In this paper, a real-time scheduling problem of a dual-resource flexible job shop with robots is studied. Multiple independent robots and their supervised machine sets form their own work cells. First, a mixed integer programming model is established, which considers the scheduling problems of jobs and machines in the work cells, and of jobs between work cells, based on the process plan flexibility. Second, in order to make real-time scheduling decisions, a framework of multi-task multi-agent reinforcement learning based on centralized training and decentralized execution is proposed. Each agent interacts with the environment and completes three decision-making tasks: job sequencing, machine selection, and process planning. In the process of centralized training, the value network is used to evaluate and optimize the policy network to achieve multi-agent cooperation, and the attention mechanism is introduced into the policy network to realize information sharing among multiple tasks. In the process of decentralized execution, each agent performs multiple task decisions through local observations according to the trained policy network. Then, observation, action, and reward are designed. Rewards include global and local rewards, which are decomposed into sub-rewards corresponding to tasks. The reinforcement learning training algorithm is designed based on a double-deep Q-network. Finally, the scheduling simulation environment is derived from benchmarks, and the experimental results show the effectiveness of the proposed method.

This paper studied a class of coupling problems of material assignment, part nesting, kit delivery and parallel machine scheduling. The aim of this paper was to solve the scheduling problem of metal structural part processing and welding assembly with eligibility constraints. A two-stage mixed-integer programming model was constructed. The eligibility constraints took into account the material type of parts and nesting. The objectives were to minimize the makespan, maximize material utilization and minimize the kit delivery metrics (kitting time and numbers of earliness and tardiness of kits). A hierarchical optimization approach was proposed. The scheduling model was solved by using the Gurobi solver in the first stage, and the results were used to constrain the second stage. The second stage of the scheduling model was solved using an improved multi-objective genetic algorithm. Due to the strong coupling relationships among the sorting of parts, the sorting of each profile and the sorting of each material, a hybrid encoding and decoding mode was designed for part sorting with eligibility constraints. Finally, the proposed scheduling approach was applied to actual production cases. The data showed that when the number of components exceeded 300 (the number of parts was about 1500), the material utilization reached 95%. Choosing a suitable number of machines, machine utilization reached 90%. The results demonstrated the effectiveness of the proposed scheduling model and algorithm.

Taking a metal structural part blanking workshop as the application background, this study addresses the challenges of high material variety, long crane feeding travel caused by heterogeneous line-side storage layouts, and frequent machine stoppages due to the limited feeding capacity of a single overhead crane. To this end, an integrated machine–crane dual-resource scheduling model is developed by explicitly considering line-side storage locations. The objective is to minimize the maximum waiting time among all machine tools. Under constraints of material assignment, processing sequence, and the crane’s single-task execution and travel requirements, the storage positions of materials in line-side buffers are jointly optimized. To solve the problem, a genetic algorithm with fitness-value-based crossover is proposed, and a simulated-annealing acceptance criterion is embedded to suppress premature convergence and enhance the ability to escape local optima. Comparative experiments on randomly generated instances show that the proposed algorithm can significantly reduce the maximum waiting time and yield more stable results for medium- and large-scale cases. Furthermore, a simulation based on real production data from an industrial enterprise verifies that, under limited feeding capacity, the proposed method effectively shortens material-waiting time, improves equipment utilization, and enhances production efficiency, demonstrating its effectiveness.

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.