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 and Zdeněk Hanzálek

European Journal of Operational Research, 2026, vol. 328, issue 1, 64-77

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.

Keywords: Scheduling; Single machine; Time of use; Machine states; Variable energy costs; Total energy cost minimization; Branch and bound (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:328:y:2026:i:1:p:64-77

DOI: 10.1016/j.ejor.2025.06.026

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