An integrated approach to distributed resource allocation and task scheduling based on work centers

Abstract

The present invention discloses an integrated method for distributed resource allocation and task scheduling based on work centers, specifically relating to the technical field of production and manufacturing resource allocation and task scheduling, including data collection, including order production content and time, processing capacity of each center equipment and transportation time; final inspection process time calculation, based on a multi-factor weighted model, to determine the actual time window of the order; establishing an integrated model for distributed resource allocation and task scheduling, including objective functions and constraints for minimizing maximum completion time and delay penalties; using a particle swarm optimization algorithm to solve the model to obtain an optimal solution; and performing resource allocation and task scheduling based on the optimal solution.

Description

Technical Field

[0001] The present invention relates to the technical field of production and manufacturing resource configuration and task scheduling, and in particular to an integrated method for distributed resource configuration and task scheduling based on a work center. Background Art

[0002] Regarding the distributed workshop scheduling problem, the existing technology (Huang Yingjie, Yao Xifan. Flexible distributed workshop scheduling based on target cascade method and particle swarm algorithm [J]. Journal of Central South University (Natural Science Edition), 2012, 43(01): 151-158.) proposed a flexible distributed workshop scheduling optimization model based on target cascade method (ATC) and particle swarm algorithm. The model is divided into a production planning layer and a workshop scheduling layer. The production planning layer is responsible for parts allocation, and the workshop scheduling layer is responsible for processing path planning, which effectively solves the problem of flexible distributed workshop scheduling. Existing technology (Chen Sanyan, Wang Xuewu, Wang Ye, et al. Multi-population hybrid evolutionary algorithm for solving distributed heterogeneous batch flow mixed flow workshop scheduling problem with process jumping [J]. Journal of East China University of Science and Technology (Natural Science Edition), 2025, 51(02): 228-241. DOI: 10.14135 / j.cnki.1006-3080.20240411001.) A multi-population hybrid evolutionary algorithm (MPHEA) is proposed for the distributed heterogeneous batch flow mixed flow workshop scheduling problem with process jumping. Through the parallel collaborative evolution strategy of the total population and the subpopulation, the optimal The algorithm is designed to optimize the maximum completion time, total flow time, machine waiting time and total weighted advance time and delay time. The experimental results show that the algorithm can effectively balance multiple optimization objectives and obtain high-quality scheduling solutions. The existing technology (Yan Binglong, Ye Chunming. Research on distributed flexible job shop scheduling problem considering worker constraints [J]. Combined Machine Tools and Automation Technology, 2025, (04): 188-194. DOI: 10.13462 / j.cnki.mmtamt.2025.04.036.) is aimed at the distributed flexible job shop scheduling problem with worker constraints (DFJSPWC). A scheduling model with the goal of minimizing the maximum completion time and minimizing the total energy consumption is constructed, and an improved cultural gene algorithm (IMA) is proposed.The algorithm comprehensively considers factory selection, process sorting, machine selection and worker allocation through a four-layer encoding method, and adopts the tight left shift insertion decoding method to improve the convergence speed. At the same time, an adaptive local search method and an elite hierarchical retention strategy are designed. The experimental results show that the algorithm has significant advantages in solving the DFJSPWC problem; Existing technology (Xuan Hua, Xiong Mengying, Cao Ying. Distributed hybrid pipeline rescheduling based on improved grey wolf optimization algorithm [J]. Journal of Zhengzhou University (Engineering Edition), 2025, 46(04): 47-54+99.DOI: 10.13705 / j.issn.1 The distributed workshop scenario studied in this paper consists of multiple heterogeneous factories, each of which has a built-in hybrid assembly line with multiple processes and parallel machines to handle the processing tasks of multiple workpieces. The constraints of machine failure and transportation time are taken into account, and an improved grey wolf optimization algorithm (IGWO) is proposed. Through a three-chain encoding method, a population initialization method based on the NEH heuristic method and random programs, a dual-mode parallel search strategy, and taboo search, the multi-objective optimization problem of minimizing the maximum completion time, total energy consumption, and total delay is effectively solved.

