Low-carbon workshop scheduling method based on disjunction graph expression

Abstract

The invention belongs to the technical field of workshop scheduling optimization, and particularly relates to a low-carbon workshop scheduling method based on disjunction graph expression, and the method comprises the steps: firstly constructing an extended disjunction graph model which comprises an operation node, a machine node, a time node and an event node; wherein the time nodes clearly represent different electricity price periods and cost coefficients thereof. On this basis, a function with the goal of minimizing the total cost is defined, and the total cost is composed of the direct energy consumption cost considering the real-time electricity price and the delivery deadline reward and punishment cost. And finally, solving the model by adopting an intelligent algorithm combining a graph neural network and near-end strategy optimization. According to the method, the dynamic energy cost can be quantified, the scheduling scheme with the optimal total production cost in the time-of-use electricity price environment is automatically generated, the unification of energy conservation, emission reduction and production economy is effectively realized, and the method is particularly suitable for manufacturing workshops which are sensitive to the cost and are influenced by the time-of-use electricity price.

Description

Technical Field

[0001] This invention relates to the field of workshop scheduling optimization technology, and specifically to a low-carbon workshop scheduling method based on disjunctive graph representation. Background Technology

[0002] The Job Shop Scheduling Problem (JSSP) and its extended forms (such as Flexible Job Shop Scheduling, FJSP) are among the core optimization problems in manufacturing production workshops. The goal is to sequence production tasks and allocate resources while satisfying constraints such as process sequence and machine capacity, in order to optimize key performance indicators such as production efficiency and cost.

[0003] While traditional and existing research on scheduling optimization has yielded fruitful results, it still has significant limitations in addressing the demands of modern intelligent manufacturing characterized by low carbon emissions and refined cost control. These limitations are manifested in the following three aspects: 1. Optimization objectives are singular or fragmented, making it difficult to achieve overall cost synergy and optimality.

[0004] Early scheduling methods mostly focused on single time indicators, such as minimizing the maximum completion time. For example, Chinese patent CN118607852A discloses a batch flow flexible workshop scheduling method, whose optimization objective is to minimize the completion time. While such methods can improve equipment utilization, they completely ignore the energy consumption costs in the production process and cannot meet the requirements of energy conservation and emission reduction industrial policies. With the popularization of the concept of green manufacturing, some studies have begun to incorporate energy consumption into the optimization objectives. For example, Chinese patent CN120106462A proposes a multi-objective optimization method that considers completion time, total energy consumption, and total waiting time simultaneously. However, such methods usually treat energy consumption as a static or average additional indicator, failing to dynamically link it with real energy costs that fluctuate over time (such as time-of-use electricity prices), resulting in the low-carbon solutions obtained not being optimal in terms of actual economics.

[0005] 2. The scheduling model is not good at representing complex real-world constraints.

[0006] To handle complex workshop constraints, disjunctive graph models are widely used due to their powerful representational capabilities. Researchers have expanded the disjunctive graph structure to incorporate more production factors. For example, Chinese patent CN115903653B constructs a two-layer disjunctive graph model, increasing the representation of material flow and process relevance. Chinese patent CN118607852A constructs an enhanced heterogeneous disjunctive graph that includes jobs, operations, and machine nodes to handle batch flows. Although these extensions enhance the model's characterization of resource and material constraints, their modeling dimension still does not cover "time" as an independent resource with cost attributes. Existing models cannot directly and structurally represent "time-of-use electricity pricing," a key production constraint that causes energy costs to fluctuate dramatically over time, thus limiting the ability of scheduling algorithms to seek globally economically optimal solutions at the model level.

[0007] 3. There is a disconnect between the solution algorithm and the refined economic model.

[0008] In recent years, intelligent optimization algorithms based on graph neural networks and deep reinforcement learning have provided powerful tools for solving complex scheduling problems. These algorithms can learn efficient scheduling strategies from complex graph-structured data. However, if the underlying scheduling model fails to accurately characterize the energy consumption cost under the influence of time-of-use pricing, even the most advanced algorithms will only provide optimization results for a distorted problem model, making it difficult to achieve true cost minimization in actual production.

