Supply chain order allocation method based on multi-stage cardinality constraint programming

Abstract

The invention relates to the technical field of supply chain order allocation, and discloses a supply chain order allocation method based on multi-stage cardinality constraint planning, which comprises the following steps: screening supplier subsets meeting cardinality constraints from all suppliers through a relationship awareness depth Q network; based on the screened supplier subsets, converting the multi-stage cardinality constraint programming model into an order allocation model only containing linear constraints, and solving to obtain an optimal order allocation weight; and repeatedly executing the two stages in a set decision period to minimize the total target cost to obtain supplier selection and order allocation results. According to the method, the optimal order allocation weight can be quickly calculated, and the rationality and high efficiency of resource allocation are ensured.

Description

Technical Field

[0001] This invention relates to the field of supply chain order allocation technology, and specifically to a supply chain order allocation method based on multi-stage cardinality constraint programming. Background Technology

[0002] In the field of supply chain management, Supplier Selection and Order Allocation (SSOA) is a core decision-making process. Essentially, it falls under the category of Multi-period Cardinality-Constrained Planning (MC2P) and is widely used in the procurement processes of manufacturing and retail industries. In these scenarios, companies need to select a limited number of partners (constrained by cardinality, such as a maximum of 5) from a large pool of candidate suppliers each procurement cycle (e.g., monthly, quarterly) and allocate limited procurement order resources to the selected suppliers. The core objective is to minimize the total long-term procurement cost (including unit procurement cost, transportation cost, supplier switching cost, and inventory cost) while meeting production needs and ensuring contract fulfillment stability. However, current traditional solutions in supply chain management face significant technical bottlenecks. Existing solutions typically transform the MC2P problem into a Mixed-Integer Linear Programming (MILP) problem or employ heuristic algorithms. However, these methods generally face the following two core challenges: (1) Short-sighted optimization problem: Focusing only on the short-term procurement cost optimization of a single procurement cycle, ignoring the impact of the current supplier selection on long-term cooperation. For example, excessively pursuing a low-priced supplier in a certain cycle may lead to supply disruptions in subsequent cycles due to insufficient capacity of that supplier, or high adjustment costs such as contract changes and logistics adaptation due to frequent switching of suppliers, which in turn increases the overall long-term cost.

[0003] (2) Ignoring dependencies between candidate suppliers: Most methods treat candidate suppliers as independent entities, failing to uncover their potential complementarity. To verify this issue, this paper conducts an analysis through a supply chain task experiment: the experiment requires selecting 10 suppliers from 29 to minimize the average unit cost. For example... Figure 1 As shown, based on the t-SNE clustering results using supplier characteristics, candidate suppliers can be divided into three different clusters. Configurations C1-C3 select suppliers from only a single cluster, while configurations C4-C6 span two different clusters (visually distinguishable by background color). After 10 randomized trials for each configuration, it was found that the cross-cluster selection configuration consistently achieves lower unit cost. This indicates that candidates from different clusters often have complementary advantages, effectively improving overall performance. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides a supply chain order allocation method based on multi-stage cardinality constraint programming.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: A supply chain order allocation method based on multi-stage cardinality constraint programming includes the following steps: In the first stage, a subset of suppliers that meet the cardinality constraint is selected from all suppliers through a relation-aware deep Q-network. The relation-aware deep Q-network explicitly models the dependencies between candidate objects based on locality-sensitive hashing clustering and self-attention mechanism, and uses a cost-aware reward function to optimize the long-term expected return. In the second stage, based on the selected supplier subset, the multi-stage cardinality-constrained programming model is transformed into an order allocation model containing only linear constraints, and the optimal order allocation weight is obtained by solving the problem. The two stages described above are repeated within a set decision-making cycle to minimize the total target cost and obtain the results of supplier selection and order allocation.

