Energy-conscious Single-machine Scheduling Problem with Release Dates under Time-of-use Electricity Tariffs

The global trend for industries to comprehensively improve the utilization of resources has attracted great attention from many researchers. Industry managers are increasingly optimizing their production strategies under time-of-use (TOU) electricity tariffs to reduce energy consumption since it accounts for the majority of total production costs. This paper investigates the single-machine scheduling problem with release dates under TOU tariffs. The key issue is to assign a group of jobs with different release dates to a single machine to minimize the total electricity cost. To solve the problem, a mixed-integer linear programming (MILP) model based on time-indexed formulation (TI-MILP) is proposed. By preliminary experiments, we find TI-MILP model is not efficient enough. Therefore, to more efficiently solve the problem, a period-based MILP (P-MILP) model is developed. Finally, extensive experimental results demonstrate that i) the proposed models can save about 25% on total electricity cost compared with the existing empirical scheduling method, and ii) P-MILP model outperforms TI-MILP model in terms of computational efficiency and problem scale.