[0009] In summary, the shortcomings of existing technologies lie in the lack of a workshop scheduling model and method that can accurately quantify the dynamic energy consumption cost under time-of-use pricing policies and integrate this cost with objectives such as production delivery deadlines for unified modeling and collaborative optimization. This results in existing scheduling schemes often deviating from the economic objectives of real-world production scenarios, failing to achieve true decarbonization and cost minimization while ensuring delivery.

[0010] Therefore, there is a need in this field for a low-carbon workshop scheduling method based on disjunctive graph representation to systematically solve the above problems. Summary of the Invention

[0011] In view of this, the present invention aims to address the shortcomings of existing scheduling models that cannot accurately represent time-of-use electricity prices and are difficult to coordinately optimize dynamic energy consumption costs and delivery deadlines. It provides a workshop scheduling model that can accurately reflect the fluctuation characteristics of time-of-use electricity prices, and on this basis, develops an effective optimization algorithm to achieve a low-carbon workshop scheduling method that minimizes total production costs.

[0012] To achieve the above objectives, this invention provides a low-carbon workshop scheduling method based on disjunctive graph representation, comprising the following key steps: Step 1: Modeling and initializing the scheduling problem, obtaining workshop scheduling data including workpieces, machines, processing time and power, and determining the time-of-use electricity price periods and their cost coefficients.

[0013] The workshop scheduling data includes at least: n independent workpieces J i (i = 1, 2, ..., n), m machines M k (k = 1, 2, ..., m), each workpiece contains operations performed sequentially. ,operate In machine M k Processing time T ijk Processing power W ijk and the planned delivery time T of the production task sche ; Step 2: Based on the workshop scheduling data, construct a four-type disjunctive graph model to represent the scheduling problem. This model introduces time nodes and event nodes in addition to traditional operation nodes and machine nodes. Nodes are connected by directed and undirected edges, establishing topological connections and constraints between nodes, forming a complete graph structure that expresses scheduling constraints and cost elements.

[0014] The node set of the constructed disjunctive graph model includes at least: (1) With each operation The corresponding operation node; (2) With each machine M k The corresponding machine node; (3) With each time-of-use electricity price period T t (t=1,2,...,T) corresponds to time nodes, with each time node accompanied by the length of that time period. and unit energy cost coefficient ; (4) The start event node S and the end event node F are used to identify the start and end of the scheduling process.

[0015] The edge set of the constructed disjunctive graph model includes at least: (1) Connect the directed edges between the starting event node S, the operation nodes with sequential order within the same workpiece and the ending event node F to form a process chain, representing the process sequence constraint.

[0016] (2) Connect adjacent time nodes T t Directed edges between them, forming a path from T1 to T. t The timeline represents the natural direction of time's passage.

[0017] (3) At operation node O ij Compatible machine node Mk An undirected edge is established between them, and the processing power of the operation on the corresponding machine is attached to the undirected edge. With processing time .

[0018] (4) At operation node O ij With time node T t An undirected time allocation edge is established between them to indicate that the operation is allowed to be executed within the corresponding time period.

[0019] Step 3: A reinforcement learning framework based on Graph Neural Networks (GNNs) and Proximal Policy Optimization (PPO) is used to optimize the model. The GNN extracts global and node feature embeddings from the disjunctive graph model and uses these embeddings as state inputs to the policy network and value network within the PPO algorithm framework. Through training, a model that minimizes the total cost is obtained. The scheduling strategy is used to obtain the scheduling scheme.

[0020] The goal of optimization is to minimize the total cost. ,in, This represents the direct energy consumption cost of the production process. This represents the penalty cost for delays in the maximum completion time under production delivery deadline constraints.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) It realizes the modeling and optimization of dynamic energy costs. By introducing time nodes with cost coefficients, the scheduling model can directly respond to time-of-use electricity price fluctuations, thereby generating an energy-saving scheduling scheme for arranging high-energy-consuming processes during periods of low electricity prices, which significantly reduces energy costs.

[0022] (2) The coordinated optimization of multi-dimensional economic objectives was completed, and the dynamic energy consumption cost and delivery deadline reward and punishment were unified into the objective function of minimizing the total cost, so that the scheduling scheme can achieve the optimal economic balance between energy saving and on-time delivery, and improve the overall economic efficiency of production.