[0006] Furthermore, the subset of suppliers satisfying the cardinality constraint is selected from all suppliers using a relation-aware deep Q-network, including: The raw feature data of suppliers is preprocessed, and global features and individual features of suppliers are generated through a task encoder; Based on the individual characteristics of suppliers, locality-sensitive hashing clustering and self-attention mechanism are used to explicitly model the fusion dependency characteristics between suppliers; Based on the fusion dependency characteristics, the Q value of each supplier is calculated by a multilayer perceptron, and the top K suppliers with the highest Q values ​​are selected to form a supplier subset.

[0007] Furthermore, based on individual supplier characteristics, locality-sensitive hashing clustering and self-attention mechanisms are used to explicitly model the fusion dependency features between suppliers, including: Based on the individual characteristics of the suppliers, locality-sensitive hashing is used to cluster the suppliers into m buckets; For each supplier in each bucket, a self-attention mechanism is used to calculate the fusion dependency features.

[0008] Furthermore, locality-sensitive hashing specifically refers to: Where hash is a locality-sensitive hash function. Let M represent the individual characteristics of the suppliers, and M be a normally distributed random matrix.

[0009] Furthermore, the self-attention mechanism is used to calculate the fusion dependency features for suppliers within each bucket, specifically as follows: in, To integrate dependency features, , , Let i be the query vector of supplier i, and j be the key vector and value vector of supplier j. Let d be the set of similar suppliers in the bucket containing supplier i. k is the dimension of the key vector.

[0010] Furthermore, a cost-aware reward function is constructed based on the reward shaping function, specifically as follows: Where R represents the perceived cost reward, and F represents the reward shaping function. τ is the target value or decision cost, χ is the curvature parameter, ε is the task-specific target value, c is the decision cost, and N is the normalization function.

[0011] Furthermore, the relation-aware deep Q-network employs an experience replay and target network mechanism during training, including: selecting actions with an ε-greedy strategy, storing transfer samples in the replay pool, and minimizing the Q-value error through gradient descent.

[0012] Furthermore, the multi-stage cardinal constraint programming model is transformed into an order allocation model containing only linear constraints as follows: Where min is the minimum value function, T is the total number of decision cycles, and t is the current decision cycle. Let be the objective function. The binary vector chosen for the supplier Assign weight vectors to orders. Here is the characteristic data of all suppliers in period t, and N is the total number of suppliers. Assign a weight vector to the orders of supplier i in period t, a i , t The binary vector chosen by supplier i for period t.

[0013] Furthermore, solving the order allocation model yields the optimal order allocation weights, including: Transform the objective function of the order allocation model into a standard QP form. ,in , For the supplier feature matrix, Let T be the target vector, and T be the transpose symbol. The linear constraints of the order allocation model are transformed into those supported by the QP solver. or Format; The optimal order allocation weights are obtained by using the QP solver, and the order allocation results for each selected supplier are calculated based on the optimal order allocation weights.

[0014] The present invention has the following beneficial effects: In the first stage, this invention uses a Relationship-Aware Deep Q-Network (RA-DQN) to screen a subset of suppliers that meet the cardinality constraint. This network explicitly models the complementary dependencies between suppliers through Locality Sensitive Hash (LSH) and self-attention mechanisms. At the same time, it incorporates a cost-aware reward function to include short-term procurement costs, long-term switching costs, and fulfillment stability into a unified optimization objective, avoiding short-sighted decision-making. Then, in the second stage, based on the screened supplier subset, the cardinality constraint is removed, and the order allocation problem is transformed into a convex optimization problem that can be efficiently solved by quadratic programming (QP). The optimal order allocation weight is quickly calculated to ensure the rationality and efficiency of resource allocation. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the t-SNE clustering results based on supplier characteristics; Figure 2 This is a schematic diagram of the method flow of the present invention; Figure 3 This is a schematic diagram illustrating the principle of the method of the present invention; Figure 4 This is a schematic diagram of the relation-aware deep Q-network structure in this invention; Figure 5 This is a schematic diagram of the cost-perceived reward function based on reward shaping in this invention; Figure 6 This is a graph showing the tracking performance of the S&P 500 in this invention; Figure 7 This is a schematic diagram illustrating the fast solution efficiency verification of the open-source solver in this invention. Detailed Implementation

