Cooperative scheduling method based on schedule optimization

Abstract

The invention discloses a collaborative scheduling method based on schedule optimization, and relates to the technical field of production scheduling, and the method comprises the following steps: decomposing a production task into a plurality of subtasks according to process requirements, and determining the priority of each subtask; carrying out resource allocation according to a pre-constructed resource allocation model in combination with the dependency relationship among the production links and the resource constraint conditions; determining a key path of the production task, arranging a production schedule, and calculating the length of the key path; the execution process is adjusted in time by establishing a collaborative scheduling model; and according to the length of the critical path and the collaborative scheduling model, based on fuzzy reasoning, evaluating a scheduling effect, and continuously optimizing a scheduling scheme. The problems that in an existing scheduling method, response is slow, a scheduling scheme cannot be adjusted in time, production is interrupted and delayed, and the scheduling effect is far lower than expectation are solved, and the method aims at breaking through existing limitation and achieving efficient configuration of production resources and collaborative optimization of the production process.

Description

Technical Field

[0001] This invention relates to the field of production scheduling technology, and more specifically, to a collaborative scheduling method based on schedule optimization. Background Technology

[0002] In the manufacturing industry, scheduling optimization is a key factor in improving production efficiency and reducing costs. Schedule-based production scheduling rationally allocates and schedules various resources (such as machines, personnel, and raw materials) in the production process by optimizing algorithms, constraints, and task requirements. This ensures that while meeting production needs, resource utilization and production efficiency are maximized, while minimizing production time and costs. Traditional production scheduling methods are usually based on manual allocation or simple rules, failing to fully consider the constraints of production resources and the synergistic effects between different stages. Modern production systems often involve complex production processes, multiple production stages, and limited resources, posing significant challenges to traditional scheduling methods. Efficient scheduling strategies are a core element for enterprises to achieve cost reduction, efficiency improvement, and enhanced competitiveness. Traditional production scheduling methods mainly rely on manual experience or simple rules, such as allocating tasks according to order sequence or equipment availability. This may meet basic needs in the early stages when production processes are simple and resources are abundant. However, with the diversification of market demands and the innovation of production technologies, modern production systems have become extremely complex.

[0003] Shortcomings of existing technology: Currently, production scheduling methods based on optimization algorithms are gradually being applied to address the aforementioned challenges. However, existing methods have significant shortcomings in multi-objective optimization and dynamic adjustment. In multi-objective optimization, it is difficult to achieve a balance between multiple objectives such as production efficiency, cost control, and product quality, often resulting in compromises. For example, pursuing production efficiency may lead to a significant increase in costs. Regarding dynamic adjustment, existing scheduling methods are slow to respond to unforeseen changes during production, such as delays in raw material supply, sudden equipment failures, and temporary order changes, failing to adjust scheduling plans in a timely manner, leading to production interruptions, delays, and scheduling results far below expectations. Most existing scheduling methods focus on single-task scheduling, lacking collaborative optimization across multiple tasks and resources. Schedule optimization, on the other hand, can dynamically adjust scheduling plans based on different task requirements and resource conditions, thereby achieving a more efficient and economical scheduling process. Therefore, proposing a collaborative scheduling method based on schedule optimization is of great significance for solving the problems of resource waste and inaccurate scheduling in existing technologies. Thus, developing a collaborative scheduling method based on schedule optimization is urgently needed, aiming to overcome existing limitations and achieve efficient allocation of production resources and collaborative optimization of the production process.

[0004] To address the above problems, this invention proposes a solution. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a collaborative scheduling method based on schedule optimization, thereby solving the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: The collaborative scheduling method based on schedule optimization includes the following steps: The production task is broken down into multiple sub-tasks according to the process requirements, and the priority of each sub-task is determined by the Analytic Hierarchy Process (AHP). Based on the determined sub-task priorities and real-time resource availability, combined with the dependencies between each production stage and resource constraints, resources are allocated according to a pre-built resource allocation model. The critical path method (CPM) is used to determine the critical path of production tasks, the production schedule is arranged according to the critical path, and the length of the critical path is calculated. During the production process, the execution status of each sub-task is monitored in real time, and the execution process is adjusted in a timely manner by establishing a collaborative scheduling model based on the monitoring results of the sub-tasks. Based on the length of the critical path and the collaborative scheduling model, the scheduling effect is evaluated using fuzzy reasoning, and the scheduling scheme is continuously optimized.

