Models and algorithms for stochastic online scheduling

Mathematics of Operations Research

Volumn 31, Issue 3, 2006, Pages 513-525

  Megow, Nicole ^a   Uetz, Marc ^b   Vredeveld, Tjark ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

Approximation; Online optimization; Scheduling; Stochastic dynamic optimization; Total weighted completion time

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; MATHEMATICAL MODELS; OPTIMIZATION; PARALLEL PROCESSING SYSTEMS; RANDOM PROCESSES; SCHEDULING;

COMBINATORIAL ONLINE SCHEDULING; ONLINE OPTIMIZATION; STOCHASTIC DYNAMIC OPTIMIZATION; TOTAL WEIGHTED COMPLETION TIME;

ONLINE SYSTEMS;

EID: 33748418908     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1060.0201     Document Type: Article

References (36)

1. Afrati, F. N., E. Bampis, C. Chekuri, D. R. Karger, C. Kenyon, S. Khanna, I. Mills, M. Queyranne, M. Skutella, C. Stein, M. Sviridenko. 1999. Approximation schemes for minimizing average weighted completion time with release dates. Proc. 40th Annual Sympos. on Foundations of Comput. Sci., New York. IEEE Computer Society, Los Alamitos, CA, 32-43.
2. Anderson, E. J., C. N. Potts. 2004. On-line scheduling of a single machine to minimize total weighted completion time. Math. Oper. Res. 29 686-697.
3. Borodin, A., R. El-Yaniv. 1998. Online Computation and Competitive Analysis. Cambridge University Press, Cambridge, UK.
4. Bruno, J. L., P. J. Downey, G. N. Frederickson. 1981. Sequencing tasks with exponential service times to minimize the expected flowtime or makespan. J. ACM 28 100-113.
5. Chakrabarti, S., S. Muthukrishnan. 1996. Resource scheduling for parallel database and scientific applications. Proc. 8th Annual ACM Sympos. on Parallel Algorithms and Architectures, Padua, Italy. ACM Press, New York, 329-335.
6. Chekuri, C., R. Johnson, R. Motwani, B. Natarajan, B. Rau, M. Schlansker. 1996. An analysis of profile-driven instruction level parallel scheduling with application to super blocks. Proc. 29th IEEE/ACM Internat. Sympos. on Microarchitecture, Paris, France. IEEE Computer Society, Los Alamitos, CA, 58-69.
7. Chou, M. C., H. Liu, M. Queyranne, D. Simchi-Levi. 2006. On the asymptotic optimality of a simple on-line algorithm for the stochastic single machine weighted completion time problem and its extensions. Oper. Res. 54(3) 464-474.
8. Correa, J., M. Wagner. 2005. LP-based online scheduling: From single to parallel machines. M. Jünger, V. Kaibel, eds. Proc. 8th Integer Programming and Combinatorial Optimization Conf., Berlin, Germany. Lecture Notes in Computer Science, Vol. 3509. Springer-Verlag, 196-209.
9. Dempster, M. A. H., J. K. Lenstra, A. H. G. Rinnooy Kan, eds. 1982. Deterministic and Stochastic Scheduling. D. Reidel Publishing Company, Dordrecht, The Netherlands.
10. Eastman, W., S. Even, I. Isaacs. 1964. Bounds for the optimal scheduling of n jobs on m processors. Management Sci. 11 268-279.
11. Fiat, A., G. J. Woeginger. 1999. On-line scheduling on a single machine: Minimizing the total completion time. Acta Informatica 36 287-293.
12. Graham, R. L., E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan. 1979. Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Discrete Math. 5 287-326.
13. Hall, W. J., J. A. Wellner. 1981. Mean residual life. M. Csörgö, D. A. Dawson, J. N. K. Rao, A. K. Md. E. Saleh, eds. Proc. Internat. Sympos. Statist. Related Topics. Ottawa, Ontario, Canada. North-Holland, Amsterdam, The Netherlands, 169-184.