[0016] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0017] This invention aims to address two core problems of existing multi-stage cardinal constraint programming (MC2P) methods in long-term planning: first, short-sighted optimization, that is, existing methods only focus on the short-term goals of a single decision cycle and cannot take into account the impact of current decisions on long-term performance; second, ignoring the dependencies between candidate objects, that is, existing methods treat candidate objects independently and fail to utilize their complementarity to improve decision-making performance.

[0018] To address the aforementioned technical problems of SSOA tasks in supply chain management, this invention proposes a two-stage approach that provides a targeted solution: The first stage uses a Relationship-Aware Deep Q-Network (RA-DQN) to filter a subset of suppliers that meet cardinality constraints. This network explicitly models complementary dependencies between suppliers using Locality Sensitive Hashing (LSH) and self-attention mechanisms, while incorporating a cost-aware reward function to integrate short-term procurement costs, long-term switching costs, and fulfillment stability into a unified optimization objective, avoiding short-sighted decisions. The second stage, based on the selected supplier subset, removes the cardinality constraints, transforming the order allocation problem into a convex optimization problem that can be efficiently solved using quadratic programming (QP). This allows for rapid calculation of the optimal order allocation weights, ensuring the rationality and efficiency of resource allocation.

[0019] In supply chain management scenarios, this invention can achieve significant technical effects: First, by optimizing long-term benefits and modeling complementary relationships with suppliers, it effectively reduces the total cost of long-term procurement and minimizes hidden losses caused by supplier switching and performance interruptions. Second, it improves performance stability under demand fluctuations by flexibly addressing risks such as insufficient capacity and delivery delays through the collaborative configuration of different types of suppliers. Third, it balances solution efficiency and decision quality. Compared with the computational explosion problem of traditional MILP methods in large-scale supplier scenarios and the performance instability of heuristic algorithms, this invention can meet the real-time requirements of procurement decisions while ensuring optimal decision-making results, providing efficient, stable, and economical decision support for enterprise supply chain procurement.

[0020] The technical solution of this invention is a two-stage framework, in which "supplier selection" and "order allocation" are executed sequentially within each procurement cycle t of the Supplier Selection and Order Analysis (SSOA) task, as detailed in the following process: Figure 2 and Figure 3 As shown. A supply chain order allocation method based on multi-stage cardinality constraint programming includes the following steps S1 to S3: S1. In the first stage, a subset of suppliers that meet the cardinality constraint is selected from all suppliers through a relation-aware deep Q-network. The relation-aware deep Q-network explicitly models the dependency relationship between candidate objects based on locality-sensitive hash clustering and self-attention mechanism, and uses a cost-aware reward function to optimize the long-term expected return. In an optional embodiment of the present invention, step S1, which uses a relation-aware deep Q-network to filter a subset of suppliers that satisfy the cardinality constraint from all suppliers, includes: The raw feature data of suppliers is preprocessed, and global features and individual features of suppliers are generated through a task encoder; Based on the individual characteristics of suppliers, locality-sensitive hashing clustering and self-attention mechanism are used to explicitly model the fusion dependency characteristics between suppliers; Based on the fusion dependency characteristics, the Q value of each supplier is calculated by a multilayer perceptron, and the top K suppliers with the highest Q values ​​are selected to form a supplier subset.

[0021] The core of this stage is to use a Relation-Aware Deep Q-Network (RA-DQN) to select a subset of candidate suppliers that meet the cardinality constraint from all candidate sets (all suppliers), while considering long-term benefits and decision costs during the selection process. Existing DRL methods (such as A2C-based policy optimization) are prone to convergence difficulties when the number of candidates is large, while RA-DQN solves this problem through structural innovation.

