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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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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DOI: https://doi.org/10.1007/3-540-45535-3_4
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