. Wein. Improved approximation algorithms for shop scheduling problems. SIAM Journal of Computing, 23:617-632, 1994.
27. M. Skutella. Approximation and randomization in scheduling. PhD thesis, Technical University of Berlin, Germany, 1998.
28. W. E. Smith. Various optimizers for single-stage production. Naval Research Logistic Quarterly, 3:59-66, 1956.
29. E. Torng and P. Uthaisombut. Lower bounds for SRPT-subsequence algorithms for non-preemptive scheduling. In Proceedings 10th ACM-SIAM Symposium on Discrete Algorithms, pages 973-974, 1999.