[0022] RA-DQN solves the complexity problem of the combined action space by "candidate-level Q-value estimation" and models the dependencies between candidate objects. The structure is shown in Figure 4 and consists of two core modules.

[0023] (1) SSOA Supplier Feature Preprocessing Module: Input the original feature data (dimensions) of the suppliers in the SSOA task. N represents the number of candidate suppliers, and L=8 represents the feature dimensions, specifically including: unit price, maximum capacity, delivery cycle, historical on-time delivery rate, green weight, quantity discount threshold, previous cycle order completion rate, and geographical location. These dimensions are transformed into a robust representation using a task-specific encoder: a gated recurrent unit (GRU) or a fully connected network (FCN) is used as the task-specific encoder, with FCN selected for SSOA tasks, adapting to the fusion of static and dynamic features; individual representation of each candidate. (d is the encoding dimension; d=64 is used in SSOA). This step references the ideas of existing feature encoding methods, but optimizes the modeling of dependencies between candidates.

[0024] (2) SSOA inter-vendor dependency modeling module: The dependency relationship between candidate objects is modeled by "Locality Sensitive Hash (LSH) + Self Attention", and the steps are as follows: 1. LSH Clustering: Angular LSH is used to group candidate objects into m buckets, with the corresponding formula being... ,in The matrix is ​​a normally distributed random matrix. In the SSOA task, m=4, corresponding to 4 types of suppliers. This represents the supplier's coded information. The clustering logic groups suppliers based on their "cost-efficiency" characteristics (e.g., "low price - slow delivery time", "high price - fast delivery time"), which aligns with the design purpose of "LSH for candidate grouping".

[0025] 2. In-bucket self-attention: Calculate self-attention for candidate objects within each bucket, fusing neighbor information. The corresponding formula is: ,in , , These are the query vector for supplier i, and the key vector and value vector for supplier j (obtained by linear transformation of the encoded representation), respectively. Let i be the set of similar suppliers in the bucket containing supplier i. By capturing the competitive relationships between similar suppliers and the complementary relationships between cross-type suppliers through self-attention (such as the synergy between "low-price-slow-delivery" and "high-price-fast-delivery" suppliers), we can achieve the core objective of the paper: "modeling inter-candidate dependencies".

[0026] 3. SSOA Supplier Q-value Calculation: Representation of Fusion Dependencies The input is a multilayer perceptron (MLP) to obtain the Q-value of each candidate object. This represents the long-term expected benefit of selecting candidate i. This value reflects the overall contribution of selecting supplier i to the long-term cost and stability of the SSOA task.

[0027] (3) SSOA Supplier Selection Logic: RA-DQN determines the final candidate subset through "greedy selection": 1. Q value for all suppliers Sort.

[0028] 2. Select the top K suppliers with the highest Q-values ​​(K=5 in the SSOA task) to form a subset of suppliers that satisfy the cardinality constraint. .

[0029] 3. The total Q-value of this subset is the sum of the Q-values ​​of the top K candidates. .

[0030] (4) Training process of RA-DQN: RA-DQN is trained using the experience replay and target network mechanism. The core steps are as follows: 1. Initialize the RA-DQN network Target network With experience replay pool .

[0031] 2. During the sampling phase in each training cycle... Greedy strategy for choosing actions Rewards are given for executing resource allocation. Next state Transfer samples deposit During the learning phase, from Medium-sampled mini-batch, calculate target Q value ( (where the discount factor is used) is minimized via gradient descent. Every Step-by-step update target network This training mechanism references the optimization approach of classic DQN, but has been adjusted to incorporate dependency modeling between candidates.

[0032] To balance "target optimization" and "cost control" (e.g., optimizing order allocation while minimizing costs) when selecting suppliers, this invention designs a cost-aware reward function based on reward shaping, as shown in Figure 5.