[0007] In a preferred embodiment, the process of determining the priority of each subtask is as follows: The production task T is broken down into n sub-tasks according to the process requirements. , ,... ; For n subtasks, construct a judgment matrix. ,in This indicates the importance of subtask i relative to subtask j; The largest eigenvalue of the judgment matrix A is calculated using the eigenvalue method. And its corresponding feature vector W, after normalization, yields the priority weight vector of the subtask. The calculation formula is: ; In the formula These are the normalized eigenvectors. It is the i-th element in the feature vector; The priority weight vector of the subtask is obtained from the normalized feature vector, and the priority of each subtask is determined.

[0008] In a preferred embodiment, the resource constraint acquisition process is as follows: During resource allocation, a limit on the total amount of resources must be met. That is, for any time t and resource j, the total amount of resources allocated to all subtasks cannot exceed the real-time available amount of that resource, expressed by the formula: ,in It is the resource requirement of subtask i for resource j at time t. For decision variables, a value of 1 indicates that resource j is allocated to subtask i at time t, and a value of 0 indicates that no allocation is made.

[0009] In a preferred embodiment, the resource allocation process according to the pre-built resource allocation model is as follows: Based on a pre-built resource allocation model, for each subtask In the initial resource allocation, the highest priority subtask is considered first, and the resources required to meet its startup conditions are allocated to it. After allocating resources to each subtask, check whether all preceding tasks of that subtask have been completed, and whether the allocation violates resource constraints. If there are incomplete predecessor tasks, or if the resource allocation exceeds the resource constraints, the resource allocation of the subtask will be suspended until all its predecessor tasks are completed, and the allocation scheme will be readjusted. The above allocation and checking process is repeated for each subtask in descending order of priority, until all subtasks are allocated resources that meet their execution conditions, or all resources have been allocated.

[0010] In a preferred embodiment, the critical path acquisition process for the production task is as follows: Define the duration of each production subtask And the sequential relationship between subtasks, that is, determining the predecessor and successor tasks of each subtask; And obtain the earliest start time (ES) and earliest finish time (EF) for each task, as follows: For the initial task (a task without a predecessor task). ; For other tasks i, Where k represents all the immediate predecessors of task i, and the earliest completion time of task i is... ; And obtain the latest start time (LS) and latest finish time (LF) for each task, as follows: For tasks that have ended (tasks with no successor tasks), LF = EF; For other tasks i, , where k are all the immediate successors of task i; Latest start time of task i ; When the task is satisfied and When these tasks are combined, the path is called the critical path.

[0011] In a preferred embodiment, the length of the critical path is calculated as follows: The start and end times of tasks on the critical path are scheduled sequentially according to their order of occurrence. Tasks on non-critical paths are scheduled based on the completion times of their predecessors and resource availability. The length L of the critical path is equal to the sum of the durations of all tasks on the critical path, as shown in the formula: Specify the duration of each production subtask. .

[0012] In a preferred embodiment, the process of real-time monitoring of the execution status of each subtask is as follows: Collect execution progress data for each sub-task and the usage of various resources, and compare and analyze the actual collected data with the pre-set production plan and resource allocation scheme; Compare the actual start time of the subtask with the planned start time. If the actual start time is later than the planned start time, there is a risk of task delay. Comparing the actual allocation of resources with the planned allocation, if the actual allocation exceeds the planned allocation or the remaining resources are insufficient, resource conflicts will occur.

[0013] In a preferred embodiment, the process of establishing the cooperative scheduling model is as follows: When task delays or resource conflicts occur, new decision variables are introduced. , This represents the decision to reallocate resource j to subtask i at time t. Represents redistribution, This means no redistribution; A collaborative scheduling model is established based on task delay time and resource reallocation amount, with the specific formula as follows: In the formula, C is the objective function of the cooperative scheduling model, which is to minimize the adjustment cost, and t is the actual execution time of the task. It is the earliest completion time of the task. It is a weighting factor for task delay time. It refers to the amount of resources allocated. It is the amount of resources redistributed. It is a resource allocation weighting factor.

[0014] In a preferred embodiment, the process of evaluating the scheduling effect based on fuzzy inference according to the length of the critical path and the collaborative scheduling model is as follows: The length of the critical path and the objective function of the collaborative scheduling model are defined as input variables, and they are divided into different fuzzy sets respectively. The scheduling effect is defined as an output variable, which is then divided into fuzzy sets. Formulate fuzzy rules to describe the impact of the critical path length and the objective function of the collaborative scheduling model on the scheduling effect; Fuzzy reasoning is performed based on fuzzy rules to evaluate scheduling effectiveness.