[0003] At present, research on distributed workshop scheduling has made great progress. Related methods mostly focus on the optimization of a specific stage, such as resource allocation or task scheduling, and often rely on more complex modeling structures or advanced algorithm strategies, which makes deployment and application in actual workshop environments difficult. Summary of the Invention

[0004] To this end, the present invention provides an integrated method for distributed resource allocation and task scheduling based on work centers. The present invention is oriented to distributed manufacturing scenarios dominated by work centers, and constructs a scheduling model that takes into account the transportation time between centers, equipment processing performance differences and batch processing requirements, which is closer to the typical task flow and resource utilization characteristics in multi-center systems. Compared with traditional research methods that emphasize algorithm complexity, the present invention pays more attention to the clarity of the model structure and the rationality of the scheduling process, and emphasizes feasibility in engineering practice. This method takes the work center as the basic scheduling unit, and reflects the actual process through a concise and effective modeling strategy, which helps to reduce deployment costs, improve the interpretability and execution efficiency of the scheduling plan, and has good application prospects and promotion value. It solves the technical problem that resource allocation and task scheduling in existing methods fail to effectively coordinate, resulting in insufficient rationality of resource allocation in the production process, and the inability to maximize task scheduling efficiency, thereby reducing overall production efficiency.

[0005] To achieve the above objectives, the present invention provides the following technical solution: an integrated method for distributed resource configuration and task scheduling based on a work center, comprising:

[0006] S1. Data collection, including order production content and time, processing capacity of each center's equipment, and transportation time;

[0007] S2. Final inspection process time calculation: Based on a multi-factor weighted model, determine the actual time window for the order, especially the end time of the time window;

[0008] S3. Establish an integrated model for distributed resource allocation and task scheduling, including the objective function and constraints for minimizing the maximum completion time and delay penalty;

[0009] S4, using particle swarm optimization algorithm to solve the model and obtain the optimal solution;

[0010] S5. Allocate resources and schedule tasks based on the optimal solution.

[0011] Preferably, the data collected by S1 includes artifacts ,center ,equipment ,batch ; For workpiece The size of (one dimension); Centered Equipment The size of (one dimension); For workpiece In the center Equipment processing time; For workpiece The time window start time; For workpiece The end time of the time window; Centered One-way transportation time to and from the main hub.

[0012] Preferably, the final inspection process time is calculated as follows:

[0013] To improve the accuracy of final inspection process time estimation, based on a multi-factor weighted model, the formula is as follows, taking into account the workpiece size and the additional time that may be caused by quality inspection:

[0014]

[0015] Where, Indicates workpiece The time required for the final inspection process; All are weight coefficients; It is the basic processing rate of the final inspection process; It indicates the time reserved for quality inspection or rework, reflecting the uncertainty factor;

[0016] Workpiece The actual time window end time is:

[0017] .

[0018] Preferably, the objective function of the integrated model of distributed resource configuration and task scheduling is as follows:

[0019] ;

[0020] Where, Indicates workpiece Maximum completion time ; For workpiece The delay time, is the penalty coefficient for unit delay;

[0021] The following assumptions are made for this model: each workpiece has an order start time and end time; centers 0-m are equipped with equipment numbered 1-k, each equipment has a certain capacity limit, and processing is carried out according to a fixed batch processing time; each equipment can process any workpiece, but the processing speed is different, that is, the batch processing time of each workpiece on each equipment in each center is different; one-dimensional capacity constraints are considered; order timeouts are allowed, but a certain penalty is imposed; orders are not allowed to be processed earlier than the start time; mixed processing of workpieces within a batch is allowed; equipment is allowed to process in multiple batches; and there is an upper limit on equipment batches.

[0022] A mixed integer programming mathematical model is established with the goal of minimizing the maximum completion time and delay penalty, and the constraints are as follows:

[0023] Each workpiece can only be assigned to one batch of one device in one center, that is:

[0024] ;

[0025] The batch size does not exceed the equipment capacity, that is:

[0026] ;

[0027] The processing time of a batch is the processing time of the workpiece with the longest processing time within the batch, that is:

[0028] ;

[0029] If the batch is not opened, there is no maximum processing time, that is:

[0030] ;

[0031] The completion time of the workpiece = starting time + processing time + transportation time * 2, that is:

[0032] ;