[0033] (1) Reward shaping function: for the target value (such as the objective function value) The cost (c) undergoes a nonlinear transformation, as shown in the formula. ,in The core indicators of SSOA ( For procurement costs, (for switching costs) The curvature parameter is set to 0.8 in the SSOA task to ensure consistency. The smaller, the better for low The greater the sensitivity to differences in values.

[0034] (2) Cost-Perceived Rewards: Considering the shaping results of goals and costs together, the formula is as follows: ,in Let c be the target value (procurement cost) of the SSOA task, and let c be the decision cost (supplier switching cost) of the SSOA task. Normalization to 0-1 ensures that the smaller the target value and the lower the cost, the higher the reward value. See Figure 5 As shown in the right figure, the colored areas correspond to high rewards. This design overcomes the shortcomings of existing reward functions that only focus on short-term procurement costs (such as MILP and genetic algorithms, which do not consider switching costs).

[0035] S2. In the second stage, based on the selected supplier subset, the multi-stage cardinality constraint programming model is transformed into an order allocation model containing only linear constraints, and the optimal order allocation weight is obtained by solving the problem. In an optional embodiment of the invention, when the supplier subset Once determined, the cardinality constraint is removed, and the MC2P problem is transformed into a resource allocation problem with only linear constraints. In other words, the SSOA task is transformed into an order allocation problem, with the corresponding formula: Where min is the minimum value function, T is the total number of decision cycles, and t is the current decision cycle. Let be the objective function. The binary vector chosen for the supplier Assign weight vectors to orders. Here is the characteristic data of all suppliers in period t, and N is the total number of suppliers. Assign a weight vector to the orders of supplier i in period t, a i , t The binary vector chosen by supplier i for period t.

[0036] Where the objective function This represents the total procurement cost of the SSOA task, corresponding to the "task-specific objective function", specifically... +Transportation costs, (Total procurement demand during period t); Constraint 1 The constraint "All order resources are allocated to suppliers" means that in SSOA, the total order weight is 1, i.e., all orders are allocated to the selected suppliers; Constraint 2 This indicates that no orders were placed with the unselected supplier, corresponding to the constraint "No resources were found among the unselected candidates".

[0037] The solution process follows the logic of "QP for resource allocation" and uses the open-source solver (CVXOPT). The steps are as follows: (1) Transform the total procurement cost objective function of SSOA into the standard QP form. (in , For the supplier feature matrix, (This is the target vector for the demand).

[0038] (2) Transform linear constraints into those supported by the QP solver. or Format (e.g., constraint 1 converted to...) ).

[0039] (3) Call the CVXOPT interface to solve for the order allocation weights. ;according to Calculate the actual order quantity for each selected supplier (e.g.) =0.3、 If there are 1000 items, then allocate 300 items), execute the order and return the result to the environment.

[0040] This step significantly improves computational efficiency compared to existing joint optimization methods (such as MILP).

[0041] S3. Repeat the above two stages within the set decision cycle to minimize the total target cost and obtain the supplier selection and order allocation results.

[0042] The overall process of this invention in SSOA tasks is as follows: 1. Initialization: Set the total decision period T, cardinality constraint K (5 in the SSOA task), RA-DQN parameters (learning rate 10^-4, discount factor 0.99) and QP solver (CVXOPT).

[0043] 2. For each decision period t=1,2,...,T: Input the current state. ( (Initially an empty set); in the first stage, supplier selection is performed by filtering a subset of suppliers using a trained RA-DQN. In the second phase, orders will be allocated. Substitute into the resource allocation model and solve using QP. Then according to Allocate resources, calculate actual rewards and costs; finally, update the status. As for the next cycle , obtain Moving on to the next cycle.

[0044] 3. End: Output the candidate selection results for all cycles. With resource allocation results .

