An Energy-Aware Flexible Job-Shop Scheduling Problem with Sequencing Flexibility and Sequence-Dependent Setup Times

The manufacturing panorama is rapidly changing to adjust to satisfy customer demands while addressing concerns over environmental impacts. Hence, this paper proposes an extension of the Flexible Job-Shop Scheduling problem. The extension allows arbitrary precedence relationships between the operations given by a directed acyclic graph. Additionally, it considers setup times that are dependent on the sequence of the jobs as well as the total energy consumption comprised of processing and idle energy. Hence, the problem consists of allocating operations to machines and sequencing them according to precedence relationships and dependent setup times. A multi-objective mixed-integer linear programming model is formulated with the objectives of makespan and total energy consumption minimization. The formulation is solved with the weighted-sum approach. A numerical experiment is performed on five small randomly generated instances to show the model’s applicability. The model allows the incorporation of real-world settings that have been studied independently.