[0023] (3) It enhances the model’s ability to express complex real-world constraints. The extended disjunctive graph structure provides a unified framework for integrating various constraints such as time, resources, and order, enabling graph neural networks and reinforcement learning algorithms to exert their optimization potential in a more realistic model, thereby improving the practicality and effectiveness of scheduling schemes.

[0024] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0025] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is the overall process of the present invention; Figure 2 It establishes relationships between time period nodes; Figure 3 It relates to the relationship between machine-operation disjunction edges and undirected time allocation edges; Figure 4 It is a disjunctive graph constructed based on machine-operational constraints and time-period characteristics; Figure 5 It is a representation of the scheduling results based on the disjunction graph. Detailed Implementation

[0026] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0027] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0028] This invention provides a method for constructing and scheduling a low-carbon workshop scheduling model based on disjunctive graph representation, which is described below in conjunction with the appendix. Figure 1-5 The preferred embodiments of the present invention will be described in further detail below.

[0029] This embodiment provides a complete low-carbon workshop scheduling solution. The overall process of the solution is as follows: Figure 1 As shown, this method first constructs a novel disjunctive graph model to accurately describe the scheduling problem with time-of-use pricing constraints, and then uses an intelligent algorithm based on deep reinforcement learning to solve it. The specific steps are as follows: S1. Scheduling problem modeling and parameter initialization.

[0030] For a given set J containing n independent workpieces i(i = 1, 2, ..., n) and m machines M k The flexible job shop scheduling problem (k = 1, 2, ..., m) is defined.

[0031] Each workpiece corresponds to a set of operations. Indicates workpiece J i The j-th operation must be executed sequentially according to the predetermined process order. Each operation It can be processed on one or more machines in its compatible machine set, with defined processing time and processing power. In machine M... k When processing is performed, the processing time is T. ijk The processing power is W ijk .

[0032] The entire production cycle is divided into T consecutive time periods according to the time-of-use electricity pricing policy. Each time period T t (t = 1, 2, ..., T) has a length L t and the corresponding unit energy consumption cost coefficient π t π t This varies with time t to simulate actual electricity price fluctuations. The planned delivery time for the production task is set as T. sche .

[0033] The system must adhere to classical constraints: there are no priority differences or interdependencies between workpieces, but there are strict sequential constraints; each process can only begin after the preceding process of the same job is completed. There are also no dependencies between different machines; each machine can only perform one operation at a time, and operations that have already started cannot be interrupted. Material transport time between machines within the system is considered zero, and buffer capacity is considered unlimited. All machines and operations can be put into use from the initial moment, and the impact of equipment failure and preventive maintenance is not considered. In addition, the preparation time required for each operation is included in its processing time and is not calculated separately.

[0034] S2. Construct an extended four-type node disjunction graph model.

[0035] Construct an extended disjunctive graph G = (V, E), where the node set V contains four types of nodes and the edge set E represents the constraints and relationships between nodes. This model is the basic data structure for subsequent feature extraction and optimization.

[0036] (1) Create an operation node: Create an operation node for each specific operation procedure. .

[0037] node A process is uniquely identified by a double subscript, where subscript i represents the workpiece number and j represents the sequential number of the operation within the process sequence of workpiece i. This numbering system uniquely determines the process represented by any operation node and its position in the global production task, providing a structural foundation for subsequently constructing the temporal and resource constraint relationships between processes.

[0038] The number of operation nodes is determined by the number of workpieces in the production scenario and the number of operations contained in each workpiece. Each production scenario's disjunctive graph contains... One operation node.

[0039] (2) Create machine nodes: For each machine M k Create a machine node. There are m machine nodes in the diagram, representing all available physical processing resources in the workshop.

[0040] Each machine node represents an independent processing machine within the scene. Each machine node is used to represent the processing capacity and status of the corresponding machine in the disjunctive graph, and to provide a resource constraint basis for subsequent process allocation and machine scheduling.

[0041] (3) Create time nodes: For each time-of-use electricity price time period T t Create a time node. There are T time nodes in the graph.

[0042] Because electricity prices vary across different time periods under the time-of-use pricing policy, the range of energy cost coefficient fluctuations over time is not divided into equal time intervals; each time period has a different duration. Each node corresponds to a continuous time period with a fixed energy cost coefficient. These time periods are numbered t (t=1, 2, …, T) according to their starting time, and are used to characterize the temporal changes in the energy cost coefficient during the production process.

