Parallel Machine Scheduling With Peak Energy Consumption Limits

In recent years, the industrial sectors, particularly in the manufacturing of steel, chemicals, automotive parts, and semiconductors, have been focusing on reducing energy usage in order to improve energy efficiency and maintain competitiveness in the global market. This study addresses an energy-conscious scheduling problem of identical parallel machines by considering the peak energy consumption limits. We provide an optimal schedule that minimizes the total energy consumption by developing novel integer programming (IP) models by reducing the number of decision variables and constraints from the previous model and a branch and bound (B&B) algorithm with three dominance properties and three lower bounds. The proposed B&B algorithm performs better than the existing IP and improved IP models. We then introduce a modified simulated annealing (MSA) algorithm, which accounts for the energy consumption rates for generating neighboring solutions, to solve large-sized instances.
Note to Practitioners
—In this work, we address parallel machine scheduling by taking into account the peak energy consumption limits imposed by various manufacturing companies. We present new mathematical programming models for the problem, demonstrating that these models provide optimal solutions faster than the previous one. Additionally, we enhance these models by developing a branch and bound (B&B) algorithm that yields optimal solutions even faster. Finally, we present a heuristic algorithm to handle large-sized instances.