[0015] In a preferred embodiment, the process of continuously optimizing the scheduling scheme is as follows: If the scheduling effect is lower than the preset threshold, it means that the scheduling effect is not good. It is necessary to continuously track the changes in the critical path, adjust the resource allocation to shorten the new critical path, and optimize the resource scheduling of each task according to the collaborative scheduling model, so as to achieve the optimization of scheduling. If the scheduling effect is higher than the preset threshold, it means that the scheduling effect is good and no optimization is needed.

[0016] The technical effects and advantages of the collaborative scheduling method based on schedule optimization in this invention are as follows: 1. This invention maximizes resource utilization efficiency and avoids resource idleness and waste through the rational scheduling and optimization of multiple tasks or resources. When multiple tasks are running in parallel, the system can rationally allocate time and space resources according to the priority and resource requirements of each task, ensuring that each task is processed in a timely manner. The collaborative scheduling method, by analyzing the relationships between tasks (such as time windows and dependencies), can effectively avoid task conflicts and ensure that tasks can be completed smoothly at different times or with the same resources. This optimization makes the scheduling system more intelligent and accurate, reducing human intervention and errors. By optimizing the scheduling strategy, task waiting time can be reduced, and task execution efficiency can be improved. The scheduling system can automatically adjust according to factors such as task priority, time requirements, and dependencies, ensuring that tasks are processed according to the optimal path and time frame, reducing overall completion time.

[0017] 2. This invention, through continuous monitoring and feedback, promptly identifies time delays and resource overload issues on critical paths during scheduling and takes corrective measures. It dynamically adapts to different situations, such as task increases or decreases, resource changes, and unforeseen events, allowing for flexible adjustments. This enables the scheduling system to operate efficiently even in the face of change, enhancing its adaptability and flexibility. The collaborative scheduling method for schedule optimization helps achieve cost optimization. By reducing resource waste, improving efficiency, and avoiding unnecessary overtime or resource occupation, it can reduce enterprise operating costs to a certain extent, especially in manufacturing or service industries where resource conservation directly impacts cost control. In coordination and cooperation among multiple participants (such as teams, departments, and equipment), collaborative scheduling can help all parties achieve more efficient collaboration. Through a centralized scheduling platform, all parties can understand resource and task status in real time, improving information flow speed, reducing communication barriers, and thus improving overall collaborative efficiency. This not only reduces the need for manual operation but also allows the system to autonomously adjust, providing efficient and accurate scheduling solutions, achieving system intelligence and automation. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the collaborative scheduling method based on schedule optimization according to the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0020] Example 1, Figure 1 The present invention presents a collaborative scheduling method based on schedule optimization.

[0021] S10, according to the process requirements, the production task is decomposed into multiple sub-tasks, and the priority of each sub-task is determined by the Analytic Hierarchy Process (AHP). The production task T is broken down into n sub-tasks according to the process requirements. , ,... ; For n subtasks, construct a judgment matrix. ,in This indicates the importance of subtask i relative to subtask j; The largest eigenvalue of the judgment matrix A is calculated using the eigenvalue method. And its corresponding feature vector W, after normalization, yields the priority weight vector of the subtask. The calculation formula is: ; In the formula These are the normalized eigenvectors. It is the i-th element in the feature vector; The priority weight vector of the subtask is obtained from the normalized feature vector, and the priority of each subtask is determined.

[0022] S20: Based on the determined sub-task priorities and real-time resource availability, combined with the dependencies between production stages and resource constraints, resources are allocated according to a pre-built resource allocation model. Obtain the total amount of various resources currently available for production. Let the real-time availability of resource j be... , ; Clearly understand the order of subtasks, i.e., if subtasks It is a subtask The immediate task, then only After completion, Only then can we begin; During resource allocation, a limit on the total amount of resources must be met. That is, for any time t and resource j, the total amount of resources allocated to all subtasks cannot exceed the real-time available amount of that resource. This can be expressed by the formula: ,in It is the resource requirement of subtask i for resource j at time t. For decision variables, a value of 1 indicates that resource j is allocated to subtask i at time t, and a value of 0 indicates that no allocation is made. Based on a pre-built resource allocation model, for each subtask In the initial resource allocation, the highest priority subtask is considered first, and the resources required to meet its startup conditions are allocated to it. After allocating resources to each subtask, check whether all preceding tasks of that subtask have been completed, and whether the allocation violates resource constraints. If there are incomplete predecessor tasks, or if the resource allocation exceeds the resource constraints, the resource allocation of the subtask will be suspended until all its predecessor tasks are completed, and the allocation scheme will be readjusted. Following the order of subtask priority from high to low, repeat the above allocation and checking process for each subtask in turn until all subtasks are allocated resources that meet their execution conditions, or all resources have been allocated. During each iteration, the real-time availability of resources must be dynamically updated, because as resources are allocated, their availability will continuously decrease.

