A multitasking workforce-constrained flexible job shop scheduling problem: An application from a real-world workshop

The flexible job shop scheduling problem with worker constraints plays a vital role in production scheduling because of workforce flexibility. Existing research assumes that single tasking workers can process one operation simultaneously. However, multitasking workers can be observed in a real-world enterprise, where they can handle multiple operations simultaneously. There is a lack of research on the effect of multitasking workers in flexible job shops. This paper investigates a flexible job-shop scheduling problem considering multitasking workers (FJSP-MW). First, a mixed-integer linear programming model with multitasking worker constraints is constructed to minimize total weighted tardiness (TWT). Second, an operation-sequence and resource-sequence (OSRS) encoding method is proposed to represent the solution space using the OS and RS vectors. Besides, a multitasking decoding method is introduced to decode the OS and RS vectors as a feasible schedule in the objective space. Third, a hybrid algorithm (IGA4MW) is proposed and consists of two aspects: (1) three modified genetic operators are designed for the OS and RS vectors to enhance the exploration ability, and (2) a resource-balanced local search method is presented to improve the exploitation ability. Finally, experiments are conducted on medium and large instances to demonstrate the effectiveness and efficiency of IGA4MW. The case study illustrates that the TWT and makespan of the obtained scheduling solution from IGA4MW are reduced by 15.43% and 41.16%, compared to the original scheduling solution. Furthermore, the performance gain of the resource-balanced local search method increases as the solution space is expanded.