[0043] To fully and accurately describe the temporal characteristics and cost attributes of each time period, each time node T t It includes two key attributes: the duration L of the time period. t and the energy cost coefficient during that period This provides structured input data for time period division and cost accounting in the subsequent production scheduling model.

[0044] (4) Create event nodes: Create two virtual event nodes, the start node S and the end node F.

[0045] S represents the initial state of the scheduling process, with a time state of 0, and all workpiece operations are in an unstarted state; F represents the final state of the scheduling process, with a time state corresponding to the end of the last time period, and all workpiece operations completed. These two event nodes provide clear time boundaries and state benchmarks for the entire scheduling process, serving as the start and end points of directed edge connections, jointly ensuring the temporal integrity and reachability of the scheduling model.

[0046] S3. Establish topological connections and constraints between nodes.

[0047] Based on production logic, directed or undirected edges are added between the created nodes to encode all scheduling constraints.

[0048] (1) Process sequence constraint (directed edge): For each workpiece J i Starting from its initial node S, and following its technological route, directed edges are established between each pair of sequential operation nodes, ultimately connecting to the terminating node F to form the process chain for that workpiece. For example, for process O... i1 → O i2 Establish directed edge O i1 → O i2 .

[0049] These edges enforce the execution order of operations within the same workpiece.

[0050] (2) Time node constraints (directed edges): In the order of natural time flow, directed edges are established between adjacent time nodes to form a time chain that runs through all time periods: T1→ T2→ ... → T T .

[0051] Figure 2 By constructing relationships between time period nodes, the time chain represents the temporal framework of energy cost evolution, providing a temporal framework basis for subsequent process arrangement and energy consumption cost calculation within the corresponding time window, and establishing the correspondence between scheduling decision results and total processing energy consumption cost in the workshop.

[0052] (3) Machine-Operation Constraints (Undirected Edges): For each operation node O ij In its relation with all machine nodes M capable of performing this operation k Establish an undirected edge between them. Edge (O) ij M k The output includes two key parameters: the processing power of the operation on this machine. With processing time .

[0053] Figure 3This relates machine-operation disjunction edges and undirected time allocation edges. These undirected edges characterize the allocation relationship on which operations can be executed on corresponding machines. These allocation edges provide key data support for accurately calculating process energy consumption costs in a time-of-use pricing environment and further optimizing machine selection and energy consumption scheduling.

[0054] (4) Operation-time constraint (undirected edge): at operation node O ij With time node T t Establish an undirected edge between them. This edge represents operation O. ij Allowed during time period T t Internal processing arrangements.

[0055] These undirected edges are used to characterize the feasibility of an operation being executed within a specific time period. They serve as a key bridge linking scheduling decisions (when to start) with dynamic cost calculations (at what electricity price), providing crucial constraints for accurately calculating the energy cost of operation execution and further optimizing the timing of processes under time-of-use pricing.

[0056] At this point, the disjunctive graph G is complete. Figure 4 It is an extract graph built based on machine operation and time period characteristics, which fully integrates all input information, physical constraints and cost calculation elements of production scheduling.

[0057] S4. Define the optimization objective function based on minimizing total cost.

[0058] Based on the above model, the optimization objective of this invention is to find a scheduling scheme that minimizes the total variable cost. Minimum. It consists of two parts: direct energy consumption costs and delay penalty costs. Direct energy consumption cost This cost precisely quantifies the energy costs consumed in production under the time-of-use electricity pricing policy.

[0059] in, Indicates in the machine workpiece The j-th operation Processing power, Indicates operation Processing time during this period, Indicates time period The electricity cost coefficient. This formula introduces a factor that varies with time t. This enables the calculation of energy consumption costs to respond in real time to fluctuations in electricity prices.

[0060] Delivery deadline, reward / penalty cost :

[0061]

[0062] in, Indicates the delay time. This indicates the actual completion time, i.e., the maximum completion time for all operations in a production scenario. Indicates the planned delivery time. Indicates the penalty coefficient per unit time when delaying. This represents the unit time bonus coefficient for early delivery.

[0063] Overall objective function :

[0064] This function reflects low carbon (as) ) and punctuality (reflected in The optimization objectives of these two dimensions are unified under a single economic indicator: minimizing total production cost.

