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arXiv · 2506.10405

Green Scheduling with Time-of-Use Tariffs and Machine States: Optimizing Energy Cost via Branch-and-Bound and Bin Packing Strategies

Ondřej Benedikt·István Módos·Antonin Novak·Zdeněk Hanzálek
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Abstract

This paper presents a branch-and-bound algorithm, enhanced with bin packing strategies, for scheduling under variable energy pricing and power-saving states. The proposed algorithm addresses the 1,TOU|states|TEC problem, which involves scheduling jobs to minimize total energy cost (TEC) while considering time-of-use (TOU) electricity prices and different machine states (e.g., processing, idle, off). Key innovations include instance pre-processing for rapid lower bound calculations, a novel branching scheme combined with initializations, a block-finding primal heuristic, and a tighter lower bound for jobs with non-coprime processing times. These enhancements result in an efficient algorithm capable of solving benchmark instances with real energy prices with 200 jobs more than 100 times faster than existing state-of-the-art methods.

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Ondřej Benedikt, István Módos, Antonin Novak, Zdeněk Hanzálek. 2025-06-12. Green Scheduling with Time-of-Use Tariffs and Machine States: Optimizing Energy Cost via Branch-and-Bound and Bin Packing Strategies. https://doi.org/10.1016/j.ejor.2025.06.026

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