A dynamic optimization method for multi-supplier order allocation on cross-border supply chain

Abstract

This invention discloses a dynamic optimization method for multi-supplier order allocation in cross-border supply chains. It acquires historical cross-border logistics timeliness data for the supplier's region, as well as historical long-term production quality, production costs, and delivery times data. The data undergoes multivariate fusion preprocessing through standardization and attention mechanisms; data decomposition is then performed; local features are extracted using a temporal convolutional network, and long short-term memory networks capture long-term dependencies, outputting a comprehensive predicted value; trapezoidal fuzzy number transformation and defuzzification are applied to the supplier's qualitative criteria to generate normalized fuzzy weights; finally, an iterative bilateral auction mechanism is used to perform iterative bilateral optimization based on the predicted values ​​and fuzzy weights, maximizing the social benefits of order allocation. This invention solves the problem of traditional methods struggling to dynamically integrate quantitative and qualitative indicators, significantly improving the efficiency and adaptability of cross-border supply chain order allocation.

Description

Technical Field

[0001] This invention belongs to the field of cross-border supply chain control technology, specifically relating to a dynamic optimization method for multi-supplier order allocation in a cross-border supply chain. Background Technology

[0002] With the rapid development of global economic integration and cross-border e-commerce, the complexity and variability of cross-border supply chains have increased significantly. Enterprises need to coordinate resources from multiple suppliers globally to cope with challenges such as fluctuating market demand, logistics timeliness, and exchange rate volatility. Order allocation, as a key link in supply chain management, directly impacts cost control, delivery efficiency, and supply chain resilience.

[0003] Existing cross-border supply chain order allocation methods largely rely on static models, making them ill-suited to the complex demands of modern cross-border supply chains. Traditional technologies suffer from the following drawbacks:

[0004] (1) At the data processing level, the fusion of multivariate time series features is insufficient and the non-stationarity of the data is not considered;

[0005] (2) The predictive model is not good at capturing long-term and short-term dependencies, which limits the accuracy of prediction.

[0006] (3) Qualitative standards (such as service stability, multilingual service capabilities, geopolitical risk scores, international compliance certification levels and cross-border payment reliability) lack quantitative means and cannot be effectively combined with quantitative indicators, making it difficult to reflect the supplier's sustainable cooperation potential and risk resilience.

[0007] (4) The allocation mechanism often adopts fixed weight or simple bidding, which cannot achieve the balanced optimization of benefits for all parties.

[0008] Therefore, there is an urgent need for a new order allocation method that can dynamically integrate multi-dimensional data, quantify qualitative standards, and dynamically optimize the interests of all parties in order to improve the agility, robustness, and sustainability of cross-border supply chains. Summary of the Invention

[0009] To address the shortcomings of existing technologies and achieve the goals of improving dynamic adaptability and avoiding the separation of qualitative and quantitative indicators, this invention adopts the following technical solution:

[0010] A dynamic optimization method for multi-supplier order allocation in a cross-border supply chain includes the following steps:

[0011] Step S1: Obtain multidimensional historical time series data of each supplier's region, eliminate dimensional differences through Z-score standardization, and use attention mechanism to fuse multiple variables into single-channel time series data;

[0012] Step S2: Generate a disturbance signal based on time series data, and decompose the disturbance signal into multiple intrinsic mode function components (IMFs) and a residual term through complementary ensemble empirical mode decomposition (CEEMD).

[0013] Step S3: Construct a Temporal Convolutional Network (TCN) and a Long Short-Term Memory (LSTM) model. Extract local features of time-series data through the TCN layer and capture long-term dependency features of time-series data through the LSTM layer. Each intrinsic mode function (IMF) and residual term is trained by deep learning through the model to predict future time-series data, obtaining predicted values ​​of multiple IMFs and residual terms. Reconstruct the predicted values ​​to obtain the supplier comprehensive score prediction value.

[0014] Step S4: Use linguistic variables to evaluate the qualitative criteria of suppliers for decision-makers (DMs), and convert the evaluation into numerical weights using trapezoidal fuzzy numbers. Based on the numerical weights, obtain the internal and external weights of suppliers based on services.

