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Weighted throughput in a single machine preemptive scheduling with continuous controllable processing times

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Abstract

We consider the problem of weighted throughput in the single machine preemptive scheduling with continuous controllable processing times. A set of tasks can be scheduled on a single machine. Each task j is associated with a nonnegative weight \(w_{j}\), a release date, a due date, and an interval of possible processing times. A task j can either be scheduled with a total processing time \(p_j\) which is in the given interval, or rejected (not participating in the schedule). The reward for processing j for \(p_{j}\) time units is \(w_{j}p_{j}\), and we are interested in constructing a feasible preemptive schedule such that the sum of rewards is maximized. We present a dynamic programming algorithm that solves the problem in pseudo-polynomial time and use it to obtain an FPTAS. Afterward, as our main contribution we propose an interesting efficient frontier approach for improved complexity bounds.

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Notes

  1. This integrality assumption is equivalent (by scaling the parameters related to time by a common factor and scaling the weights of all tasks by another factor) to the assumption of rational input, but since we look for a pseudo-polynomial time algorithm with time complexity depending on these parameters, we state the problem under the assumption that the input parameters are integers.

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Authors and Affiliations

  1. Faculty of Industrial Engineering and Management, The Technion, 32000, Haifa, Israel

    Asaf Levin & Tal Shusterman

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  1. Asaf Levin
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  2. Tal Shusterman
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Correspondence to Asaf Levin.

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This work was supported by ISF - Israel Science Foundation (grant number 308/18). The authors have no competing interests to declare that are relevant to the content of this article. Data sharing not applicable to this article as no datasets were generated or analyzed during the current study. There is no software for this work.

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Partially supported by ISF—Israeli Science Foundation grant number 308/18.

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Levin, A., Shusterman, T. Weighted throughput in a single machine preemptive scheduling with continuous controllable processing times. Acta Informatica 60, 101–122 (2023). https://doi.org/10.1007/s00236-022-00430-4

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