This study considers a flexible job-shop scheduling problem where energy cost savings are the primary objective and where the classical objective of the minimization of the make-span is replaced by the satisfaction of due times for each job. An original two-level mixed-integer formulation of this optimization problem is proposed, where the processed flows of material and their timing are explicitly considered. Its exact solution is discussed, and, considering its computational complexity, a comprehensive heuristic, balancing energy performance and due time constraint satisfaction, is developed to provide acceptable solutions in polynomial time to the minimum-energy flexible job-shop scheduling problem, even when considering its dynamic environment. The proposed approach is illustrated through a small-scale example.
