Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bounds

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

Volumn 1084, Issue , 1996, Pages 301-315

  Schulz, Andreas S ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; COMBINATORIAL OPTIMIZATION; INTEGER PROGRAMMING; LINEAR PROGRAMMING; MACHINE SHOP PRACTICE; POLYNOMIAL APPROXIMATION; SCHEDULING;

IDENTICAL PARALLEL MACHINES; LINEAR PROGRAMMING FORMULATION; LINEAR PROGRAMMING RELAXATION; PARALLEL MACHINE PROBLEMS; PERFORMANCE GUARANTEES; POLYNOMIAL TIME APPROXIMATION ALGORITHMS; TOTAL WEIGHTED COMPLETION TIME; WORST-CASE PERFORMANCE;

SCHEDULING ALGORITHMS;

EID: 84947916207     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-61310-2_23     Document Type: Conference Paper

References (30)

1. [BCS74] J. L. Bruno, E. G. Coffman Jr., and R. Sethi. Scheduling independent tasks to reduce mean finishing time. Communications of the Association for Computing Machinery, 17:382-387, 1974.
2. +96] S. Chakrabarti, C. A. Phillips, A. S. Schulz, D. B. Shmoys, C. Stein, and J. Wein. Improved scheduling algorithms for minsum criteria, 1996. To appear in Springer Lecture Notes in Computer Science, Proceedings of the 23rd ICALP Conference.
3. [DW90] M. E. Dyer and L. A. Wolsey. Formulating the single machine sequencing problem with release dates as a mixed integer program. Discrete Applied Mathematics, 26:255-270, 1990.
4. [GJS76] M. R. Garey, D. S. Johnson, and R. Sethi. The complexity of flowshop andjobshop scheduling. Mathematics of Operations Research, 1:117-129, 1976.
5. [GLLRK79] R. L. Graham, E. L. Lawler, J. K. Lenstra, and A. H. G. Rinnooy Kan. Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 5:287-326, 1979.
6. [GLS88] M. Grötschel, L. Lovász, and A. Schrijver. Geometric Algorithms and Combinatorial Optimization, volume 2 of Algorithms and Combinatorics. Springer, Berlin, 1988.
7. [Goe96] M. X. Goemans. A supermodular relaxation for scheduling with release dates. This volume, 1996.
8. [GS78] T. Gonzalez and S. Sahni. Flowshop and jobshop schedules: Complexity and approximation. Operations Research, 26:36-52, 1978.
9. [HHLV] J. A. Hoogeveen, C. Hurkens, J. K. Lenstra, and A. Vandevelde. Lower bounds for the multiprocessor flow shop. In preparation.
10. [HS88] D. S. Hochbaum and D. B. Shmoys. A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach. SIAM Journal on Computing, 17:539-551, 1988.
11. [HSSW96] L. A. Hall, A. S. Schulz, D. B. Shmoys, and J. Wein. Scheduling to minimize average completion time: Off-line and on-line algorithms, 1996. In preparation.
12. [HSW95] L. A. Hall, D. B. Shmoys, and J. Wein. Personal communication, September 1995.
13. [HSW96] L. A. Hall, D. B. Shmoys, and J. Wein. Scheduling to minimize average completion time: Off-line and on-line algorithms. In Proceedings of the 7th ACM-SIAM Symposium on Discrete Algorithms, pages 142-151, January 1996.
14. [KK86] T. Kawaguchi and S. Kyan. Worst case bound of an LRF schedule for the mean weighted flow-time problem. SIAM Journal on Computing, 15:1119-1129, 1986.
15. [Law78] E. L. Lawler. Sequencing jobs to minimize total weighted completion time subject to precedence constraints. Annals of Discrete Mathematics, 2:75-90, 1978.
16. [LLRKS93] E. L. Lawler, 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, editors, Logistics of Production and Inventory, volume 4 of Handbooks in Operations Research and Management Science, pages 445-522. North-Holland, Amsterdam, The Netherlands, 1993.
17. [LRKB77] J. K. Lenstra, A. H. G. Rinnooy Kan, and P. Brucker. Complexity of machine scheduling problems. Annals of Discrete Mathematics, 1:343-362, 1977.
18. [LST90] J. K. Lenstra, D. B. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Mathematical Proqramminq, 46:259-271, 1990.
19. [MSS96] R. H. Möhring, M. W. Schäffter, and A. S. Schulz. Scheduling with communication delays: Minimizing the average weighted completion time. Preprint, Department of Mathematics, Technical University of Berlin, Berlin, Germany, 1996.
20. [PSW95] C. Phillips, C. Stein, and J. Wein. Scheduling jobs that arrive over time. In Proceedings of the Fourth Workshop on Algorithms and Data Structures, number 955 in Lecture Notes in Computer Science, pages 86-97. Springer, Berlin, 1995.
21. [QS94] M. Queyranne and A. S. Schulz. Polyhedral approaches to machine scheduling. Preprint 408/1994, Department of Mathematics, Technical University of Berlin, Berlin, Germany, 1994.
22. [QS95] M. Queyranne and A. S. Schulz. Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds. In E. Balas and J. Clausen, editors, Integer Programming and Combinatorial Optimization, number 920 in Lecture Notes in Computer Science, pages 307-320. Springer, Berlin, 1995. Proceedings of the 4th International IPCO Conference.
23. [Que93] M. Queyranne. Structure of a simple scheduling polyhedron. Mathematical Programming, 58:263-285, 1993.
24. [Que95] M. Queyranne. Personal communication, September 1995.
25. [QW91] M. Queyranne and Y. Wang. A cutting plane procedure for precedence-constrained single machine scheduling. Working paper. Faculty of Commerce, University of British Columbia, Vancouver, Canada, 1991.
26. [RC92] C. Rajendran and D. Chaudhuri. A multi-stage parallel-processor flow-shop problem with minimum flowtime. European Journal of Operational Research, 57:111-122, 1992.
27. [Sch95a] A. S. Schulz. Polytopes and Scheduling. PhD thesis, Technical University of Berlin, Berlin, Germany, 1995.
28. [Sch95b] A. S. Schulz. Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bounds. Preprint 474/1995, Department of Mathematics, Technical University of Berlin, Berlin, Germany, 1995.
29. [Smi56] W. E. Smith, Various optimizers for single-stage production. Naval Research and Logistics Quarterly, 3:59-66, 1956.
30. [ST93] D. B. Shmoys and É, Tardos. An approximation algorithm for the generalized assignment problem. Mathematical Programming, 62:461-474, 1993.