[0033] The definition of maximum completion time is:

[0034] ;

[0035] Batch continuous processing, i.e.:

[0036] ;

[0037] The batch numbers are consecutive, i.e.:

[0038] ;

[0039] Workpieces can only be allocated if the batch is opened, that is:

[0040] ;

[0041] If no workpiece is assigned, the batch cannot be opened to avoid empty batches, that is:

[0042] ;

[0043] The start time of each workpiece must not be earlier than the start time of the time window, that is:

[0044] ;

[0045] The end time of each workpiece must not be later than the end time of the time window, that is:

[0046] ;

[0047] Decision variable constraints, namely:

[0048] ;

[0049] In the above formula, Represented as artifacts Whether to allocate to the center Equipment No. batch; Representation Center Equipment No. Whether the batch is enabled; is the maximum completion time; Representation Center Equipment No. The processing time of the batch; Centered Equipment No. The start time of the batch; Indicates workpiece completion time; For workpiece delay time.

[0050] Preferably, the particle swarm optimization algorithm is as follows:

[0051] S1. Initialize data information, input data including workpiece Collection, Center Collection, equipment Collection, and size parameters of each workpiece , processing time , time window start time and deadline ; At the same time, set the capacity limit of each center equipment , penalty coefficient for delay per unit time and transportation time between centers parameter;

[0052] S2. Construct a two-layer encoding structure. The upper-layer encoding uses a one-dimensional integer vector structure to represent the resource allocation plan for workpieces. The vector length is equal to the number of workpieces, and each element is an integer corresponding to a center-equipment combination. The integers and specific combinations are encoded and decoded through a mapping table. The lower-layer scheduling does not explicitly participate in the evolutionary operation. Instead, it is dynamically generated through heuristic rules during each fitness evaluation phase. The specific steps are as follows: Based on the upper-layer allocation results, the workpieces on the same equipment are sorted by the time window start time and processing time, and batches are divided and the processing sequence is arranged according to the equipment capacity limit, thereby generating a specific and feasible scheduling plan.

[0053] S3. Initialize the population. Use the particle swarm optimization framework to initialize several individual particles. Each individual particle represents a set of resource allocation schemes in the form of an integer vector whose element values ​​meet the preset encoding boundaries. Each particle corresponds to a scheduling scheme search starting point and explores better resource configurations through speed updates and position adjustments during the search process.

[0054] S4. Scheduling evaluation: Decode each particle in the population to determine its corresponding center-device assignment. Based on this assignment, cluster the workpieces by device and divide them into multiple processing batches using a heuristic batch partitioning algorithm. Consider the time window start time and the maximum processing time of the workpiece to determine the start and completion time of each batch. On this basis, record the actual start time, completion time, and delay time of each workpiece to provide support for subsequent objective function calculations.

[0055] S5. Fitness function calculation: Based on the scheduling results of each particle, the objective function value is calculated as the fitness function input. The fitness function adopts a weighted combination form: the weighted sum of the maximum completion time and the total delay time. The smaller the objective function value, the better the scheduling solution.

[0056] S6, Particle swarm evolution operation, in each generation, the evolutionary search process of the particle swarm is realized through the following steps:

[0057] S61, speed update: for each particle, based on its historical optimal position and the current optimal position of the population, combined with inertia weight, self-learning factor and group learning factor, update the speed of its current position;

[0058] S62, position update: the particle adjusts its current position (i.e., resource allocation vector) according to the updated velocity, and performs boundary clipping and discretization on the result to ensure that it remains in the valid coding space;

[0059] S63, scheduling evaluation and fitness update, re-decoding resource allocation, scheduling construction and fitness calculation for the updated position, and updating the individual historical optimal position and group optimal solution;

[0060] S7, iteration and optimal solution output, repeat the scheduling evaluation and particle evolution operations until the set maximum number of iterations is reached or the optimization process is stopped after the convergence criterion is met; finally, the individual with the smallest objective function value is output, and its corresponding resource allocation and batch scheduling solution is the global optimal scheduling result.

