Approximation in stochastic scheduling: The power of LP-based priority policies

Journal of the ACM

Volumn 46, Issue 6, 1999, Pages 924-942

  Möhring, Rolf H ^a   Schulz, Reas S ^a,b   Uetz, Marc ^c  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Approximation; Asymptotic optimality; Lp relaxation; Priority policy; Stochastic scheduling; Worst case performance; Wsept rule

Indexed keywords

COMBINATORIAL ALGORITHMS; PARALLEL MACHINES; STOCHASTIC SCHEDULING;

ALGORITHMS; APPROXIMATION THEORY; COMBINATORIAL MATHEMATICS; PARALLEL PROCESSING SYSTEMS; PROBABILITY; PROBLEM SOLVING; SCHEDULING;

STOCHASTIC PROGRAMMING;

EID: 0001175654     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/331524.331530     Document Type: Article

References (32)

1. BERTSIMAS, D., AND NINO-MORA, J. 1996. Conservation laws, extended polymatroids and multiarmed bandit problems: A polyhedral approach to indexable systems. Math. Oper. Res. 21, 257-306.
2. BRUNO, J. L., COFFMAN JR., E. G., AND SETHI, R. 1974. Scheduling independent tasks to reduce mean finishing time. Commun. ACM 17, 7 (July), 382-387.
3. BRUNO, J. L., DOWNEY, P. J., AND FREDERICKSON, G. N. 1981. Sequencing tasks with exponential service times to minimize the expected flow time or makespan. J. ACM, 28, 1 (Jan.), 100-113.
4. CHAN, L. M. A., MURIEL, A., AND SIMCHI-LEVI, D. 1998. Parallel machine scheduling, linear programming, and parameter list scheduling heuristics. Oper. Res. 46, 5, 729-741.
5. DACRE, M., GLAZEBROOK, K. D., AND NINO-MORA, J. 1999. The achievable region approach to the optimal control of stochastic systems. J. Roy. Stat. Soc. Ser. B. 61, 747-791.
6. EASTMAN, W. L., EVEN, S., AND ISAACS, I. M. 1964. Bounds for the optimal scheduling of n jobs on m processors. Manage. Sei. 11, 268-279.
7. EDMONDS, J. 1970. Submodular functions, matroids and certain polyhedra. In Proceedings of the International Conference on Combinatorics (Calgary, Canada), pp. 69-87.
8. FUJISHIGE, S. 1991. Submodular functions and optimization. In Annals of Discrete Mathematics, vol. 47. North-Holland, Amsterdam.
9. GLAZEBROOK, K. D. 1979. Scheduling tasks with exponential service times on parallel machines. J. Appl. Prob. 16, 685-689.
10. GLAZEBROOK, K. D., AND NINO-MORA, J. 1997. Scheduling multiclass queueing networks on parallel servers: Approximate and heavy-traffic optimality of Klimov's rule. In Proceedings of the 5th Annual European Symposium on Algorithms (ESA '97) (Graz, Austria). R. Burkard and G. Woeginger, eds., Lecture Notes in Computer Science, vol. 1284, Springer-Verlag, New York, pp. 232-245.
11. GRAHAM, R. L., LAWLER, E. L., LENSTRA, J. K., AND RINNOOY KAN, A. H. G. 1979. Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Disc. Math. 5, 287-326.
12. GRöTSCHEL, M., LOVâSZ, L., AND SCHRIJVER, A. 1988. Geometric algorithms and combinatorial optimization. In Algorithms and Combinatorics, vol. 2. Springer, Berlin, Germany.
13. HALL, L. A., SCHULZ, A. S., SHMOYS, D. B., AND WEIN, J. 1997. Scheduling to minimize average completion time: Off-line and on-line approximation algorithms. Math. Oper. Res. 22, 513-544.
14. HALL, W. J., AND WELLNER, J. A. 1981. Mean residual life. In Proceedings of the International Symposium on Statistics and Related Topics (Ottawa, Ont., Canada). M. Csörgö, D. A. Dawson, J. N. K. Rao, and A. K. Md. E. Saleh, eds. North-Holland, Amsterdam, The Netherlands, pp. 169-184.