[0015] Step S5: Based on the predicted comprehensive supplier score and the internal and external weights, the enterprise bid and supplier bid are iteratively optimized through an iterative bilateral auction mechanism to maximize social benefits under the constraint of supply and demand balance, and then the orders are allocated.

[0016] Further, step S1 includes the following steps:

[0017] Step S1.1: Standardize and preprocess the multidimensional historical data of each supplier to obtain feature vectors of multiple dimensions corresponding to the historical data;

[0018] Step S1.2: Fuse multiple variables through attention mechanism; input feature vector for each time step, calculate attention score through fully connected layer, calculate attention weight of multi-dimensional features through normalization operation of attention score, fuse multi-dimensional features based on attention weight, generate supplier historical fused data features based on time step, and finally obtain complete time series data.

[0019] Furthermore, in step S1.1, the Z-score normalization preprocessing for the multidimensional historical data of each supplier is performed independently for each dimension, and the formula is as follows:

[0020]

[0021] in, Representing historical data The corresponding standardized value, t represents the time step, μ i and σ iLet represent the mean and standard deviation of the i-th dimension, respectively; T represents cross-border logistics timeliness; Q represents production quality; C represents production cost; and D represents delivery time.

[0022] Furthermore, in step S1.2, multiple variables are fused through an attention mechanism; a feature vector is input for each time step t. Attention scores are calculated using fully connected layers.

[0023]

[0024] Where ReLU represents the activation function, and W and b represent the learnable weights and biases, respectively;

[0025] Attention weights are calculated using the normalized function Softmax for the four features T, Q, C, and D at each time step.

[0026]

[0027] Where exp(·) represents the exponential function;

[0028] The four features are weighted and summed to generate the supplier's historical fused data features based on time step t:

[0029]

[0030] By iterating through all time steps t, the final complete time series data X is obtained. fused = [x1, x1, ..., x t ].

[0031] Furthermore, the complementary set empirical mode decomposition (CEEMD) in step S2 includes the following steps:

[0032] Step S2.1: Add white noise to the time series data X. fused Add Gaussian white noise w i (t), generating a disturbance signal:

[0033] x i (t)=x(t)+∈0w i (t), (i = 1, 2, ..., N)

[0034] Where x(t) represents the data feature at time step t, ∈ 0 represents the noise intensity, and N represents the number of times noise is added. i (t) represents the disturbance signal at time step t after adding the i-th white noise;

[0035] Step S2.2: Decompose and extract the intrinsic mode function (IMF) components; for each disturbance signal xi (t) Perform Empirical Mode Decomposition (EMD) to obtain K intrinsic mode function (IMF) components and a residual term R. The final decomposition result is:

[0036]

[0037] Each intrinsic mode function (IMF) component IMF k Both the residual R and the time series data are time series data, and k represents the index of the intrinsic mode function (IMF) component.

[0038] Furthermore, the model construction in step S3 includes the following steps:

[0039] Step S3.1: The Temporal Convolutional Network (TCN) extracts local features of the time series through dilated causal convolution and residual connections. Each intrinsic mode function (IMF) component and residual term is used as an independent input sequence, for a total of K+1 inputs.

[0040] Step S3.2: Input the feature sequence extracted by the Temporal Convolutional Network (TCN) into the Long Short-Term Memory (LSTM) network. The long-term dependencies are captured through the gating mechanism. The LSTM layer updates the cell state through the input gate, forget gate, and output gate, outputs the hidden state, and maps it to the predicted value.

[0041] Furthermore, in step S3.1, causal convolution ensures that each time step in the output sequence depends only on the data at the current time step and before it, maintaining the causal order of time and preventing future information leakage; the formula for calculating causal convolution is:

[0042]

[0043] Among them, y t x represents the output at time step t. t-k This represents the value of the input sequence at time step tk, where K represents the kernel size and w k This represents the k-th weight of the convolution kernel; causal convolution ensures that the convolution operation does not introduce future information.

[0044] Dilated Convolution: To expand the receptive field, TCN introduces dilated convolution. Dilated convolution, based on standard convolution, increases the spacing between inputs by introducing a dilation factor 'd', thus expanding the receptive field without increasing the number of parameters. The formula for calculating dilated convolution is:

[0045]

[0046] Where d represents the expansion factor;

[0047] Residual connections add the input to the output after convolution, forming skip connections, which alleviates the gradient vanishing problem and accelerates the training of deep networks.