[0061] Preferably, the global optimal scheduling result is analyzed as follows:

[0062] Based on the optimal scheduling plan obtained by the particle swarm algorithm, the workshop organizes efficient production and can clearly determine whether each workpiece meets the time window requirements, whether it is delivered on time, and whether there are delays. This provides a basis for analyzing the feasibility and delivery controllability of the production plan, and at the same time assists managers in capacity assessment, bottleneck identification, and resource optimization allocation decisions.

[0063] Beneficial effects:

[0064] 1. This invention is aimed at manufacturing systems with multiple work centers and constructs a scheduling model that takes into account the transportation time and equipment processing performance differences between centers. It can more accurately reflect the task flow and resource load characteristics in actual production, and effectively improve the executability of the scheduling plan and the system response speed.

[0065] 2. In order to improve the scheduling model's ability to match the process rhythm, the present invention further introduces a final inspection time estimation model based on multi-factor weighting on the basis of integrated modeling of resource allocation and task scheduling. This model comprehensively considers the workpiece size and potential rework reserve time in quality inspection, constructs a more accurate workpiece time window constraint, and thus dynamically corrects the feasible scheduling space to ensure the coordination and accuracy between each process link. At the same time, through the orderly connection of the batch division strategy and the final inspection process, under the premise of meeting the time window, equipment capacity and detection resource constraints, the rationality of task organization and the efficiency of workpiece circulation are improved, and the feasibility of the scheduling plan and the degree of fit with actual production are further enhanced.

[0066] 3. The scheduling scenario design proposed in this invention is concise and logically clear, which is convenient for docking with the actual process flow, reduces deployment costs, improves the interpretability of the solution, and can be quickly applied in the actual workshop environment. It has good engineering practice value and promotion potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 A flow chart of the integrated method for distributed resource configuration and task scheduling based on work centers provided by the present invention;

[0068] Figure 2 A schematic diagram of a workshop scene provided by the present invention;

[0069] Figure 3 This is a flow chart of the particle swarm algorithm provided by the present invention for solving the optimal production scheduling solution. DETAILED DESCRIPTION

[0070] The following describes the implementation of the present invention using specific embodiments. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. Obviously, the embodiments described are only a portion of the present invention, not all of it. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0071] Example: Please refer to Figure 1-Figure 3 This embodiment proposes an integrated method for distributed resource allocation and task scheduling based on work centers. By rationally allocating workpieces between centers and equipment, and combining a collaborative processing mechanism of batch division and scheduling optimization, it not only effectively improves resource utilization efficiency and overall task scheduling efficiency, but also provides a practical and rapidly deployable solution for workshop production. Please refer to Figure 1 , the method comprises the following steps:

[0072] S1. Data collection, including order production content and time, processing capacity of each center equipment, transportation time, etc.; specific data information includes workpiece ,center ,equipment ,batch ; Workpiece The size (one dimension); the center Equipment Size (one-dimensional) Workpiece In the center Equipment Processing time Workpiece The time window start time Workpiece The time window end time ;center One-way transportation time to the main center .

[0073] S2. Final inspection process time calculation: Based on a multi-factor weighted model, determine the actual time window for the order, especially the end time of the time window;

[0074] S3. Establish an integrated model for distributed resource allocation and task scheduling, including the objective function and constraints for minimizing the maximum completion time and delay penalty. For specific scenarios, please refer to Figure 2 ;

[0075] S4. Use particle swarm optimization to find the optimal solution for the model. Please refer to Figure 3 ;

[0076] S5. Allocate resources and schedule tasks based on the optimal solution.

[0077] Based on specific production information, this method pre-processes the actual order time window, rationally establishes an objective function that minimizes the maximum completion time and delay penalty, and uses a particle swarm algorithm to solve the problem. This method derives the optimal allocation plan for workshop production, providing a reliable resource allocation and task scheduling solution for workshop production. Furthermore, this embodiment constructs a distributed workshop manufacturing example and incorporates the method of this invention for production scheduling.

