Bi-objective optimization approach for energy aware scheduling considering electricity cost and preventive maintenance using genetic algorithm

In light of various environmental issues regarding electricity generation and usage, several approaches have been suggested to decrease energy usage. One well-known method on the supplier side is time-of-use (TOU) pricing, through which demand on the customer side is controlled by adjusting electricity prices. Several studies have investigated the scheduling problem in such an environment to efficiently handle energy usage from the customer perspective, and have addressed its effectiveness. However, in most energy-aware scheduling problems considering TOU pricing, machine failure is not considered. This is a significant assumption because it implies that machines are available at all times. In this study, we examined a single machine scheduling problem that reflects preventive maintenance under TOU pricing. To solve this problem, a bi-objective mixed-integer non-linear programming model is designed, and a hybrid multi-objective genetic algorithm (HMOGA) is proposed to handle medium- and large-sized problems. In addition, α- and P-improvement methods are proposed to efficiently generate a better Pareto frontier. The performance of the algorithm is compared with that of a non-dominated sorting genetic algorithm (NSGA)-2 to demonstrate the effectiveness of the proposed HMOGA. Numerical experiments showed that the HMOGA yields better outcomes than the NSGA-2 and faster than Baron solver. The major contribution of this study lies in building a trade-off relationship between the total electricity cost and machine unavailability in a TOU pricing environment.