[0048] Furthermore, in step S3.2, the core formula of the gating mechanism is as follows:

[0049] The input gate controls the updating of the cell state with new information:

[0050]

[0051] Among them, i t The input gate weights (between 0 and 1) are represented by σ, which represents the sigmoid activation function, and W is the input gate weight. i ,b i h represents the weight matrix and bias term of the input gate. t-1 Let x represent the hidden state at the previous time step. t This represents the input at the current moment;

[0052] The forget gate determines which old information is discarded from the cell state:

[0053] f t =σ(W f [h t-1 ]+b f )

[0054] Among them, f t Indicates the forget gate weight;

[0055] Candidate cell states generate new candidate values, which are used to update the cell state:

[0056] C t-1 =tanh(W C [h t-1 ]+b C )

[0057] Cell state update combines forget gate and input gate to update cell state:

[0058] C t =f t ⊙C t-1 +i t ⊙

[0059] Where ⊙ represents element-wise multiplication;

[0060] The output gate generates the current hidden state:

[0061] o t =σ(W O [h t-1 ]+b O )

[0062] ht =o t ⊙tanh(C t )

[0063] Among them, o t Indicates the output gate weights;

[0064] The fully connected layer maps the hidden states of the Long Short-Term Memory (LSTM) network to predicted values:

[0065] y t+1 =W FCL *h t +b FCL

[0066] Among them, W FCL ,b FCL This represents the weights and bias parameters of the fully connected layer, y t+1 This represents the predicted value of the intrinsic mode function component (IMF) at time t+1.

[0067] Using the above formula, high-frequency components are captured by the local convolution of the temporal convolutional network (TCN), while low-frequency trends are modeled by the intrinsic mode function (IMF) components. The prediction results of each IMF component and the residual term are summed to restore the complete prediction of the original sequence, resulting in a comprehensive score.

[0068]

[0069] in, Residual represents the predicted value of the i-th intrinsic mode function component (IMF). t+1 S represents the predicted value of the residual term. t+1 This represents the final overall score forecast, reflecting the supplier's overall performance in terms of quality, cost, and delivery time, and representing the supplier's comprehensive capabilities at a future point in time.

[0070] Further, step S4 includes the following steps:

[0071] Step S4.1: Convert the linguistic variables (such as "high", "medium", "low") used by decision-makers (DMs) to evaluate suppliers into trapezoidal fuzzy numbers;

[0072] Step S4.2: Aggregation and Defuzzification; Averaging the fuzzy numbers evaluated by multiple decision-makers to reduce individual subjective bias, and using the centroid method for defuzzification to transform the comprehensive fuzzy numbers into definite weights;

[0073] Step S4.3: Normalize the weight range of different evaluation criteria to obtain the normalized supplier weights, so as to avoid the impact of differences in dimensions on the comparison.

[0074] Step S4.4: Integrate internal and external weights; multiply the supplier weights of the same standard with the determined weights, and sum them according to the internal and external standards of the service to obtain the internal and external weights respectively.

[0075] Furthermore, step S5 specifically includes the following steps:

[0076] Step S5.1: Construct a dynamic pricing model to determine the prices quoted by both parties;

[0077] Company Quotation:

[0078]

[0079] T ij =Tariff rate j *d ij +Exchange rate volatility ij *p j

[0080] Among them, a i S represents the total demand of the enterprise. j This represents the supplier's overall score, z ij p represents the distance factor. j d represents the benchmark exchange rate between the currency of supplier j's country and the settlement currency of company i. ij This represents the number of orders that supplier j receives from enterprise i;

[0081] Supplier quotation:

[0082]

[0083] Where, m j This represents the marginal cost coefficient (which increases with order volume), n j S represents the fixed cost coefficient. j The higher the value, the lower the cost-sharing; ∈ represents the prevention of division by zero constant.

