A dynamic control approach for energy-efficient production scheduling on a single machine under time-varying electricity pricing

This paper proposes a dynamic control algorithm to enable an energy-aware single machine scheduling under the time-varying electricity pricing policy, in which price rates remain fixed day-to-day over the season. The key issue is to assign a set of jobs to available time periods where different electricity prices are assigned, while considering requested due dates of jobs so as to minimize total penalty costs for earliness and tardiness of jobs and total energy consumption costs, simultaneously. As the first contribution of this study, we develop a new mixed integer nonlinear programming (MINLP) model that aims at determining job arrival times and resulting earliness and tardiness of jobs and energy consumption costs for machine idle and normal processing. Second, an efficient heuristic approach based on continuous-time variable control models and algorithm is developed. The proposed heuristic adaptively changes job arrival times and due dates, which finally determine production sequence over the time periods of different electricity prices, machine turn-off, and machine idle with minimum energy consumption costs and just-in-time (JIT) penalty. Energy and JIT performance of the proposed approach is examined using real energy and machining parameters of a HAAS machine and compared to those of the metaheuristic approach. For relatively large size data groups, the proposed approach incurs about 4∼11% higher energy consumption costs on average, which are offset by up to 99% lower JIT costs, resulting in 10∼94% lower total costs on average compared to the metaheuristic approach. The proposed time-scaled heuristic algorithm yields extremely short computational time, which enables production managers to flexibly select proper production strategies and to implement them for different production environments.