[0065] S5. Intelligent solution algorithm based on graph neural network and proximal policy optimization (PPO).

[0066] To efficiently solve the aforementioned complex combinatorial optimization problem, this embodiment employs a hybrid intelligent optimization architecture, the process of which is as follows: Figure 1 The scheduling solution method based on disjunctive graphs is shown in the figure.

[0067] 5.1 Input Feature Extraction: The disjunctive graph G corresponding to the current scheduling scheme is input into a graph neural network (GNN). The GNN aggregates the self-attributes of each node and its neighboring node information through a multi-layer message passing mechanism. For example, an operation node... The final embedding vector incorporates information from its predecessor / successor processes, features of the optional machine set, and cost features of the time window that may be assigned. Ultimately, the GNN outputs a global embedding representation of the entire graph G and the embedding vector of each node, which together constitute the "state" s of the agent's decision.

[0068] 5.2 Reinforcement Learning: (1) State s: the feature representation of the current disjunctive graph extracted by GNN.

[0069] (2) Action a: At each decision step, the agent needs to select an operation from the set of all schedulable operations. And assign it a compatible machine M k A feasible start time, corresponding to a certain time node T t Or a specific moment.

[0070] (3) Reward r: Design a reward function based on total cost optimization. Whenever the agent completes an action, the scheduling environment transitions to a new state s', and the estimated total cost caused by the action is calculated. The reduction amount is used as an immediate reward r. That is, r = (s)- (s'), this design directly drives the agent to learn strategies to reduce total cost.

[0071] 5.3 Decision Making and Evaluation: Construct two neural networks, the policy network π θ (a|s) and value network V φ (s). The policy network receives state s and outputs the probability distribution of each possible action, including action selection such as machine allocation and process sequencing; the value network evaluates the long-term expected return of the current state and provides a benchmark reference for policy updates.

[0072] 5.4 Training and Optimization Cycle: Multi-round iterative training is adopted, using a general deep reinforcement learning training process: collecting trajectory data of agent-environment interaction; calculating the advantage function and value objective; updating the policy network and value network parameters; and re-exploring the solution space based on the new policy.

[0073] a. Interactive sampling: Using the current strategy π θ It interacts with the environment to generate a large amount of trajectory data (s, a, r, s').

[0074] b. Advantage estimation: Utilizing the value network V φ Based on the collected rewards, calculate the advantage function A(s, a) for each action, which measures the quality of that action relative to the average level.

[0075] c. Policy update: The policy network parameters θ are updated by minimizing the objective function of PPO, ensuring that the policy improves steadily and the update magnitude is not too large.

[0076] d. Value update: The parameter φ of the value network is updated by minimizing the error between the predicted value and the actual return.

[0077] e. Repeat step ad until the policy converges. Ultimately, the agent learns a near-optimal scheduling policy π*.

[0078] 5.5 Scheduling Scheme Generation: For a new production task instance, its corresponding disjunctive graph is first constructed based on S2 and S3. This graph is then input into the trained policy network π*. The agent, based on the learned policy, progressively assigns a machine and start time to each operation until all operations are scheduled, ultimately outputting a complete scheduling Gantt chart and the estimated total cost. , Figure 5The diagram shows the scheduling results based on the disjunctive graph. This scheme minimizes the total production cost under time-of-use pricing while satisfying all constraints.

[0079] S6. Application Example.

[0080] Suppose a workshop has 2 machines (M1, M2) and needs to process 2 workpieces. The time-of-use electricity price is divided into 3 time periods: peak (T1), intermediate (T2), and low (T3), with π1>π2>π3.

[0081] After training using this method, the agent can perform a high-power, time-consuming operation O. A Choose to process on M1 during the lowest electricity price period T3; simultaneously, perform an emergency short operation O. B The system schedules processing on M2 immediately during peak electricity price periods (T1) to avoid hefty penalties for delivery delays. This scheduling scheme intelligently balances dynamic energy consumption costs (C). e Delivery reward and penalty cost C de This achieved the sum of the two total costs. The global minimum value fully verifies the effectiveness of this invention in economical and low-carbon dispatching under the time-of-use pricing policy.

