Energy-Aware Production Scheduling with Power-Saving Modes

This study addresses optimization of production processes where machines have high energy consumption. One efficient way to reduce the energy expenses in production is to turn a machine off when it is not being used or switch it into an energy-saving mode. If the production has several machines and production demand that varies in time, the energy saving can be substantial; the cost reduction can be achieved by an appropriate production schedule that could control the switching between the energy modes with respect to the required production volume. Therefore, inspired by real production processes of glass tempering and steel hardening, this paper addresses the scheduling of jobs with release times and deadlines on parallel machines. The objective is to find a schedule of the jobs and a switching between the power modes of the machines so that the total energy consumption is minimized. Moreover, to further generalize the scheduling problem to other production processes, we assume that the processing time of the jobs is mode-dependent, i.e., the processing time of a job depends on the mode in which a machine is operating. The study provides an efficient Branch-and-Price algorithm and compares two approaches (based on Integer Linear Programming and Constraint Programming) for solving the subproblem.