[0078] A production workshop has one central work center and three sub-work centers, each equipped with four production machines. All machines are batch processors, with varying processing efficiency. Furthermore, there is a certain amount of transport time between the central work center and each sub-center: the one-way transport time between the central work center and sub-center 1 is 2 time units, 1.8 time units to sub-center 2, and 1.5 time units to sub-center 3. The workshop currently accepts a processing order for a batch of 30 workpieces. Each workpiece has specific dimensional parameters (calculated based on one dimension), a time when processing can begin (i.e., the start processing window), and a maximum completion time (i.e., the expected delivery time). Given that all workpieces undergo final inspection after completing routine processing, sufficient time must be reserved for quality inspection and potential rework to ensure that the final inspection process can be completed before delivery. The number of dimensions that can be processed per unit time in the final inspection process is 10, with a weight of 0.6. The time for quality inspection and potential rework is 2, with a weight of 0.4. Each device has a limited maximum carrying capacity (measured in size) and supports parallel scheduling of up to 5 batches of tasks. Detailed information such as the relevant workpiece dimensions, start and end times, and equipment capacity are shown in Tables 1 and 2. The processing time of each workpiece on different central equipment varies. Considering the large data dimension, the processing time in this embodiment is simulated by generating random numbers within the range of 3 to 6 time units. The data in actual production can be recorded and called into the database. In addition, in order to reflect the timeliness requirements in production scheduling, the system sets a penalty mechanism for overdue delivery of workpieces, charging a penalty cost of 0.5 per unit of delay time. It is now necessary to solve how to arrange equipment and schedule tasks in workshop production so that production can be completed faster within the delivery period.

[0079] Table 1 Capacity data of each device in each center

[0080]

[0081] Table 2 Workpiece size and time window information

[0082]

[0083] According to the above order deadline, the actual end time of the processing time window needs to be solved according to the final inspection time described in step S2 of the present invention, as follows:

[0084] To improve the accuracy of the final inspection process time estimation, the present invention is based on a multi-factor weighted time calculation model that comprehensively considers the workpiece size and the additional time that may be caused by quality inspection. The formula is as follows:

[0085]

[0086] Where, Indicates workpiece The time required for the final inspection process; All are weight coefficients; It is the basic processing rate of the final inspection process; It indicates the time reserved for quality inspection or rework, reflecting the uncertainty factor.

[0087] Therefore, the workpiece The actual time window end time is:

[0088]

[0089] According to the calculation formula, the end time of the actual processing time window of the workpiece is solved as shown in Table 3:

[0090] Table 3 Workpiece actual processing time window information

[0091]

[0092] According to the above information, the particle swarm algorithm described in step S4 of the present invention can be used to solve the problem, as follows:

[0093] S1. Initialize data information, input data including workpiece Collection, Center Collection, equipment Collection, and size parameters of each workpiece , processing time , time window start time and deadline ; At the same time, set the capacity limit of each center equipment , penalty coefficient for delay per unit time and transportation time between centers parameter;

[0094] S2. Construct a two-layer coding structure. The upper-layer coding uses a one-dimensional integer vector structure to represent the resource allocation plan for the workpiece. The vector length is equal to the number of workpieces. Each element is an integer, corresponding to a center-equipment combination. The integers and specific combinations are encoded and decoded through a mapping table. The lower-layer scheduling does not explicitly participate in the evolutionary operation, but is dynamically generated through heuristic rules in each fitness evaluation phase. The specific steps are: according to the upper-layer allocation results, the workpieces on the same equipment are sorted according to the time window start time and processing time, and the batches are divided and the processing sequence is arranged according to the equipment capacity limit, so as to generate a specific and feasible scheduling plan;

[0095] S3. Initialize the population. Use the particle swarm optimization framework to initialize several individual particles. Each individual particle represents a set of resource allocation schemes in the form of an integer vector whose element values ​​meet the preset encoding boundaries. Each particle corresponds to a scheduling scheme search starting point and explores better resource configurations through speed updates and position adjustments during the search process.

[0096] S4. Scheduling evaluation: Decode each individual particle in the population to determine its corresponding center-device assignment. Based on this assignment, cluster workpieces by device and divide them into multiple processing batches using a heuristic batch partitioning algorithm. Consider the time window start time and the maximum processing time of the workpiece to determine the start and completion time of each batch. On this basis, record the actual start time, completion time, and delay time of each workpiece to provide support for subsequent objective function calculations.

