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

TL;DR

This paper introduces an advanced branch-and-bound algorithm with bin packing strategies for energy-efficient scheduling under variable TOU tariffs and machine states, significantly improving solution speed and accuracy.

Contribution

It develops a novel algorithm combining branch-and-bound, bin packing, and heuristics to efficiently solve complex energy-aware scheduling problems with real-world data.

Findings

Solves benchmark instances with 200 jobs over 100 times faster than previous methods.

Provides tighter lower bounds for non-coprime processing times.

Demonstrates effectiveness on real energy price data.

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.