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This study addresses the low production efficiency in manufacturing enterprises caused by the diversification of order products, small batches, and frequent production changeovers. Focusing on minimizing the makespan, this study establishes a Flexible Job-Shop Scheduling Problem (FJSP) model incorporating machine setup and workpiece transportation times, and proposes an improved sparrow search algorithm to effectively solve the problem. Based on the sparrow search algorithm, this study proposes a novel location update strategy that expands the search direction in each dimension and strengthens each individual’s local search capability. In addition, a critical-path-based neighborhood search strategy is introduced to enhance individual search efficiency, and an earliest completion time priority rule is employed during population initialization to further improve solution quality. Several experiments are conducted to validate the effectiveness of the improved strategy, and the results are compared with those obtained using the particle swarm optimization and gray wolf optimization algorithms to demonstrate the efficiency of the proposed model and algorithm. The improved sparrow search algorithm can effectively generate feasible solutions for large-scale problems, provide practical manufacturing scheduling schemes, and enhance the production efficiency of manufacturing enterprises.