Large-scale energy-conscious bi-objective single-machine batch scheduling under time-of-use electricity tariffs via effective iterative heuristics

Time-of-use (TOU) electricity pricing policy is widely encountered in the world, which provides new opportunities for power-intensive enterprises to save their energy cost. A good trade-off between the total electricity cost and production efficiency is desired by decision makers. This work addresses an energy-conscious bi-objective single-machine batch scheduling problem under TOU electricity tariffs, in which electricity price varies with time. The objective of the problem is to simultaneously minimize total electricity cost and makespan. Due to its strong NP-hard nature, two fast new ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-constraint-based constructive heuristic algorithms are developed to solve it. The core idea is to transform the bi-objective problem into a series of single-objective problems that are fast and heuristically solved to obtain an approximate Pareto front. Especially, for each transformed single-objective problem, two novel constructive heuristic algorithms are proposed by solving a series of multiple knapsack problems and 0–1 knapsack problems, respectively. Computational results on 145 benchmark and 80 newly generated larger-scale instances show that the proposed algorithms are quite efficient and are able to find high-quality Pareto solutions for large-scale problems with up to 200 batches.