[0082] In summary, this invention addresses the challenge of optimizing energy consumption and delivery time under time-of-use (TOU) pricing policies using existing technologies. It constructs an extended disjunctive graph model comprising operation nodes, machine nodes, time nodes, and event nodes. The time nodes explicitly represent different electricity price periods and their cost coefficients. Based on this, a function is defined to minimize the total cost, which consists of direct energy consumption costs considering real-time electricity prices and delivery deadline incentive / penalty costs. Finally, an intelligent algorithm combining graph neural networks and near-end strategy optimization is used to solve the model. This method quantifies dynamic energy costs and automatically generates the optimal scheduling scheme for total production cost under TOU pricing, effectively achieving a balance between energy conservation, emission reduction, and production economics. It is particularly suitable for cost-sensitive manufacturing workshops affected by TOU pricing.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A low-carbon workshop scheduling method based on disjunctive graph representation, comprising the following steps: Step 1: Modeling and initializing the scheduling problem, obtaining shop floor scheduling data, which includes: n independent workpieces J i m machines M k Where i = 1, 2, ..., n, k = 1, 2, ..., m, and each workpiece contains operations executed sequentially. ,operate In machine M k Processing time T ijk Processing power W ijk and the planned delivery time T of the production task sche ; Step 2: Based on the workshop scheduling data, construct four types of node disjunctive graph models to represent the scheduling problem, and establish the topological connections and constraints between the nodes; Step 3: Optimize the model using a solution framework based on graph neural networks and reinforcement learning to obtain the scheduling scheme; The characteristic feature is that, in step two, the node set of the constructed disjunctive graph model further includes: With each operation The corresponding operation node; and each machine M k The corresponding machine node; and each time-of-use electricity price period T. t The corresponding time nodes, where t=1,2,...,T, each time node is accompanied by the length of the time period. and unit energy cost coefficient ; In step three, the objective of the optimization solution is to minimize the total cost. The calculation formula is as follows: in, This represents the direct energy consumption cost of the production process. This represents the penalty cost for delays in the maximum completion time under production delivery deadline constraints. direct energy consumption cost The calculation formula is: in, Indicates the k-th machine For the i-th workpiece The j-th operation Processing power Indicates operation Processing time during this period, Indicates time period Electricity cost coefficient; The delivery deadline incentive cost The calculation formula is: in, Indicates the delay time. Indicates the actual completion time. Indicates the planned delivery time. Indicates the penalty coefficient per unit time when delaying. This represents the unit time bonus coefficient for early delivery.

2. The method according to claim 1, characterized in that, In step two, the node set of the disjunctive graph model also includes: a start event node S and a termination event node F used to identify the start and end of the scheduling process.

3. The method according to claim 2, characterized in that, In step two, the edge set of the disjunctive graph model includes directed edges connecting the starting event node S, the operation nodes with sequential order within the same workpiece, and the ending event node F, to form a process chain and characterize the process sequence constraints.

4. The method according to claim 2 or 3, characterized in that, In step two, the edge set of the disjunctive graph model includes: edges connecting adjacent time nodes T. t Directed edges between them, forming a path from T1 to T. t The timeline represents the natural direction of time's passage.

5. The method according to claim 4, characterized in that, In step two, the edge set of the disjunctive graph model further includes: at operation node O ij Compatible machine node M k An undirected edge is established between them, and the processing power of the operation on the corresponding machine is attached to the undirected edge. With processing time .

6. The method according to claim 5, characterized in that, In step two, the edge set of the disjunctive graph model further includes: at operation node O ij With time node T t An undirected time allocation edge is established between them to indicate that the operation is allowed to be executed within the corresponding time period.

7. The method according to any one of claims 1 to 6, characterized in that, In step three, the solution framework based on graph neural networks and reinforcement learning specifically involves: using a graph neural network to extract global and node feature embeddings from the disjunctive graph model, and using these feature embeddings as state inputs to the policy network and value network in the near-end policy optimization algorithm framework. Through training, a solution is obtained that minimizes the total cost. The scheduling strategy.

8. The method according to claim 7, characterized in that, In the algorithmic framework described above, the reward function r is designed to be based on the total cost. The reduction amount is specifically: r = (s)- (s'), where s and s' represent the states before and after the scheduling action, respectively. (s) and (s') represent the total cost estimates for the corresponding states.

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