15. KäMPKE, T. 1987. On the optimality of static priority policies in stochastic scheduling on parallel machines. J. Appl. Prob. 24, 430-448.
16. KAWAGUCHI, T., AND KYAN, S. 1986. Worst case bound on an LRF schedule for the mean weighted flow-time problem. SLAM J. Comput. 15, 1119-1129.
17. LAWLER, E. L., LENSTRA, J. K., RINNOOY KAN, A. H. G., AND SHMOYS, D. B. 1993. Sequencing and scheduling: Algorithms and complexity. In Logistics of Production and Inventory. Handbooks in Operations Research and Management Science, vol. 4. North-Holland, Amsterdam, pp. 445-522.
18. MöHRING, R. H., RADERMACHER, F. J., AND WEISS, G. 1984. Stochastic scheduling problems I: General strategies. ZOR-Zeits. Oper. Res. 28, 193-260.
19. MöHRING, R. H., RADERMACIIER, F. J., AND WEISS, G. 1985. Stochastic scheduling problems II: Set strategies. ZOR-Zeits. Oper. Res. 29, 65-104.
20. MöHRING, R. H., SCHULZ, A. S., AND UETZ, M. 1998. Approximation in stochastic scheduling: The power of LP-based priority policies. Tech. Rep. 595/1998. Department of Mathematics, Berlin University of Technology, Berlin, Germany.
21. MöHRING, R. H., SCHULZ, A. S., AND UETZ, M. 1999. Stochastic machine scheduling: Performance guarantees for LP-based priority policies. In Proceedings of the 2nd International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (Berkeley, Calif.), D. Hochbaum, K. Jansen, J. O. P. Rolim and A. Sinclair, Eds. Lecture Notes in Computer Science, vol. 1671. Springer-Verlag, New York, pp. 144-155.
22. PHILLIPS, C. A., STEIN, C., AND WEIN, J. 1998. Minimizing average completion time in the presence of release dates. Math. Prog. 82, 199-223.
23. QUEYRANNE, M. 1993. Structure of a simple scheduling polyhedron. Math. Prog. 58, 263-285.
24. ROTHKOPF, M. H. 1966. Scheduling with random service times. Manag. Sei. 12, 703-713.
25. SCHULZ, A. S. 1996. Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bounds. In Proceedings of the 5th International Conference on Integer Programming and Combinatorial Optimization (Vancouver, B.C., Canada). W. H. Cunningham, S. T. McCormick, and M. Queyranne, eds., Lecture Notes in Computer Science, vol. 1084. Springer-Verlag, New York, pp. 301-315.
26. SGALL, J. 1998. On-line scheduling. In Proceedings of the Dagstuhl Workshop on On-Line Algorithms, A. Fiat and G. J. Woeginger, eds. Lecture Notes in Computer Science, vol. 1442. Springer-Verlag, New York, pp. 196-231.
27. SMITH, W. E. 1956. Various optimizers for single-stage production. Nov. Res. Log. Quarterly 3, 59-66.
28. SPACCAMELA, A. M., RHEE, W. S., STOUGIE, L., AND VAN DE GEER, S. 1992. Probabilistic analysis of the minimum weighted flowtime scheduling problem. Oper. Res. Lett. 11, 67-71.
29. WEBER, R. R., VARAIYA, P., AND WALRAND, J. 1986. Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime. J. Appl. Prob. 23, 841-847.
30. WEISS, G. 1990. Approximation results in parallel machines stochastic scheduling. Ann. Oper. Res. 26, 195-242.
31. WEISS, G. 1992. Turnpike optimality of Smith's rule in parallel machines stochastic scheduling. Math. Oper. Res. 17, 255-270.
32. WEISS, G., AND PINEDO, M. 1980. Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions. J. Appl. Prob. 17, 187-202.