[0045] This invention, through a two-stage framework and RA-DQN design, effectively overcomes the shortcomings of existing MC2P methods, with the following main advantages: 1. Address short-sighted optimization issues and improve long-term performance. Existing MILP and heuristic methods only optimize short-term objectives within a single cycle, while this invention optimizes long-term expected rewards through MDP modeling and DRL, rather than short-term gains; the cost-aware reward function explicitly penalizes "high-cost short-term operations" (such as frequent asset rebalancing). Experimental verification is shown in Table 1: In the Sparse Exponential Tracking (SIT) task, the turnover rate (TO) of this invention is significantly lower than that of MILP, LAIT, and other methods (e.g., TO=0.20 on the Hang Seng dataset, only 51% of that of the NNF method); in a 14-year backtest of the S&P 500, as shown in Table 1... Figure 6 As shown, the tracking error (Gap) is always minimized, and the long-term stability is optimal.

[0046] Table 1. Performance Comparison of 7 Benchmark Datasets 2. Model the dependencies between candidates and explore complementary value. Existing methods (such as LAIT, MSW-Lasso, and NNF) ignore the complementarity between candidate objects, while this invention explicitly models the dependencies between candidate objects through the "LSH + self-attention" module of RA-DQN. Experimental verification (see Figure 1) shows that the configuration of selecting candidate objects across clusters (C4~C6) has a unit cost that is 10%~15% lower than that of single-cluster configuration (C1~C3). In the supplier selection and order allocation task (Table 1), the demand gap (Gap) and total cost of this invention are the lowest (e.g., Gap=3.27 on Dataset 2, lower than MILP's 3.30 and PSO's 3.34).

[0047] 6.3 Balancing solution efficiency and performance, adapting to large-scale scenarios Existing MILP methods exhibit exponentially increasing computational costs as the number of candidates N increases. Heuristic methods (such as genetic algorithms and PSO) require numerous iterations. However, this invention, RA-DQN, reduces the combinatorial space complexity in the first stage through "candidate-level Q-value estimation." Reduced to N; the second-stage QP problem can be solved quickly using an open-source solver; efficiency verification is as follows: Figure 7 As shown, Figure 7 The left side corresponds to the Russell 2000 dataset. Figure 7 (Right corresponds to Dataset 3): On the Russell 2000 dataset (N=1318), the average running time of this invention is only 1 / 50 of MILP and 1 / 10 of genetic algorithm, and there is no time capping required.

[0048] The key technical points of this invention include: 1. Two-stage framework design: By adopting a phased strategy of "candidate selection - resource allocation", the complex MC2P problem is decoupled into two easily solvable subproblems. The first stage uses DRL to handle cardinality constraints and long-term planning, and the second stage uses standard optimization techniques to handle resource allocation. This design overcomes the shortcomings of existing joint optimization methods (such as MILP) in terms of high complexity and unstable performance of heuristic methods, and balances "feasibility, efficiency, and optimization".

[0049] 2. Relationship-Aware Deep Q-Network (RA-DQN): Innovatively integrates "LSH clustering + self-attention" into DQN, achieving two major breakthroughs: First, it solves the high complexity problem of the combined action space through "candidate-level Q-value estimation", avoiding the convergence difficulties of existing DRL methods (such as A2C) in large-scale candidate scenarios; Second, it explicitly models the dependencies between candidate objects, explores complementary values, and overcomes the shortcomings of existing methods that "process candidates independently" (such as LAIT, NNF).

[0050] 3. Cost-Aware Reward Function: Based on non-linear reward shaping, this function jointly optimizes task objectives and decision costs, guiding the DRL agent to avoid "short-sighted, high-cost operations" and ensuring long-term performance stability. This function uses parameters... It adapts to the different task requirements regarding the sensitivity of "goal-cost" and has greater flexibility than existing single-goal reward functions.

