Energy-efficient single-machine scheduling problem with controllable job processing times under differential electricity pricing

Abstract The framework of Industry 3.5 has stimulated the development of smart manufacturing systems that efficiently utilize available resources, including energy; this has led to disruptive innovations in the paradigm of manufacturing systems. The key aim of daily planning and scheduling systems is to maximize productivity by optimizing resource allocation in an organization. This study addresses the energy-efficient single-machine scheduling problem in which the job processing time depends on the quantity of allocated resources and the resource allocation cost is uncertain due to differential electricity pricing. The described problem must respond to the three prominent aspects of Industry 3.5: total resource management, digital decision-making, and smart manufacturing. To meet the total resource management and smart manufacturing requirements, a mixed-integer programming model is developed to determine the operation status of the single machine (i.e., “on” or “idle”) with variable electricity costs, assigned job processing times for time periods, and resource allocation quantities to reduce job processing times. The objective is to minimize the total energy consumption cost by considering both financial (i.e., budget for resource allocation) and environmental constraints (i.e., carbon footprint threshold). This study proposes a type-2 fuzzy control approach integrated with a genetic algorithm (GA), which could be implemented in a decision-support system, thus responding to the digital decision-making requirements of Industry 3.5. The GA is utilized to re-optimize the output of the type-2 fuzzy controller to provide an effective scheduling solution. Our experimental results indicate a 4.20% reduction in the total energy consumption cost compared to the GA approach without controllable processing times. The proposed algorithm can efficiently address the studied problem on a large scale (approximately 200 jobs), where the average computational time required is less than 1 h.

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