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Resource level minimization in the discrete-continuous scheduling

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  • Gorczyca, Mateusz
  • Janiak, Adam

Abstract

A discrete-continuous problem of non-preemptive task scheduling on identical parallel processors is considered. Tasks are described by means of a dynamic model, in which the speed of the task performance depends on the amount of a single continuously divisible renewable resource allotted to this task over time. An upper bound on the completion time of all the tasks is given. The criterion is to minimize the maximum resource consumption at each time instant, i.e., the resource level. This problem has been observed in many industrial applications, where a continuously divisible resource such as gas, fuel, electric, hydraulic or pneumatic power, etc., has to be distributed among the processing units over time, and it affects their productivity. The problem consists of two interrelated subproblems: task sequencing on processors (discrete subproblem) and resource allocation among the tasks (continuous subproblem). An optimal resource allocation algorithm for a given sequence of tasks is presented and computationally tested. Furthermore, approximation algorithms are proposed, and their theoretical and experimental worst-case performances are analyzed. Computer experiments confirmed the efficiency of all the algorithms.

Suggested Citation

  • Gorczyca, Mateusz & Janiak, Adam, 2010. "Resource level minimization in the discrete-continuous scheduling," European Journal of Operational Research, Elsevier, vol. 203(1), pages 32-41, May.
    • Handle: RePEc:eee:ejores:v:203:y:2010:i:1:p:32-41
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    References listed on IDEAS

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    1. Jozefowska, Joanna & Mika, Marek & Rozycki, Rafal & Waligora, Grzegorz & Weglarz, Jan, 1998. "Local search metaheuristics for discrete-continuous scheduling problems," European Journal of Operational Research, Elsevier, vol. 107(2), pages 354-370, June.
    2. Jacek Błażewicz & Maciej Machowiak & Jan Węglarz & Mikhail Kovalyov & Denis Trystram, 2004. "Scheduling Malleable Tasks on Parallel Processors to Minimize the Makespan," Annals of Operations Research, Springer, vol. 129(1), pages 65-80, July.
    3. Moshe Dror & Helman I. Stern & Jan Karel Lenstra, 1987. "Parallel Machine Scheduling: Processing Rates Dependent on Number of Jobs in Operation," Management Science, INFORMS, vol. 33(8), pages 1001-1009, August.
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    Cited by:

    1. Li, Shisheng & Ng, C.T. & Cheng, T.C.E. & Yuan, Jinjiang, 2011. "Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 210(3), pages 482-488, May.
    2. Bahram Alidaee & Haibo Wang & R. Bryan Kethley & Frank Landram, 2019. "A unified view of parallel machine scheduling with interdependent processing rates," Journal of Scheduling, Springer, vol. 22(5), pages 499-515, October.

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