A faster checker of the energetic reasoning for the cumulative scheduling problem

Jacques Carlier, Abderrahim Sahli, Antoine Jouglet and Eric Pinson

International Journal of Production Research, 2022, vol. 60, issue 11, 3419-3434

Abstract: This paper constitutes a step forward in resource-constrained scheduling theory. We introduce an $O(n \times \alpha (n) \times \log n) $O(n×α(n)×log⁡n) checker for energetic reasoning (ER), where $\alpha (n) $α(n) is Ackermann's inverse function. Until now, after more than 20 years of research, the best technique, recently obtained by Ouellet and Quimper, was in $O(n\log ^2 n) $O(nlog2⁡n). We identify mathematical properties that allow the number of useful intervals to be reduced. We also discuss the interest of integrating this checker into industrial solvers developed for addressing optimisation problems.

Date: 2022
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DOI: 10.1080/00207543.2021.1923853

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