Scheduling on Dedicated Machines with Energy Consumption Limit

This work studies a problem of scheduling non-preemptive independent jobs on dedicated machines while considering an energy consumption limit. The problem is motivated by energy-demanding production processes, such as glass tempering and steel hardening, in which a material is heated to high temperature in furnaces. The production companies have contracts with electric utilities that specify a maximum energy consumption limit. If the heating in the furnaces is not planned carefully, the energy spikes overshoot the energy consumption limit, and the companies must pay large penalty fees. In this paper, we propose two exact methods that find schedules with the minimum makespan such that the energy limit is satisfied. The first proposed method is a Constraint Programming model and the second one finds the optimal solution by iteratively re-solving a Mixed Integer Linear Programming model with a decreasing scheduling horizon. The iterative algorithm exploits the fact that the start times do not need to be modeled explicitly, which leads to an efficient method for solving instances with a higher number of shorter jobs. The experimental results show that our methods outperform an adapted approach from the literature for a related problem.