[0084] Step S5.2: Define the objective function and constraints:

[0085] Enterprise utility (maximizing order fulfillment efficiency):

[0086]

[0087] Among them, a ij This represents the order quantity that company i allocates to supplier j;

[0088] Supplier costs (minimizing resource consumption):

[0089]

[0090] Where, dj This represents the total number of orders received by supplier j;

[0091] Maximizing social benefits:

[0092]

[0093] Where, N i N represents the number of companies. j λ represents the number of suppliers, and λ represents the adjustment factor (balancing economic utility and risk resilience);

[0094] Resource allocation constraints: Ensure supply and demand balance and do not exceed the supplier's maximum capacity;

[0095]

[0096] Where, d ji This represents the number of orders supplier j receives from company i. This represents the maximum production capacity limit of supplier j;

[0097] Step S5.3: Iterative optimization and updating of enterprise quotations and supplier price guarantees to generate an order allocation matrix;

[0098] Buyer offer update:

[0099]

[0100] Where η represents the learning rate, which controls the speed of price adjustment. This represents the quote from company i to supplier j in the k-th iteration;

[0101] Seller price update:

[0102]

[0103] in, Let γ represent the price quoted by supplier j to company i in the k-th iteration, and let γ represent the learning rate (controlling the speed of price adjustment). Optimization terminates when the rate of change of price is less than the threshold (e.g., Δ < 1%) for two consecutive rounds or when the maximum number of iterations is reached.

[0104] The advantages and beneficial effects of this invention are as follows:

[0105] The present invention provides a dynamic optimization method for multi-supplier order allocation in a cross-border supply chain. Based on iterative bilateral auction, the method dynamically optimizes order allocation decisions in a cross-border supply chain, which can solve the problems of poor dynamic adaptability and the separation of qualitative and quantitative indicators in the prior art. Attached Figure Description

[0106] Figure 1 This is an overall flowchart of the method in the embodiments of the present invention.

[0107] Figure 2 This is a flowchart of the iterative bilateral auction mechanism in an embodiment of the present invention. Detailed Implementation

[0108] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0109] like Figure 1 As shown, a dynamic optimization method for multi-supplier order allocation in a cross-border supply chain is proposed. This method involves data preprocessing, time-frequency feature extraction, TCN-LSTM modeling, fuzzy SWOT analysis, and iterative auction optimization. Based on iterative bilateral auctions, it dynamically allocates multi-supplier orders, specifically including the following steps:

[0110] Step S1: Data preprocessing; Obtain historical cross-border logistics timeliness of each supplier's region, as well as multi-dimensional time series data on historical production quality, production cost, and delivery time of each supplier. Eliminate dimensional differences through Z-score standardization and use attention mechanism to fuse multiple variables into single-channel time series data.

[0111] Specifically, historical data x for each supplier is obtained, with a time step t. Each time step has four feature dimensions: cross-border logistics timeliness T, quality Q, cost C, and delivery time D. To eliminate differences in dimensions, the four features are standardized so that each feature is a sequence with a mean of 0 and a standard deviation of 1. An attention mechanism is used to calculate the weights of the four features at each time step, and the four features are merged into a univariate time series.

[0112] The preprocessing of historical data for each supplier includes the following steps:

[0113] Step S1.1: Standardization Processing; Perform Z-score standardization on the multi-dimensional data of each supplier, with each dimension performed independently. The formula is as follows:

[0114]

[0115] Where, μ i and σ i Let be the mean and standard deviation of the i-th dimension, respectively. Its corresponding standardized value.

[0116] Step S1.2: Attention mechanism to fuse multiple variables: Input feature vector for each time step t Calculate the attention score using a fully connected layer:

[0117]

[0118] in, and Learnable parameters

[0119] Next, attention weights are calculated for the four features at each time step using the Softmax function:

[0120]

[0121] The four features are weighted and summed to generate the supplier's historical fused data features based on time step t:

[0122]

[0123] By iterating through all time steps t, the final complete time series X is obtained. fused = [x1, x1, ..., x t ].

[0124] Step S2: Perform Complementary Ensemble Empirical Mode Decomposition (CEEMD) on the fused time series data; add white noise to the preprocessed data to generate perturbation signals, and decompose each perturbation signal into multiple intrinsic mode function components (IMFs) and a residual term through CEEMD.