14. Hoogeveen, H., A. P. A. Vestjens. 1996. Optimal on-line algorithms for single-machine scheduling. W. H. Cunningham, S. T. McCormick, M. Queyranne, eds. Proc. 5th Integer Programming and Combinatorial Optimization Conf., Vancouver, British Columbia, Canada. Lecture Notes in Computer Science, Vol. 1084. Springer-Verlag, 404-414.
15. Karlin, A., M. Manasse, L. Rudolph, D. Sleator. 1988. Competitive snoopy paging. Algorithmica 3 70-119.
16. Koutsoupias, E., C. H. Papadimitriou. 2000. Beyond competitive analysis. SIAM J. Comput. 30 300-317.
17. Lenstra, E. L., A. H. G. Rinooy Kan, P. Brucker. 1977. Complexity of machine scheduling problems. Ann. Discrete Math. 1 243-362.
18. Megow, N., A. S. Schulz. 2004. On-line scheduling to minimize average completion time revisited. Oper. Res. Lett. 32 485-490.
19. Megow, N., M. Uetz, T. Vredeveld. 2005. Stochastic online scheduling on parallel machines. G. Persiano, R. Solis-Oba, eds. Proc. Second Workshop on Approximation and Online Algorithms, Bergen, Norway. Lecture Notes in Computer Science, Vol. 3351. Springer-Verlag, 167-180.
20. Möhring, R. H., F. J. Radermacher, G. Weiss. 1984. Stochastic scheduling problems I: General strategies. ZOR - Zeitschrift für Oper. Res. 28 193-260.
21. Möhring, R. H., A. S. Schulz, M. Uetz. 1999. Approximation in stochastic scheduling: The power of LP-based priority policies. J. ACM 46 924-942.
22. Pruhs, K., J. Sgall, E. Torng. 2004. Online scheduling. J. Leung, ed. Handbook of Scheduling: Algorithms, Models, and Performance. Analysis, Chapter 15. CRC Press, Boca Raton, FL.
23. Rothkopf, M. H. 1966. Scheduling with random service times. Management Sci. 12 703-713.
24. Scharbrodt, M., T. Schickinger, A. Steger. 2002. A new average case analysis for completion time scheduling. Proc. 34th Annual ACM Sympos. on the Theory of Comput., Montreal, Quebec, Canada. ACM Press, New York, 170-178.
25. Schulz, A. S. 2005. New old algorithms for stochastic scheduling. S. Albers, R. H. Möhring, G. Ch. Pflug, R. Schultz, eds. Algorithms for Optimization with Incomplete Information. Dagstuhl Seminar Proceedings, 05031. Internationales Begegnungs- und Forschungszen-trum (IBFI), Schloss Dagstuhl, Germany.
26. Schulz, A. S., M. Skutella. 2002. Scheduling unrelated machines by randomized rounding. SIAM J. Discrete Math. 15 450-469.
27. Skutella, M., M. Uetz. 2005. Stochastic machine scheduling with precedence constraints. SIAM J. Comput. 34 788-802.
28. Skutella, M., G. J. Woeginger. 2000. A PTAS for minimizing the total weighted completion time on identical parallel machines. Math. Oper. Res. 25 63-75.
29. Sleator, D., R. Tarjan. 1985. Amortized efficiency of list update and paging rules. Comm. ACM 28 202-208.
30. Smith, W. 1956. Various optimizers for single-stage production. Naval Res. Logist. Quart. 3 59-66.
31. Souza, A., A. Steger. 2004. The expected competitive ratio for weighted completion time scheduling. V. Diekert, M. Habib, eds. Proc. 21st Sympos. on Theoret. Aspects of Comput. Sci., Montpellier, France. Lecture Notes in Computer Science, Vol. 2996. Springer-Verlag, 620-631.
32. Uetz, M. 2002. Algorithms for Deterministic and Stochastic Scheduling, Cuvillier Verlag, Göttingen, Germany.
33. Vestjens, A. P. A. 1997. On-line machine scheduling. Doctoral dissertation, Eindhoven University of Technology, Eindhoven, The Netherlands.
34. Weiss, G. 1990. Approximation results in parallel machines stochastic scheduling. Ann. Oper. Res. 26 195-242.
35. Weiss, G. 1992. Turnpike optimality of Smith's rule in parallel machines stochastic scheduling. Math. Oper. Res. 17 255-270.
36. Weiss, G., M. Pinedo. 1980. Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions. J. Appl. Probab. 17 187-202.