[0023] Assuming that in the pre-built resource allocation model, the proportion of resources j allocated to subtask i is... The amount of resource j allocated to subtask i is... The calculation formula is: ; After allocating resources according to the above formula, if the following occurs: In cases where resource constraints are exceeded, the allocation ratio needs to be readjusted. Using a linear programming algorithm, the priorities of all subtasks and the dependencies between production processes are redefined. The value of ensures that resource allocation satisfies the constraints while also guaranteeing the resource needs of high-priority subtasks as much as possible.

[0024] S30, use the Critical Path Method (CPM) to determine the critical path of the production task, schedule the production according to the critical path, and calculate the length of the critical path; Define the duration of each production subtask And the sequential relationship between subtasks, that is, determining the predecessor and successor tasks of each subtask; And obtain the earliest start time (ES) and earliest finish time (EF) for each task, as follows: For the initial task (a task without a predecessor task). ; For other tasks i, Where k represents all the immediate predecessors of task i, and the earliest completion time of task i is... ; And obtain the latest start time (LS) and latest finish time (LF) for each task, as follows: For tasks that have ended (tasks with no successor tasks), LF = EF; For other tasks i, , where k are all the immediate successors of task i; Latest start time of task i ; When the task is satisfied and When these tasks are combined, the path is called the critical path.

[0025] The start time of the earliest task on the critical path is used as the start time of the entire production schedule. The start and end times of tasks on the critical path are arranged sequentially according to their order. Tasks on non-critical paths are arranged flexibly based on the completion time of their predecessors and resource availability, without affecting the tasks on the critical path.

[0026] The length L of the critical path is equal to the sum of the durations of all tasks on the critical path, as shown in the formula: ; The impact of the critical path on coordinated scheduling: A shorter critical path means a shorter overall production cycle, enabling faster delivery of products or services and improving a company's responsiveness and market competitiveness. At the same time, a shorter critical path reduces resource occupation time, lowers costs and risks, and facilitates more efficient collaboration between departments in collaborative planning, as the connections between each stage are closer, and communication and coordination costs are lower. The longer the critical path, the longer the production cycle, and the greater the uncertainty and risks encountered during this period, such as fluctuations in raw material prices and changes in market demand, which may lead to increased costs and decreased revenue for the entire project. In collaborative planning, a long critical path will increase the time span of work for each department, increase the difficulty of coordination, and easily lead to problems such as untimely information transmission and poor task coordination. In collaborative scheduling, the shorter the critical path, the better, as it helps improve production efficiency, reduce costs and risks, and promote collaboration among departments.

[0027] S40 monitors the execution of each subtask in real time during the production process, and adjusts the execution process in a timely manner by establishing a collaborative scheduling model based on the monitoring results of the subtasks. Through production management systems, sensors, and other tools, the execution progress data of each subtask is collected in real time, including task start time, current completion status, and estimated completion time; at the same time, the usage of various resources is collected, such as the allocated amount of resources, the remaining amount of resources, and the availability status of resources. The actual collected data is compared and analyzed with the pre-set production plan and resource allocation scheme. For example, comparing the actual start time of a sub-task with the planned start time, if the actual start time is later than the planned start time, there may be a risk of task delay; comparing the actual allocated amount of resources with the planned allocated amount, if the actual allocated amount exceeds the planned allocated amount or the remaining resources are insufficient, it may cause resource conflicts.

