Single-machine scheduling with energy generation and storage systems

This paper considers a single-machine scheduling problem with sequence-dependent setup times and energy-generation and storage systems. Each job requires a sequence-dependent setup to be processed on the machine, and both setup and processing of the job require job-dependent amounts of energy. The energy consumed by the machine can be bought from an Electric Power Company (EPC) or generated by own Distributed Energy Resource (DER), such as solar photovoltaic or wind, and the energy can be stored in an Energy Storage System (ESS). The objective is to minimise the total cost, the sum of production cost depending on makespan and energy cost by considering energy usage from the EPC, DER and ESS. For the problem, a mathematical programming model is first derived by using period-based indexes. Then, a hybrid genetic algorithm, which adds appropriate idle times between jobs and determines an efficient energy schedule by storing some energy during less expensive periods into the ESS for later use in high-price periods, is developed. Finally, computational experiments show that the proposed algorithm provides effective solutions, and which component of the total cost affects the performance the most, how effective adding idle times between jobs is, and how much cost can be saved by having a DER and ESS.