Abstract
In this paper, we analyse the parallel machine makespan minimization problem with the general sum of processing time based learning or aging effects. First, we prove that an optimal solution to the single machine case can be found by priority rules. Next, for the considered parallel machine problem, we construct the exact dynamic programming algorithm that can operate on real-valued job processing times, which is the only exact algorithm for the analysed problem. The computational analysis confirms that it can solve optimally moderate problem instances.
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Notes
The algorithm DP-R was coded in C++ and simulations were run on PC, CPU Intel\(^{\circledR }\) Core\(^{\mathrm {TM}}\)i7-2600K 3.40 GHz and 8GB RAM.
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We are grateful to the Editor and the Referees for their valuable comments on an earlier version of our paper.
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The research presented in this paper has been supported by the Polish Ministry of Science and Higher Education under Iuventus Plus Programme (No. IP2014 040673).
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Rudek, R. Parallel machine scheduling with general sum of processing time based models. J Glob Optim 68, 799–814 (2017). https://doi.org/10.1007/s10898-017-0509-x
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DOI: https://doi.org/10.1007/s10898-017-0509-x