[0028] When task delays or resource conflicts occur, new decision variables are introduced. , This represents the decision to reallocate resource j to subtask i at time t. Represents redistribution, This means no redistribution; A collaborative scheduling model is established based on task delay time and resource reallocation amount, with the specific formula as follows: In the formula, C is the objective function of the cooperative scheduling model, which is to minimize the adjustment cost, and t is the actual execution time of the task. It is the earliest completion time of the task. It is a weighting factor for task delay time. It refers to the amount of resources allocated. It is the amount of resources redistributed. It is a resource allocation weighting factor.

[0029] S50 evaluates the scheduling effect based on fuzzy reasoning according to the length of the critical path and the collaborative scheduling model, and continuously optimizes the scheduling scheme.

[0030] Step C1: Define the length of the critical path and the objective function of the collaborative scheduling model as input variables, and divide them into different fuzzy sets.

[0031] For example, "Low", "Medium", "High" represent the length of the critical path, and "Low", "Medium", "High" represent the objective function of the cooperative scheduling model.

[0032] Step C2: The scheduling effect is defined as an output variable, which is then divided into fuzzy sets, such as "High" and "Low", for the scheduling effect.

[0033] Step C3 involves developing a set of fuzzy rules to describe the impact of different input variables on the output variable. The rules can be defined based on professional knowledge or obtained through data analysis and experimentation. For example: Let L be the length of the critical path, C be the objective function of the collaborative scheduling model, and P be the scheduling effect, then we can define... Rule 1: IF (L is High) AND (C is High) THEN (P is Low ) Rule 2: IF (L is Low) AND (C is Low) THEN (P is High ) Step C4: Perform fuzzy reasoning based on fuzzy rules to evaluate the scheduling effect.

[0034] It should be noted that the division of fuzzy sets can be adjusted according to the actual situation. For example, although this embodiment uses three fuzzy sets as an example, in reality, the length of the critical path, the objective function of the collaborative scheduling model, and the scheduling effect can be divided into more than three sets to facilitate more accurate identification.

[0035] Furthermore, regarding the length of the critical path, the judgment of whether the objective function of the collaborative scheduling model is high, medium, or low can be made by setting thresholds according to the actual situation; marking a critical path length higher than 20 as "High", marking a collaborative scheduling model objective function higher than 50 as "High", etc., will not be elaborated here.

[0036] If the scheduling effect P is Low, it means that the scheduling effect is not good. It is necessary to continuously track the changes in the critical path, adjust the resource allocation to shorten the new critical path, and optimize the resource scheduling of each task according to the collaborative scheduling model, so as to achieve the optimization of scheduling. If the scheduling effect P is High, it means that the scheduling effect is good and no optimization is needed.

[0037] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0038] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0039] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0040] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0041] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0042] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A collaborative scheduling method based on schedule optimization, characterized in that, Includes the following steps: The production task is broken down into multiple sub-tasks according to the process requirements, and the priority of each sub-task is determined by the analytic hierarchy process. Based on the determined sub-task priorities and real-time resource availability, combined with the dependencies between each production stage and resource constraints, resources are allocated according to a pre-built resource allocation model. The critical path method is used to determine the critical path of production tasks, the production schedule is arranged according to the critical path, and the length of the critical path is calculated. During the production process, the execution status of each sub-task is monitored in real time, and the execution process is adjusted in a timely manner by establishing a collaborative scheduling model based on the monitoring results of the sub-tasks. Based on the length of the critical path and the collaborative scheduling model, the scheduling effect is evaluated using fuzzy reasoning, and the scheduling scheme is continuously optimized.

2. The collaborative scheduling method based on schedule optimization according to claim 1, characterized in that, The process of determining the priority of each subtask is as follows: The production task T is broken down into n sub-tasks according to the process requirements. , ,... ; For n subtasks, construct a judgment matrix. ,in This indicates the importance of subtask i relative to subtask j; The largest eigenvalue of the judgment matrix A is calculated using the eigenvalue method. And its corresponding feature vector W, after normalization, yields the priority weight vector of the subtask. The calculation formula is: ; In the formula These are the normalized eigenvectors. It is the i-th element in the feature vector; The priority weight vector of the subtask is obtained from the normalized feature vector, and the priority of each subtask is determined.

3. The collaborative scheduling method based on schedule optimization according to claim 2, characterized in that, The process for obtaining the resource constraints is as follows: During resource allocation, a limit on the total amount of resources must be met. That is, for any time t and resource j, the total amount of resources allocated to all subtasks cannot exceed the real-time available amount of that resource. This can be expressed by the formula: ,in It is the resource requirement of subtask i for resource j at time t. For decision variables, a value of 1 indicates that resource j is allocated to subtask i at time t, and a value of 0 indicates that no allocation is made.