[0097] S5. Fitness function calculation: Based on the scheduling results of each particle, the objective function value is calculated as the fitness function input. The fitness function adopts a weighted combination form: the weighted sum of the maximum completion time and the total delay time. The smaller the objective function value, the better the scheduling solution.

[0098] S6, Particle swarm evolution operation, in each generation, the evolutionary search process of the particle swarm is realized through the following steps:

[0099] S61, speed update: for each particle, based on its historical optimal position and the current optimal position of the population, combined with inertia weight, self-learning factor and group learning factor, update the speed of its current position;

[0100] S62, position update: the particle adjusts its current position (i.e., resource allocation vector) according to the updated velocity, and performs boundary clipping and discretization on the result to ensure that it remains in the valid coding space;

[0101] S63, scheduling evaluation and fitness update, re-decoding resource allocation, scheduling construction and fitness calculation for the updated position, and updating the individual historical optimal position and group optimal solution;

[0102] S7, iteration and optimal solution output, repeat the scheduling evaluation and particle evolution operations until the set maximum number of iterations is reached or the optimization process is stopped after the convergence criterion is met; finally, the individual with the smallest objective function value is output, and its corresponding resource allocation and batch scheduling solution is the global optimal scheduling result.

[0103] According to the above algorithm steps and specific data information, the output results are shown in Table 4 and Table 5:

[0104] Table 4 Workpiece processing time details

[0105]

[0106] Table 5 Workpiece production allocation details

[0107]

[0108] The algorithm solves the problem and finds that the minimum maximum completion time is 12 time units, and there is no delay, and all tasks are completed within the delivery deadline.

[0109] In summary, the present invention is based on an integrated method for distributed resource allocation and task scheduling based on the work center. It establishes a model based on the problem scenario, with the goal of minimizing the maximum completion time and delay penalty. It also uses the particle swarm optimization algorithm to construct a two-layer encoding to find the optimal solution to the problem, minimize production scheduling time, and effectively improve the production efficiency of the workshop and make rational use of resources. Therefore, the scheduling scenario design proposed by the present invention is concise and logically clear, which is convenient for docking with the actual process flow, reducing deployment costs, improving the interpretability of the solution, and can be quickly applied in the actual workshop environment. It has good engineering practice value and promotion potential.

[0110] Those skilled in the art will appreciate that all or part of the steps in the above-described embodiment methods can be accomplished by instructing related hardware through a program. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0111] Although the present invention has been described in detail above using general descriptions and specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made thereto. Therefore, such modifications and improvements, without departing from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. An integrated method of distributed resource allocation and task scheduling based on work centers, characterized by: include: S1. Data collection, including order production content and time, processing capacity of each center equipment and transportation time, including workpiece ,center ,equipment ,batch ; For workpiece size; Centered Equipment size; For workpiece In the center Equipment processing time; For workpiece The time window start time; For workpiece The end time of the time window; Centered One-way transportation time to and from the main hub; S2. Final inspection process time calculation: Based on a multi-factor weighted model, determine the actual time window for the order; The final inspection process time is calculated as follows: Based on a multi-factor weighted model, taking into account the workpiece size and the additional time required for quality inspection, the formula is as follows: ； Where, Indicates workpiece The time required for the final inspection process; All are weight coefficients; It is the basic processing rate of the final inspection process; Indicates the time reserved for quality inspection or rework; Workpiece The actual time window end time is: ； S3. Establish an integrated model for distributed resource allocation and task scheduling, including the objective function and constraints for minimizing the maximum completion time and delay penalty; The objective function of the integrated model of distributed resource configuration and task scheduling is as follows: ； Where, Indicates workpiece Maximum completion time ; For workpiece The delay time, is the penalty coefficient for unit delay; The constraints are as follows: Each workpiece can only be assigned to one batch of one device in one center, that is: ； The batch size does not exceed the equipment capacity, that is: ； The processing time of a batch is the processing time of the workpiece with the longest processing time within the batch, that is: ； If the batch is not opened, there is no maximum processing time, that is: ； The completion time of the workpiece = starting time + processing time + transportation time * 2, that is: ； The definition of maximum completion time is: ； Batch continuous processing, i.e.: ； The batch numbers are consecutive, i.e.: ； Workpieces can only be allocated if the batch is opened, that is: ； If no workpiece is assigned, the batch cannot be opened to avoid empty batches, that is: ； The start time of each workpiece must not be earlier than the start time of the time window, that is: ； The end time of each workpiece must not be later than the end time of the time window, that is: ； Decision variable constraints, namely: ； Represented as artifacts Whether to allocate to the center Equipment No. batch; Representation Center Equipment No. Whether the batch is enabled; is the maximum completion time; Representation Center Equipment No. The processing time of the batch; Centered Equipment No. The start time of the batch; Indicates workpiece completion time; For workpiece Delay time; S4, using particle swarm optimization algorithm to solve the model and obtain the optimal solution; S5. Allocate resources and schedule tasks based on the optimal solution.

