The power of preemption on unrelated machines and applications to scheduling orders

Mathematics of Operations Research

Volumn 37, Issue 2, 2012, Pages 379-398

  Correa, José R ^a   Skutella, Martin ^b   Verschae, José ^b  

^a UNIVERSITY OF CHILE   (Chile)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Approximation algorithms; Machine scheduling

Indexed keywords

CONSTANT-FACTOR APPROXIMATION ALGORITHMS; FLEXIBLE ENVIRONMENTS; MACHINE SCHEDULING; MAKESPAN; NEW YORK; NON-PREEMPTIVE; OPTIMAL PREEMPTIVE SCHEDULE; PACKING CONSTRAINTS; PARALLEL MACHINE; POLYNOMIAL TIME APPROXIMATION SCHEMES; SCHEDULING JOBS; TOTAL WEIGHTED COMPLETION TIME; UNIFORM MACHINE; UNRELATED MACHINES; UNRELATED PARALLEL MACHINES; UPPER BOUND; WEIGHTED COMPLETION;

APPROXIMATION ALGORITHMS; MACHINERY; SCHEDULING ALGORITHMS;

SCHEDULING;

EID: 84861415304     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1110.0520     Document Type: Article

References (39)

1. Afrati, F., E. Bampis, C. Chekuri, D. Karger, C. Kenyon, S. Khanna, I. Milis, M. Queyranne, M. Skutella, C. Stein, M. Sviridenko. 1999. Approximation schemes for minimizing average weighted completion time with release dates. Proc. 40th Annual IEEE Sympos. Foundations Comput. Sci. (FOCS), IEEE Computer Society, Washington, DC, 32-43. (Pubitemid 129306182)
2. Ambühl, C., M. Mastrolilli. 2009. Single machine precedence constrained scheduling is a vertex cover problem. Algorithmica 53 488-503.
3. Ambühl, C., M. Mastrolilli, O. Svensson. 2011. Inapproximability results for maximum edge biclique, minimum linear arrangement, and sparsest cut. SIAM J. Comput. 40 567-596.
4. Bansal, N., S. Khot. 2009. Optimal long code test with one free bit. Proc. 50th Annual IEEE Sympos. Foundations Comput. Sci. (FOCS), IEEE Computer Society, Washington, DC, 453-462.
5. Bansal, N., S. Khot. 2010. Inapproximability of hypergraph vertex cover and applications to scheduling problems. Proc. 37th Internat. Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, Vol. 6198. Springer-Verlag, Berlin, 250-261.
6. Canetti, R., S. Irani. 1998. Bounding the power of preemption in randomized scheduling. SIAM J. Comput. 27 993-1015. (Pubitemid 128689441)
7. Chekuri, C., R. Motwani. 1999. Precedence constrained scheduling to minimize sum of weighted completion times on a single machine. Discrete Appl. Math. 98 29-38. (Pubitemid 129639765)
8. Chen, Z., N. G. Hall. 2001. Supply chain scheduling: Assembly systems. Technical report, Ohio State University, Columbus.
9. Chen, Z., N. G. Hall. 2007. Supply chain scheduling: Conflict and cooperation in assembly systems. Oper. Res. 55 1072-1089. (Pubitemid 351159518)
10. Chudak, F., D. S. Hochbaum. 1999. A half-integral linear programming relaxation for scheduling precedence-constrained jobs on a single machine. Oper. Res. Lett. 25 199-204. (Pubitemid 30523556)
11. Correa, J. R., A. S. Schulz. 2005. Single machine scheduling with precedence constraints. Math. Oper. Res. 30 1005-1021. (Pubitemid 43134188)
12. Correa, J. R., M. Skutella, J. Verschae. 2009. Proc. 12th Internat. Workshop and 13th Internat. Workshop on Approximation, Randomization, and Combinatorial Optimization (APPROX-RANDOM), Lecture Notes in Computer Science, Vol. 5687. Springer-Verlag, Berlin, 84-97.
13. Dyer, M. E., L. A. Wolsey. 1999. Formulating the single machine sequencing problem with release dates as a mixed integer program. Discrete Appl. Math. 26 255-270.
14. Eastman, W. L., S. Even, I. M. Isaacs. 1964. Bounds for the optimal scheduling of n jobs on m processors. Management Sci. 11 268-279.
15. Graham, R. L. 1966. Bounds for certain multiprocessing anomalies. AT&T Tech. J. 45 1563-1581.
16. Hall, L. A., A. S. Schulz, D. B. Shmoys, J. Wein. 1997. Scheduling to minimize average completion time: Off-line and on-line approximation algorithms. Math. Oper. Res. 22 513-544. (Pubitemid 127653350)
