Flexible Job Shop Scheduling Based on Order and Operation Consolidation with Job Hierarchy Constraints

Modern manufacturing enterprises are increasingly transitioning to multi-variety, small-batch production. This shift introduces significant scheduling challenges, particularly due to the job hierarchy constraints inherent in assembling multi-level intermediate parts. Furthermore, non-machining preparation times—such as tool switching, material handling, and equipment standby—significantly impact production efficiency. To address these challenges, this paper investigates the flexible job shop batch scheduling problem by integrating order and operation consolidation under strict job hierarchy constraints. To mathematically formulate the scheduling problem with non-serial operation precedence networks and dynamic batching, we develop a mixed-integer programming model. The primary objective is to simultaneously minimize the maximum completion time (makespan) and total tardiness. To solve this efficiently, an Improved Grey Wolf Optimization (IGWO) algorithm is proposed. The algorithm features a novel two-tier coding scheme tailored for consolidation logic and employs a hybrid population initialization strategy to enhance initial solution quality. Moreover, it improves the standard hunting mechanism, utilizes Variable Neighborhood Search (VNS) for local exploitation, and independently applies a Simulated Annealing (SA) dynamic acceptance mechanism to balance global exploration and local exploitation. Extensive experiments using small-, medium-, and large-scale industrial data from a power station valve manufacturer validate the effectiveness of the proposed model and algorithm in optimizing complex batch scheduling schemes.