Abstract
We investigate a scheduling problem with two different criteria. When considering the criterion of the minimal length of a schedule, the value of the objective function of the problem under consideration is a lower bound for the objective function of the strip packing problem. We demonstrate by an example that there exist some lists of jobs in which the ratio of values of optimum functions can attain 5/4. For the case of the maximum total profit we show by examples that the values of the objective function can differ from the optimal values arbitrarily. We propose some exact lower bounds provided that the jobs parameters satisfy some additional constraints.
This research was supported by the Russian Foundation for basic Research (Grant 93-01-00489)
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References
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© 1997 Springer Science+Business Media Dordrecht
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Sharygin, P.I. (1997). Bounds for Approximate Solution of a Scheduling Problem. In: Operations Research and Discrete Analysis. Mathematics and Its Applications, vol 391. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5678-3_20
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DOI: https://doi.org/10.1007/978-94-011-5678-3_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6395-1
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