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

arXiv: https://arxiv.org/abs/2506.10405 · HTML: https://mlsanity.com/paper/2506.10405/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [Resource-constrained Project Scheduling with Time-of-Use Energy Tariffs and Machine States: A Logic-based Benders Decomposition Approach](https://mlsanity.com/paper/2601.06542/) (2026)

## Abstract (arXiv)

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.