Cross-border commodity regional demand prediction sub-warehouse method and system

Abstract

The present application relates to the technical field of cross-border e-commerce supply chain intelligent warehousing, and discloses a cross-border commodity regional demand prediction warehousing method and system, which comprises the following steps: extracting features from historical multi-dimensional data, constructing a reverse state transition Markov chain, and outputting a reverse performance cost expectation matrix; splicing the features into a full-link feature tensor, and generating a yield prediction dynamic mapping table by using a support vector regression; constructing a mixed integer programming equation, and outputting a global optimal warehousing decision by using a branch and bound algorithm; obtaining the allocation quantity by analyzing the decision, and planning the shortest logistics route to generate a pre-delivery instruction to execute commodity distribution; and through reverse cost quantification modeling and global optimization solving, the present application solves the problem of ignoring the return and exchange link cost in the warehousing decision, and realizes the maximization of full-link yield and efficient cross-border supply chain collaboration.

Description

Technical Field

[0001] This invention relates to the field of intelligent warehousing technology in cross-border e-commerce supply chains, and particularly to a method and system for regional demand forecasting and warehousing of cross-border goods. Background Technology In cross-border e-commerce supply chain management, regional demand forecasting and warehouse planning often rely on data modeling and operations optimization techniques. Predictive models are built by collecting data such as historical transaction records, target market attributes, transportation rates, and warehouse capacity. These technologies are primarily used to calculate the demand for goods in different regions, aiming for low delivery costs and optimal warehouse network coverage, and outputting a distribution plan for pre-positioned storage nodes. This assists cross-border e-commerce companies in completing cross-regional inventory allocation and fulfillment resource allocation, meeting the shopping needs of consumers in different regions.

[0002] In actual cross-border warehousing network scheduling operations, after on-site finance and operations engineers implement regional warehouse allocation based on forecast plans, they often observe that although some overseas distribution centers initially meet their positive outbound volume targets, when faced with concentrated returns and exchanges, the various miscellaneous expenses incurred in the return process directly offset or even far exceed the previous positive sales gross profit, leading to a continuous negative operating loss for the overall warehousing node. This operational loss caused by returns and exchanges not only results in a large backlog of returned goods within the overseas warehouse network, ineffectively occupying valuable physical storage space and preventing subsequent batches of regular goods from being smoothly stored and shelved, but also generates additional manual inventory handling costs and warehousing fees, continuously pushing up the unit cost per item. Simultaneously, the accumulation of large amounts of slow-moving returned goods that cannot be quickly transferred directly causes slow cash flow for cross-border e-commerce companies and inventory devaluation at overseas warehousing nodes, increasing the risk of a financial disruption in the overall supply chain. Therefore, how to reduce the node operational losses caused by returns and exchanges during the regional warehouse allocation planning process for cross-border goods is a problem that urgently needs to be solved in this field. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the present invention aims to provide a method and system for predicting and allocating regional demand for cross-border commodities. By extracting positive sales features and reverse fulfillment features from historical multidimensional data of cross-border commodities to construct a full-link feature tensor for regional demand prediction, and combining the expected reverse fulfillment cost matrix to construct a mixed integer programming equation that maximizes the expected total revenue for global solution, the invention achieves the technical effect of maximizing the full-link revenue of cross-border commodities and precise and efficient scheduling of pre-positioned distribution.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, this invention provides a method for regional demand forecasting and warehouse allocation of cross-border commodities, comprising: extracting features from historical multidimensional data of cross-border commodities to generate a positive sales feature vector and a reverse fulfillment feature vector; constructing a reverse state transition Markov chain based on the reverse fulfillment feature vector and calculating the state transition probability, outputting a reverse fulfillment cost expectation matrix; concatenating the positive sales feature vector and the reverse fulfillment cost expectation matrix into a full-link feature tensor, using a support vector regression algorithm to calculate the regional demand of the full-link feature tensor, generating a full-link revenue forecasting dynamic mapping table; constructing a mixed integer programming equation with the objective function of maximizing expected total revenue based on the full-link revenue forecasting dynamic mapping table, using a branch and bound algorithm to solve the mixed integer programming equation, outputting a globally optimal warehouse allocation decision feature set; parsing the globally optimal warehouse allocation decision feature set to obtain the allocation quantity and the shortest logistics route configuration, generating a pre-shipment instruction sequence based on the allocation quantity and the shortest logistics route configuration, and executing the pre-shipment operation of the commodities.