[0125] The preprocessed data is decomposed using CEEMD, including the following steps:

[0126] Step S2.1: Add white noise; adjust the original signal X fused Add Gaussian white noise w i (t), generating a disturbance signal:

[0127] x i (t)=x(t)+∈0w i (t), (i = 1, 2, ..., N)

[0128] Where ∈0 represents the noise intensity, and N represents the number of times noise is added.

[0129] Step S2.2: Decompose and extract the IMF: For each disturbance signal x i (t) Perform EMD decomposition to obtain K IMF (Intrinsic Mode Function) components and one residual term R. The final decomposition result is as follows:

[0130]

[0131] Each IMF component IMF kBoth the residual R and the time series are time series, and k is the number of IMF components.

[0132] Step S3: TCN-LSTM Modeling; Construct a combined structure of Temporal Convolutional Network (TCN) and Long Short-Term Memory Network (LSTM). Extract local features of time-series data through the TCN layer and capture long-term dependency features of time-series data through the LSTM layer. Each IMF component and residual is trained by an independent TCN-LSTM sub-model. Multiple TCN-LSTM models are trained by deep learning based on multiple IMF components and residual terms R. Predict future time data through multiple trained TCN-LSTM models to obtain predicted values ​​of multiple IMF components and residual terms. Reconstruct the predicted values ​​of multiple IMF components and residual terms, i.e., add the prediction results to obtain the final predicted value of the supplier comprehensive score.

[0133] The construction of the TCN-LSTM combination structure includes the following steps:

[0134] Step S3.1: TCN extracts local features of the time series through dilated causal convolution and residual connections. Each component and residual is used as an independent input sequence, for a total of K+1 inputs.

[0135] Causal convolution: Causal convolution ensures that each time step in the output sequence depends only on the data at the current time step and before it, preserving the causal order of time and avoiding the leakage of future information; the formula for calculating causal convolution is:

[0136]

[0137] Among them, y t For the output at time t, x t-k Let w be the value of the input sequence at time tk, K be the kernel size, and w be the value of the input sequence at time tk. k is the k-th weight of the convolution kernel; causal convolution ensures that the convolution operation does not introduce future information.

[0138] Dilated Convolution: To expand the receptive field, TCN introduces dilated convolution. Dilated convolution, based on standard convolution, increases the spacing between inputs by introducing a dilation factor 'd', thus expanding the receptive field without increasing the number of parameters. The formula for calculating dilated convolution is:

[0139]

[0140] Where d is the expansion factor.

[0141] Residual connections: These add the input to the output of the convolution, forming a skip connection. This alleviates the vanishing gradient problem and accelerates the training of deep networks. The formula for implementing residual connections is:

[0142] Output = Conv(Input) + Input

[0143] Step S3.2: LSTM captures long-term dependencies through a gating mechanism. The input is the feature sequence extracted by TCN. The LSTM layer updates the cell state through input gate, forget gate, and output gate, and outputs the hidden state and maps it to the predicted value. Its core formula is as follows:

[0144] The input gate controls the updating of the cell state with new information:

[0145]

[0146] Among them, i t The input gate weights are between 0 and 1, σ is the sigmoid activation function, and W... i ,b i It is the weight matrix and bias term of the input gate, h t-1 It is the hidden state from the previous moment, x t It is the input at the current moment;

[0147] The forget gate determines which old information is discarded from the cell state:

[0148] f t =σ(W f [h t-1 ]+b f )

[0149] Among them, f t Weight for the forget gate;

[0150] Candidate cell states generate new candidate values, which are used to update the cell state:

[0151] C t-1 =tanh(W C [h t-1 ]+b C )

[0152] Cell state update combines forget gate and input gate to update cell state:

[0153] C t =f t ⊙C t-1 +i t ⊙

[0154] Where ⊙ represents element-wise multiplication;

[0155] The output gate generates the current hidden state:

[0156] o t =σ(W O [h t-1 ]+b O)

[0157] h t =o t ⊙tanh(C t )

[0158] Among them, o t The output gate weights;

[0159] The fully connected layer maps the hidden states of the LSTM to the predicted values:

[0160] y t+1 =W FCL *h t +b FCL

[0161] Among them, W FCL ,b FCL For the weights and bias parameters of the fully connected layer, y t+1 This represents the predicted value of the IMF component at time t+1.

