A Three-Machine Flowshop Scheduling Problem with Linear Fatigue Effect

Highly customized requirements in smart manufacturing result in the unavoidable manual execution of complex operational procedures. Physical and mental fatigue from long work periods for assembly-line operators induces production issues, such as defective work-in-processes or equipment failure. An effective production schedule should account for worker fatigue. This study investigates a three-machine flowshop scheduling problem with the objective of makespan minimization, in which a linear fatigue effect function provides an approximate mathematical representation of fatigue and recovery processes in workers. A mixed integer programming (MIP) model is developed to optimize the integration of automated and human-operated production in manufacturing systems. Given its NP-hardness, an improved tabu search (ITS) algorithm is designed to obtain high-quality solutions, incorporating multiple initial solutions, a well-designed encoding-decoding strategy, and a tabu-based adaptive search mechanism to enhance efficiency. Numerical simulations indicate the veracity of the MIP model and the effectiveness of the ITS algorithm.