Abstract
Jobs arriving over time must be non-preemptively processed on one of m parallel machines, each of which running at its own speed, so as to minimize a weighted sum of the job completion times. In this on-line environment, the processing requirement and weight of a job are not known before the job arrives. The Weighted Shortest Processing Requirement (WSPR) on-line heuristic is a simple extension of the well known WSPT heuristic, which is optimal for the single machine problem without release dates. We prove that the WSPR heuristic is asymptotically optimal for all instances with bounded job processing requirements and weights. This implies that the WSPR algorithm generates a solution whose relative error approaches zero as the number of jobs increases. Our proof does not require any probabilistic assumption on the job parameters and relies extensively on properties of optimal solutions to a single machine relaxation of the problem.
Research supported in part by ONR Contracts N00014-95-1-0232 and N00014-01-1-0146, NSF Contracts DDM-9322828 and DMI-9732795, and a research grant from the Natural Sciences and Research Council of Canada (NSERC).
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References
Chekuri, C., Motwani, R., Natarajan, B., Stein, C.: (1997). Approximation Techniques for Average Completion Time Scheduling. Proceedings of the Eight Annual ACM-SIAM Symposium on Discrete Algorithms (1997) 609–618
Eastman, W. L., Even, S., Isaacs, I. M.: Bounds for the Optimal Scheduling of n Jobs on m Processors. Management Science 11 (1964) 268–279
Goemans, M. X.: Improved Approximation Algorithms for Scheduling with Release Dates. Proceedings of the 8th ACM-SIAM Symposium on Discrete Algorithms (1997) 591–598
Goemans, M. X., Queyranne, M., Schulz, A. S., Skutella, M., Wang, Y.: Single Machine Scheduling with Release Dates. Report 654, Fachbereich Mathematik (1999),Technische Universität Berlin, Germany. Available at URL: http://www.math. tu-berlin.de/coga/publications/techreports/1999/Report-654-1999.html
Graham, R.L., Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5 (1979) 287–326
Kaminsky, P., Simchi-Levi, D.: Probabilistic Analysis of an On-Line Algorithm the Single Machine Completion Time Problem With Release Dates. Under review (1997)
Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., Shmoys, D. B.: Sequencing and Scheduling: Algorithms and Complexity. In: S. C. Graves, A. H. G. Rinnooy Kan and P. H. Zipkin (eds.), Logistics of Production and Inventory, Handbooks in Operations Research and Management Science 4 (1993), North-Holland, Amsterdam.
Lenstra, J. K., Rinnooy Kan, A. H. G., Brucker, P.: Complexity of Machine Scheduling Problems. Annals of Discrete Math 1 (1977) 343–362
Queyranne, M., Sviridenko, M.: Approximation algorithms for shop scheduling problems with minsum objective. Faculty of Commerce, University of British Columbia (1999)
Sgall, J.: On-line scheduling — a survey. In: A. Fiat and G.J. Woeginger (eds.), Online Algorithms: The State of the Art, Lecture Notes in Computer Science 1442 (1998) 196–231, Springer, Berlin.
Smith, W.: Various optimizers for single-stage production. Naval Res. Logist. Quart. 3 (1956) 59–66
Uma, R. N., Wein, J.: On the Relationship between Combinatorial and LP-Based Approaches to NP-hard Scheduling Problems. In: R. E. Bixby, E. A. Boyd and R. Z. Rios-Mercado (eds.), Integer Programming and Combinatorial Optimization. Proceedings of the Sixth International IPCO Conference, Lecture Notes in Computer Science 1412 (1998) 394–408, Springer, Berlin.
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Chou, CF.M., Queyranne, M., Simchi-Levi, D. (2001). The Asymptotic Performance Ratio of an On-Line Algorithm for Uniform Parallel Machine Scheduling with Release Dates. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_4
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