2. The integrated method for distributed resource configuration and task scheduling based on work centers according to claim 1 is characterized by: The particle swarm optimization algorithm is as follows: S1. Initialize data information, input data including workpiece Collection, Center Collection, equipment Collection, and size parameters of each workpiece , processing time , time window start time and deadline ; At the same time, set the capacity limit of each center equipment , penalty coefficient for delay per unit time and transportation time between centers parameter; S2. Construct a two-layer coding structure. The upper layer uses a one-dimensional integer vector structure to represent the resource allocation plan of the workpiece. The vector length is equal to the number of workpieces. Each element is an integer corresponding to a center-device combination. The integers and specific combinations are encoded and decoded using a mapping table. The lower-level scheduling does not explicitly participate in the evolutionary operation. Instead, it is dynamically generated through heuristic rules during each fitness evaluation phase. The specific steps are as follows: based on the upper-level allocation results, the workpieces on the same equipment are sorted by the time window start time and processing time, and batches are divided and the processing sequence is arranged according to the equipment capacity limit, thus generating a specific and feasible scheduling plan; S3. Initialize the population. Use the particle swarm optimization framework to initialize several individual particles. Each individual particle represents a set of resource allocation schemes in the form of an integer vector whose element values ​​meet the preset encoding boundaries. Each particle corresponds to a scheduling scheme search starting point and explores better resource configurations through speed updates and position adjustments during the search process. S4, Scheduling Evaluation: Decode each particle in the population to determine its corresponding center-device assignment. Based on this assignment, the workpieces are clustered by device and divided into multiple processing batches using a heuristic batch partitioning algorithm. The start and completion times of each batch are determined by considering the time window start time and the maximum processing time of the workpieces. On this basis, the actual start time, completion time and delay time of each workpiece are recorded to provide support for subsequent objective function calculation; S5. Fitness function calculation: Based on the scheduling results of each particle, the objective function value is calculated as the fitness function input. The fitness function adopts a weighted combination form: the weighted sum of the maximum completion time and the total delay time. The smaller the objective function value, the better the scheduling solution. S6, particle swarm evolution operation, in each generation, the particle swarm evolution search process is realized through S61-S63: S61, speed update: for each particle, based on its historical optimal position and the current optimal position of the population, combined with inertia weight, self-learning factor and group learning factor, update the speed of its current position; S62, position update: the particle adjusts its current position according to the updated velocity, i.e., the resource allocation vector, and performs boundary clipping and discretization on the result to ensure that it remains in the valid coding space; S63, scheduling evaluation and fitness update, re-decoding resource allocation, scheduling construction and fitness calculation for the updated position, and updating the individual historical optimal position and group optimal solution; S7, iteration and optimal solution output, repeat the scheduling evaluation and particle evolution operations until the set maximum number of iterations is reached or the optimization process is stopped after the convergence criterion is met; finally, the individual with the smallest objective function value is output, and its corresponding resource allocation and batch scheduling solution is the global optimal scheduling result.

3. The integrated method for distributed resource allocation and task scheduling based on work centers according to claim 2 is characterized by: The analysis of the global optimal scheduling results is as follows: Based on the optimal scheduling plan obtained by the particle swarm algorithm, the workshop organizes efficient production and can clearly determine whether each workpiece meets the time window requirements, whether it is delivered on time, and whether there are delays. This provides a basis for analyzing the feasibility and delivery controllability of the production plan, and at the same time assists managers in capacity assessment, bottleneck identification, and resource optimization allocation decisions.

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