[0162] Using the above formula, high-frequency components are captured by local convolution of TCN, and low-frequency trends are modeled by LSTM. The prediction results of each IMF component and the residual are summed to restore the complete prediction of the original sequence and obtain a comprehensive score.

[0163]

[0164] in, For the predicted value of the i-th IMF component, Residual t+1 S is the predicted value of the residual term. t+1 The final overall score forecast reflects the supplier's overall performance in terms of quality, cost, and delivery time, representing the supplier's comprehensive capabilities at a future point in time.

[0165] Step S4: Use the fuzzy SWOT model to analyze the qualitative standards of suppliers. Convert the linguistic variables of multiple decision-makers' evaluation of suppliers into trapezoidal fuzzy numbers, aggregate, defuzzify and normalize them to obtain the transformed definite weights. Based on the internal and external standards of supplier services, generate the internal and external weights of suppliers.

[0166] Specifically, decision-makers (DMs) use linguistic variables to evaluate suppliers' qualitative criteria (such as service stability, multilingual service capabilities, geopolitical risk scores, international compliance certification levels, and cross-border payment reliability). These evaluations are converted into numerical weights using trapezoidal fuzzy numbers, and the final supplier weights are obtained through defuzzification. Fuzzy SWOT analysis of qualitative criteria includes the following steps:

[0167] Step S4.1: Decision makers (DMs) evaluate suppliers using linguistic variables (such as "high", "medium", "low"), and convert these linguistic variables into trapezoidal fuzzy numbers. For example, "high" could correspond to (4, 6, 8, 8);

[0168] Step S4.2: Aggregation and Deblurring:

[0169] By averaging the fuzzy evaluations of multiple decision-makers, individual subjective biases can be reduced.

[0170]

[0171] Among them, f sj Let s be the comprehensive fuzzy number of supplier s under standard j;

[0172] The centroid method is used for defuzzification, transforming the comprehensive fuzzy number into a definite value:

[0173]

[0174] Step S4.3: Normalize the weight ranges of different standards to avoid the influence of differences in dimensions on the comparison.

[0175]

[0176] Where, N sj The normalized supplier weights (range 0-1), The determined weights after deblurring;

[0177] Step S4.4: Integrating internal and external weights:

[0178]

[0179] in, For the importance weight of the j-th criterion (set by the decision-maker), I s To incorporate the importance weights of internal standards (such as service stability and multilingual service capabilities), E s To incorporate the importance weights of external standards (such as geopolitical risk scores, international compliance certification levels, and cross-border payment reliability).

[0180] Step S5: The iterative two-sided auction algorithm dominates order allocation; based on the comprehensive score in Step S3 and the fuzzy SWOT weights in Step S4, such as... Figure 2 As shown, an iterative bilateral auction mechanism is designed to iteratively optimize the enterprise's bid X and the supplier's bid Y, maximizing social benefits under the constraint of supply and demand balance, and completing order allocation. The specific steps include:

[0181] Step S5.1: Construct a dynamic pricing model to determine the prices quoted by both parties;

[0182] Company Quotation:

[0183]

[0184] T ij =Tariff rate j *d ij +Exchange rate volatility ij *p j

[0185] Among them, a i For the total demand of the enterprise, S j For the overall evaluation of suppliers, z ij p is the distance factor. j Let d be the benchmark exchange rate between the currency of supplier j's country and the settlement currency of company i. ij Let J be the number of orders that supplier j receives from enterprise i.

[0186] Supplier quotation:

[0187]

[0188] Where, m j n is the marginal cost coefficient (increasing with order volume). j Fixed cost coefficient (subject to S) j Impact, S j The higher the value, the lower the cost sharing), where ∈ is a constant to prevent division by zero;

[0189] Step S5.2: Define the objective function and constraints:

[0190] Enterprise utility (maximizing order fulfillment efficiency):

[0191]

[0192] Among them, a ij The order quantity allocated to supplier j for company i;

[0193] Supplier costs (minimizing resource consumption):

[0194]

[0195] Where, d j The total number of orders obtained by supplier j;

[0196] Maximizing social benefits:

[0197]

[0198] Where, N i N represents the number of firms. jλ represents the number of suppliers, and λ is a moderating factor (balancing economic utility and risk resilience).

