An optimal energy-efficient scheduling with processing speed selection and due date constraint in a single-machine environment

To relive the pressure of electricity grid during the peak period, time-of-use (TOU) pricing strategy has been implemented in industries to encourage manufacturers to transfer some processing tasks from peak periods to non-peak periods, and the due date of each job cannot be violated. Under these contexts, this paper addresses a speed-scaling single machine scheduling problem with due date constraint to minimize the total electricity cost (TEC). More precisely, the main innovative works are described as follows: (1) seven critical problem properties (including four theorems and three lemmas) based on different processing time window forms are formally derived; and (2) a property-based genetic algorithm (PGA) with hybrid initialization method is designed according to the characteristics of the studied problem. In the numerical experiments, the Taguchi method of design-of-experiment is employed to seek the optimal combination of four key parameters in PGA. Subsequently, the effectiveness and superiority of the proposed hybrid initialization method and problem properties are separately demonstrated by randomly generated 20 instances. After that, compared with other two traditional scheduling strategies, the proposed energy-efficient strategy can save at least 16% of TEC on average. Next, a relaxation coefficient (CR) is designed to measure the intrinsic link between TEC and the instance parameters (i.e. the due date and normal processing time). Finally, a real case is presented to verify the benefits of the proposed PGA algorithm and variable processing speeds, and the results show that the newly generated scheduling scheme based on the proposed PGA can reduce up to 46.36% of TEC compared with the existing company’s scheduling scheme.