[0005] Furthermore, the process of extracting features from historical multidimensional data of cross-border commodities to generate positive sales feature vectors and negative fulfillment feature vectors, and outputting the expected negative fulfillment cost matrix, includes: obtaining historical multidimensional data of cross-border commodities from cross-border logistics terminals and regional e-commerce front-ends; discretizing and reducing the dimensionality of the historical multidimensional data of cross-border commodities to extract positive sales feature vectors and negative fulfillment feature vectors respectively; and constructing a negative state transition Markov chain using the negative fulfillment feature vectors. Specifically, the method of constructing a negative state transition Markov chain using the negative fulfillment feature vectors is as follows: parse the return rate of goods in the target area, the goods... The system calculates the exchange rate and customs detention rate; it defines the discrete state space of the reverse state transition Markov chain, which includes normal receipt, local return, cross-border return, and local destruction states; it calculates the transition probability matrix between each state in the discrete state space based on the return rate, exchange rate, and customs detention rate, and combines them to generate the reverse state transition Markov chain; based on the reverse state transition Markov chain and the transition probability matrix, it inputs the reverse tariff value of the target area, the return logistics pricing value, and the unit price of destruction of unsold goods into the reverse state transition Markov chain to solve for the steady-state probability distribution, generating the expected reverse fulfillment cost matrix.

[0006] Furthermore, the process of concatenating the forward sales feature vector and the reverse fulfillment cost expectation matrix into a full-link feature tensor and generating a dynamic mapping table for full-link revenue prediction includes: performing dimension alignment calculations on the vector dimension of the forward sales feature vector and the matrix dimension of the reverse fulfillment cost expectation matrix to obtain aligned forward features and aligned reverse matrices; concatenating the aligned forward features and aligned reverse matrices along the feature dimension direction to generate a full-link feature tensor; initializing the Gaussian radial basis kernel function parameters and penalty coefficients of the support vector regression algorithm; inputting the full-link feature tensor into the initialized support vector regression algorithm, calculating the functional distance from the full-link feature tensor to the optimal hyperplane of the support vector regression algorithm, and outputting the regional demand prediction value; calculating the expected net revenue per unit of goods in each target region based on the regional demand prediction value, the pricing of forward sales goods, and the expected cost value in the reverse fulfillment cost expectation matrix; and mapping the expected net revenue per unit of goods in each target region and the regional demand prediction value to the three-dimensional coordinate nodes of the target region to generate a dynamic mapping table for full-link revenue prediction.

[0007] Furthermore, the process of constructing a mixed-integer programming equation based on the dynamic mapping table of end-to-end revenue prediction and solving it to output the globally optimal warehouse allocation decision feature set includes: extracting the distribution sequence of expected net revenue per unit of goods in the target area from the dynamic mapping table of end-to-end revenue prediction; obtaining the real-time inventory value, maximum capacity threshold, and forward delivery logistics cost value of each regional warehouse; calculating the total revenue value by multiplying the distribution sequence of expected net revenue per unit of goods by the warehouse allocation delivery quantity variable, and calculating the total logistics cost value by multiplying the warehouse allocation delivery quantity variable by the forward delivery logistics cost value; using the total revenue value minus the total logistics cost value as the objective function to maximize the expected total revenue; setting the real-time inventory value and the maximum capacity threshold as linear constraints of the objective function, and combining the objective function and the linear constraints to construct a mixed-integer programming equation. The mixed integer programming equation is solved using a branch and bound algorithm. Specifically, the branch and bound algorithm is used to solve the mixed integer programming equation as follows: remove the integer constraints on the warehouse delivery quantity variable in the mixed integer programming equation to obtain a linear programming relaxation problem; use the simplex algorithm to solve the linear programming relaxation problem to obtain an initial fractional solution; perform floor and floor operations on the warehouse delivery quantity variable based on the initial fractional solution to generate left and right branch nodes; recursively traverse the left and right branch nodes, compare the function bound values ​​of the left and right branch nodes, and remove non-optimal branch nodes whose function bound values ​​are lower than the current optimal solution, until all traversed nodes satisfy the integer constraints, and extract the node values ​​that satisfy the integer constraints as the global optimal warehouse allocation decision feature set.