[0051] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0052] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0053] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0054] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0055] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A supply chain order allocation method based on multi-stage cardinality constraint programming, characterized in that, Includes the following steps: In the first stage, a subset of suppliers that meet the cardinality constraint is selected from all suppliers through a relation-aware deep Q-network. The relation-aware deep Q-network explicitly models the dependencies between candidate objects based on locality-sensitive hashing clustering and self-attention mechanism, and uses a cost-aware reward function to optimize the long-term expected return. In the second stage, based on the selected supplier subset, the multi-stage cardinality-constrained programming model is transformed into an order allocation model containing only linear constraints, and the optimal order allocation weight is obtained by solving the problem. The two stages described above are repeated within a set decision-making cycle to minimize the total target cost and obtain the results of supplier selection and order allocation.

2. The supply chain order allocation method based on multi-stage cardinality constraint programming according to claim 1, characterized in that, The subset of suppliers that meet the cardinality constraint is selected from all suppliers using a relation-aware deep Q-network, including: The raw feature data of suppliers is preprocessed, and global features and individual features of suppliers are generated through a task encoder; Based on the individual characteristics of suppliers, locality-sensitive hashing clustering and self-attention mechanism are used to explicitly model the fusion dependency characteristics between suppliers; Based on the fusion dependency characteristics, the Q value of each supplier is calculated by a multilayer perceptron, and the top K suppliers with the highest Q values ​​are selected to form a supplier subset.

3. The supply chain order allocation method based on multi-stage cardinality constraint programming according to claim 2, characterized in that, Based on individual supplier characteristics, locality-sensitive hashing clustering and self-attention mechanisms are used to explicitly model the fusion dependency features between suppliers, including: Based on the individual characteristics of the suppliers, locality-sensitive hashing is used to cluster the suppliers into m buckets; For each supplier in each bucket, a self-attention mechanism is used to calculate the fusion dependency features.

4. The supply chain order allocation method based on multi-stage cardinality constraint programming according to claim 3, characterized in that, Locality-sensitive hashing specifically refers to: Where hash is a locality-sensitive hash function. Let M represent the individual characteristics of the suppliers, and M be a normally distributed random matrix.

5. The supply chain order allocation method based on multi-stage cardinality constraint programming according to claim 3, characterized in that, For each bucket, a self-attention mechanism is used to calculate the fusion dependency features of the suppliers. Specifically: in, To integrate dependency features, , , Let i be the query vector of supplier i, and j be the key vector and value vector of supplier j. Let d be the set of similar suppliers in the bucket containing supplier i. k is the dimension of the key vector.

6. The supply chain order allocation method based on multi-stage cardinality constraint programming according to claim 1, characterized in that, The cost-aware reward function is constructed based on the reward shaping function, specifically as follows: Where R represents the perceived cost reward, and F represents the reward shaping function. τ is the target value or decision cost, χ is the curvature parameter, ε is the task-specific target value, c is the decision cost, and N is the normalization function.

7. The supply chain order allocation method based on multi-stage cardinality constraint programming according to claim 1, characterized in that, The relation-aware deep Q-network employs an empirical replay and target network mechanism during training, including: selecting actions with an ε-greedy policy, storing transfer samples in the replay pool, and minimizing the Q-value error through gradient descent.

8. The supply chain order allocation method based on multi-stage cardinality constraint programming according to claim 1, characterized in that, The transformation of the multi-stage cardinal constraint programming model into an order allocation model containing only linear constraints is as follows: Where min is the minimum value function, T is the total number of decision cycles, and t is the current decision cycle. Let be the objective function. The binary vector chosen for the supplier Assign weight vectors to orders. Here is the characteristic data of all suppliers in period t, and N is the total number of suppliers. Assign a weight vector to the orders of supplier i in period t, a i , t The binary vector chosen by supplier i for period t.

9. A supply chain order allocation method based on multi-stage cardinality constraint programming according to claim 1, characterized in that, Solving the order allocation model yields the optimal order allocation weights, including: Transform the objective function of the order allocation model into a standard QP form. ,in , For the supplier feature matrix, Let T be the target vector, and T be the transpose symbol. The optimal order allocation weights are obtained by using the QP solver, and the order allocation results for each selected supplier are calculated based on the optimal order allocation weights.

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