4. The collaborative scheduling method based on schedule optimization according to claim 3, characterized in that, The resource allocation process according to the pre-built resource allocation model is as follows: Based on a pre-built resource allocation model, for each subtask In the initial resource allocation, the highest priority subtask is considered first, and the resources required to meet its startup conditions are allocated to it. After allocating resources to each subtask, check whether all preceding tasks of that subtask have been completed, and whether the allocation violates resource constraints. If there are incomplete predecessor tasks, or if the resource allocation exceeds the resource constraints, the resource allocation of the subtask will be suspended until all its predecessor tasks are completed, and the allocation scheme will be readjusted. The above allocation and checking process is repeated for each subtask in descending order of priority, until all subtasks are allocated resources that meet their execution conditions, or all resources have been allocated.

5. The collaborative scheduling method based on schedule optimization according to claim 4, characterized in that, The critical path acquisition process for the production task is as follows: Define the duration of each production subtask And the sequential relationship between subtasks, that is, determining the predecessor and successor tasks of each subtask; And obtain the earliest start time ES and earliest finish time EF for each task, as follows: For the initial task ; For other tasks i, Where k represents all the immediate predecessors of task i, and the earliest completion time of task i is... ; And obtain the latest start time LS and latest finish time LF for each task, as follows: For the task termination, LF=EF; For other tasks i, , where k are all the immediate successors of task i; Latest start time of task i ; When the task is satisfied and When these tasks are combined, the path is called the critical path.

6. The collaborative scheduling method based on schedule optimization according to claim 5, characterized in that, The calculation process for the length of the critical path is as follows: The start and end times of tasks on the critical path are scheduled sequentially according to their order of occurrence. Tasks on non-critical paths are scheduled based on the completion times of their predecessors and resource availability. The length L of the critical path is equal to the sum of the durations of all tasks on the critical path, as shown in the formula: Specify the duration of each production subtask. .

7. The collaborative scheduling method based on schedule optimization according to claim 6, characterized in that, The process of real-time monitoring of the execution status of each sub-task is as follows: Collect execution progress data for each sub-task and the usage of various resources, and compare and analyze the actual collected data with the pre-set production plan and resource allocation scheme; Compare the actual start time of the subtask with the planned start time. If the actual start time is later than the planned start time, there is a risk of task delay. Comparing the actual allocation of resources with the planned allocation, if the actual allocation exceeds the planned allocation or the remaining resources are insufficient, resource conflicts will occur.

8. The collaborative scheduling method based on schedule optimization according to claim 7, characterized in that, The process of establishing the collaborative scheduling model is as follows: When task delays or resource conflicts occur, new decision variables are introduced. , This represents the decision to reallocate resource j to subtask i at time t. Represents redistribution, This means no redistribution; A collaborative scheduling model is established based on task delay time and resource reallocation amount, with the specific formula as follows: In the formula, C is the objective function of the cooperative scheduling model, which is to minimize the adjustment cost, and t is the actual execution time of the task. It is the earliest completion time of the task. It is a weighting factor for task delay time. It refers to the amount of resources allocated. It is the amount of resources redistributed. It is a resource allocation weighting factor.

9. The collaborative scheduling method based on schedule optimization according to claim 8, characterized in that, The process of evaluating the scheduling effect based on the length of the critical path and the collaborative scheduling model using fuzzy inference is as follows: The length of the critical path and the objective function of the collaborative scheduling model are defined as input variables, and they are divided into different fuzzy sets respectively. The scheduling effect is defined as an output variable, which is then divided into fuzzy sets. Formulate fuzzy rules to describe the impact of the critical path length and the objective function of the collaborative scheduling model on the scheduling effect; Fuzzy reasoning is performed based on fuzzy rules to evaluate scheduling effectiveness.

10. The collaborative scheduling method based on schedule optimization according to claim 9, characterized in that, The process of continuously optimizing the scheduling scheme is as follows: If the scheduling effect is lower than the preset threshold, it means that the scheduling effect is not good. It is necessary to continuously track the changes in the critical path, adjust the resource allocation to shorten the new critical path, and optimize the resource scheduling of each task according to the collaborative scheduling model, so as to achieve the optimization of scheduling. If the scheduling effect is higher than the preset threshold, it means that the scheduling effect is good and no optimization is needed.

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