[0199] Resource allocation constraints: Ensure supply and demand balance and do not exceed the supplier's maximum capacity;

[0200]

[0201] Where, d ji Let j be the number of orders that supplier j receives from enterprise i. This represents the maximum production capacity limit for supplier j.

[0202] Step S5.3: Iterative optimization and updating of enterprise quotations and supplier price guarantees to generate an order allocation matrix;

[0203] Buyer offer update:

[0204]

[0205] Where η is the learning rate, which controls the speed of price adjustment. Let $\frac{i}{j}$ be the price quoted by company $i$ to supplier $j$ in the $k$-th iteration.

[0206] Seller price update:

[0207]

[0208] in, Let γ be the price quoted by supplier j to company i in the k-th iteration, and let γ be the learning rate (controlling the speed of price adjustment). Optimization terminates when the price change rate is less than the threshold (e.g., Δ < 1%) for two consecutive rounds or when the maximum number of iterations is reached.

[0209] 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 the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dynamic optimization method for multi-supplier order allocation in a cross-border supply chain, characterized in that... Includes the following steps: Step S1: Obtain multidimensional historical time-series data for each supplier's region; including the following steps: Step S1.1: Standardize and preprocess the multidimensional historical data of each supplier to obtain feature vectors of multiple dimensions corresponding to the historical data; Step S1.2: Fuse multiple variables through attention mechanism; input feature vector for each time step, calculate attention score through fully connected layer, calculate attention weight of multi-dimensional features through normalization operation of attention score, fuse multi-dimensional features based on attention weight, generate supplier historical fused data features based on time step, and finally obtain complete time series data; Step S2: Generate a disturbance signal based on time series data, and decompose the disturbance signal into multiple intrinsic mode function components and a residual term through complementary set empirical mode decomposition; Step S3: Construct a temporal convolutional network and a long short-term memory network model. Extract local features of time-series data through the temporal convolutional network layer and capture long-term dependency features of time-series data through the long short-term memory network layer. Each intrinsic mode function component and the residual term are trained by deep learning through the model to predict future time-series data, and the predicted values ​​of multiple intrinsic mode function components and residual terms are obtained. The predicted values ​​are reconstructed to obtain the predicted value of the supplier comprehensive score. Step S4: Evaluate the qualitative criteria of suppliers using linguistic variables for decision-makers, and convert the evaluation into numerical weights using trapezoidal fuzzy numbers. Based on the numerical weights, obtain the internal and external weights of suppliers based on services. Step S5: Based on the predicted comprehensive supplier score and the internal and external weights, the enterprise bid and supplier bid are iteratively optimized through an iterative bilateral auction mechanism to maximize social benefits under the constraint of supply and demand balance, and then the orders are allocated.

2. The dynamic optimization method for multi-supplier order allocation in a cross-border supply chain according to claim 1, characterized in that: In step S1.1, the Z-score normalization preprocessing for the multidimensional historical data of each supplier is performed independently for each dimension, and the formula is as follows: in, Representing historical data The corresponding standardized value, where t represents the time step. and They represent the first The mean and standard deviation of each dimension, where T represents cross-border logistics timeliness, Q represents production quality, C represents production cost, and D represents delivery time.

3. The dynamic optimization method for multi-supplier order allocation in a cross-border supply chain according to claim 2, characterized in that: In step S1.2, multiple variables are fused using an attention mechanism; a feature vector is input for each time step t. Attention scores are calculated through fully connected layers. : Where ReLU represents the activation function. and These represent the learnable weights and biases, respectively. Attention weights are calculated for the four features T, Q, C, and D at each time step using a normalization function. : Where exp(·) represents the exponential function; The four features are weighted and summed to generate the supplier's historical fused data features based on time step t: Traverse all time steps To obtain the final complete time series data .