17. Hochbaum, D., D. B. Shmoys. 1987. Using dual approximation algorithms for scheduling problems: Theoretical and practical results. J. ACM 34 144-162. (Pubitemid 17601592)
18. Hoogeveen, H., P. Schuurman, G. J. Woeginger. 2001. Nonapproximability results for scheduling problems with minsum criteria. INFORMS J. Comput. 13 157-168. (Pubitemid 33645990)
19. Khot, S. 2002. On the power of unique 2-prover 1-round games. Proc. 34th Annual ACM Sympos. Theory Comput. (STOC), ACM, New York, 767-775. (Pubitemid 35009440)
20. Lawler, E. L., J. Labetoulle. 1978. On preemptive scheduling of unrelated parallel processors by linear programming. J. ACM 25 612-619. (Pubitemid 9399485)
21. Lawler, E. L., J. K. Lenstra, A. H. G. Rinnooy Kan, D. B. Shmoys. 1993. Sequencing and scheduling: Algorithms and complexity. S. C. Graves, A. H. G. Rinnooy Kan, P. H. Zipkin, eds. Handbooks in Operations Research and Management Science, Logistics of Production and Inventory, Vol. 4. North-Holland, Amsterdam, 445-522.
22. Lenstra, J. K., A. H. G. Rinnooy Kan. 1978. Complexity of scheduling under precedence constraints. Oper. Res. 26 22-35.
23. Lenstra, J. K., D. B. Shmoys, É. Tardos. 1990. Approximation algorithms for scheduling unrelated parallel machines. Math. Programming 46 259-271.
24. Leung, J., H. Li, M. Pinedo. 2006. Approximation algorithm for minimizing total weighted completion time of orders on identical parallel machines. Naval. Res. Logist. 53 243-260.
25. Leung, J., H. Li, M. Pinedo. 2007. Scheduling orders for multiple product types to minimize total weighted completion time. Discrete Appl. Math. 155 945-970. (Pubitemid 46436154)
26. Leung, J., H. Li, M. Pinedo, J. Zhang. 2007. Minimizing total weighted completion time when scheduling orders in a flexible environment with uniform machines. Inform. Processing Lett. 103 119-129. (Pubitemid 46719171)
27. Lin, J.-H., J. S. Vitter. 1992. α-approximations with minimum packing constraint violation. Proc. 24th Annual ACM Sympos. Theory of Comput. (STOC), ACM, New York, 771-782.
28. Margot, F., M. Queyranne, Y. Wang. 2003. Decompositions, network flows, and a precedence constrained single machine scheduling problem. Oper. Res. 51 981-992.
29. Mastrolilli, M., M. Queyranne, A. S. Schulz, O. Svensson, N. A. Uhan. 2010. Minimizing the weighted sum of completion times in concurrent open shops. Oper. Res. Lett. 38 390-395.
30. Queyranne, M. 1993. Structure of a simple scheduling polyhedron. Math. Programming 58 263-285.
31. Schulz, A. S., M. Skutella. 2002. Scheduling unrelated machines by randomized rounding. SIAM J. Discrete Math. 15 450-469. (Pubitemid 35355419)
32. Shachnai, H., T. Tamir. 2002. Multiprocessor scheduling with machine allotment and parallelism constraints. Algorithmica 32 651-678.
33. Shmoys, D. B., É. Tardos. 1993. An approximation algorithm for the generalized assignment problem. Math. Programming 62 461-474.
34. Skutella, M. 2001. Convex quadratic and semidefinite programming relaxations in scheduling. J. ACM 48 206-242.
35. Skutella, M., G. J. Woeginger. 2000. Minimizing the total weighted completion time on identical parallel machines. Math. Oper. Res. 25 63-75.
36. Smith, W. E. 1956. Various optimizers for single-stage production. Naval Res. Logist. Quart. 3 59-66.
37. Verschae, J. 2008. Approximation algorithms for scheduling orders on parallel machines. Mathematical engineering thesis, Universidad de Chile, Santiago, Chile.
38. Woeginger, G. J. 2003. On the approximability of average completion time scheduling under precedence constraints. Discrete Appl. Math. 131 237-252.
39. Yang, J., M. E. Posner. 2005. Scheduling parallel machines for the customer order problem. J. Sched. 8 49-74. (Pubitemid 40536259)