4. The dynamic optimization method for multi-supplier order allocation in a cross-border supply chain according to claim 1, characterized in that: The complementary set empirical mode decomposition in step S2 includes the following steps: Step S2.1: Add white noise to the time series data. Add Gaussian white noise Generate a disturbance signal: in, This represents the data characteristics at time step t. The noise level is represented by N, which represents the number of times the noise was added. This represents the disturbance signal at time step t after the i-th instance of white noise has been added; Step S2.2: Decompose and extract intrinsic mode function components; for each disturbance signal Empirical mode decomposition is performed to obtain K eigenmode function components and a residual term R. The final decomposition result is as follows: Each intrinsic mode function component Both the residual term R and the residual term R are time series data, and k represents the index of the intrinsic mode function component.

5. The dynamic optimization method for multi-supplier order allocation in a cross-border supply chain according to claim 1, characterized in that: The model construction in step S3 includes the following steps: Step S3.1: The temporal convolutional network extracts local features of the time series through dilated causal convolution and residual connections, with each intrinsic mode function component and residual term serving as an independent input sequence; Step S3.2: Input the feature sequence extracted by the temporal convolutional network into the long short-term memory network. The long short-term memory network layer captures long-term dependencies through the gating mechanism. The long short-term memory network layer updates the cell state through the input gate, forget gate, and output gate, outputs the hidden state and maps it to the predicted value.

6. The dynamic optimization method for multi-supplier order allocation in a cross-border supply chain according to claim 5, characterized in that: In step S3.1, the formula for calculating causal convolution is: in, This represents the output at time step t. This represents the value of the input sequence at time step tk, where K represents the kernel size. This represents the k-th weight of the convolution kernel; The formula for calculating dilated convolution is: Where d represents the expansion factor; Residual connections add the input to the output after convolution.

7. The dynamic optimization method for multi-supplier order allocation in a cross-border supply chain according to claim 1, characterized in that: Step S4 includes the following steps: Step S4.1: Convert the linguistic variables used by decision-makers to evaluate suppliers into trapezoidal fuzzy numbers; Step S4.2: Aggregation and Defuzzification; Averaging the fuzzy numbers evaluated by multiple decision-makers and using the centroid method for defuzzification, transforming the comprehensive fuzzy numbers into definite weights; Step S4.3: Normalize the weight range of different evaluation criteria to obtain the normalized supplier weights; Step S4.4: Integrate internal and external weights; multiply the supplier weights of the same standard with the determined weights, and sum them according to the internal and external standards of the service to obtain the internal and external weights respectively.

8. The dynamic optimization method for multi-supplier order allocation in a cross-border supply chain according to claim 1, characterized in that: Step S5 specifically includes the following steps: Step S5.1: Construct a dynamic pricing model to determine the prices quoted by both parties; Company Quotation: in, This represents the total demand of enterprises. This indicates the supplier's overall score. Represents the distance factor. This represents the benchmark exchange rate between the currency of supplier j's country and the settlement currency of company i. This represents the number of orders that supplier j receives from enterprise i; Supplier quotation: in, This represents the marginal cost coefficient. This represents the fixed cost coefficient. The higher the value, the lower the cost per unit. Indicates the prevention of zero constant; Step S5.2: Define the objective function and constraints: Corporate utility: in, This represents the order quantity that company i allocates to supplier j; Supplier costs: in, This represents the total number of orders received by supplier j; Maximizing social benefits: in, Indicates the number of companies. Indicates the number of suppliers. Indicates the regulating factor, I s E represents the importance weighting based on internal standards. s This indicates the importance weight incorporating external standards; Resource allocation constraints: Ensure supply and demand balance and do not exceed the supplier's maximum capacity; in, This represents the number of orders supplier j receives from company i. This represents the maximum production capacity limit of supplier j; Step S5.3: Iterative optimization and updating of enterprise quotations and supplier price guarantees to generate an order allocation matrix; Buyer offer update: Among them, represents the learning rate and controls the quotation adjustment speed. represents the quotation of enterprise i for supplier j in the k-th round of iteration. Seller price update: in, This represents the price quoted by supplier j to company i in the k-th iteration. This represents the learning rate. Optimization terminates when the rate of change of prices is less than a threshold for two consecutive rounds or when the maximum number of iterations is reached.

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