[0008] Furthermore, the process of parsing the global optimal warehouse allocation decision feature set and executing the pre-positioning of goods includes: performing key-value pair reading operations on the global optimal warehouse allocation decision feature set to extract the starting warehouse identifier, target area warehouse identifier, and transfer quantity from the global optimal warehouse allocation decision feature set; querying the directed graph of the cross-border logistics network and using the Dijkstra algorithm to calculate the shortest logistics route configuration between the starting warehouse identifier and the target area warehouse identifier; combining and encapsulating the starting warehouse identifier, target area warehouse identifier, transfer quantity, and shortest logistics route configuration according to a standard data exchange protocol to generate a pre-positioning delivery instruction sequence; and sending the pre-positioning delivery instruction sequence to the warehouse automation control terminal, which then parses the pre-positioning delivery instruction sequence and executes the pre-positioning of goods.

[0009] Secondly, this invention provides a cross-border commodity regional demand forecasting and warehousing system for implementing the above-mentioned method, comprising: a data feature extraction and reverse cost quantification module, used to extract features from historical multidimensional data of cross-border commodities to generate positive sales feature vectors and reverse fulfillment feature vectors, construct a reverse state transition Markov chain based on the reverse fulfillment feature vectors and calculate the state transition probability, and output a reverse fulfillment cost expectation matrix; and a full-link revenue prediction mapping module, used to concatenate the positive sales feature vectors and the reverse fulfillment cost expectation matrix into a full-link feature tensor, and use a support vector regression algorithm to perform... The system calculates regional demand using a full-link feature tensor and generates a dynamic mapping table for full-link revenue prediction. A global warehouse allocation decision optimization module constructs a mixed-integer programming equation with the objective function of maximizing expected total revenue based on the dynamic mapping table. It then solves the mixed-integer programming equation using a branch-and-bound algorithm, outputting a globally optimal warehouse allocation decision feature set. A pre-schedule execution control module parses the globally optimal warehouse allocation decision feature set to obtain the allocation quantity and shortest logistics route configuration. Based on these parameters, it generates a pre-shipment instruction sequence and executes the pre-shipment of goods.

[0010] Compared to existing technologies, the advantages of this invention are as follows: By constructing a reverse state transition Markov chain and using the fundamental matrix of the absorption chain to solve for the steady-state probability, this invention accurately quantifies the multi-stage return, exchange, tariff, and destruction costs of cross-border e-commerce, effectively overcoming the shortcomings of traditional static calculations that ignore the complex cost accumulation of the reverse link, leading to an overestimation of warehouse distribution revenue. The forward sales features and the reverse cost matrix are concatenated into a full-link feature tensor, and a support vector regression algorithm is introduced for nonlinear regional demand prediction. Kernel method mapping and convex optimization characteristics ensure the model's generalization ability and global optimality. Based on this, a mixed-integer programming equation maximizing the expected total revenue is constructed, and a branch-and-bound algorithm is used to coordinate multi-warehouse inventory and capacity constraints to solve the global allocation scheme, completely avoiding the local optimum risk of greedy algorithms. This method establishes a data link between cost quantification, dynamic prediction, and optimal decision-making, significantly improving the accuracy of pre-positioning in the cross-border supply chain and the net revenue of the entire link, providing a highly reliable algorithmic framework for intelligent computing modeling and operations optimization decision-making in complex logistics scenarios. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of the cross-border commodity regional demand forecasting and warehousing method in this invention; Figure 2 This is a binning discretization interval diagram of positive sales dimension data in an embodiment of the present invention; Figure 3 This is a directed graph of a Markov chain with reverse state transitions, as shown in an embodiment of the present invention. Figure 4 This is a diagram of the horizontal splicing structure of the full-link feature tensor in an embodiment of the present invention; Figure 5 This is a constraint map of the support vector regression-insensitive tubular region in an embodiment of the present invention; Figure 6 This is a diagram showing the data node structure of the full-link predictive dynamic mapping table in an embodiment of the present invention; Figure 7 This is a diagram of an integer programming-based pruning tree structure with rounding up and down branches, as shown in an embodiment of the present invention. Figure 8 This is a Dijkstra shortest logistics time-efficiency route network diagram in an embodiment of the present invention; Figure 9 This is a standard encapsulation structure diagram of the pre-shipment instruction message field in an embodiment of the present invention; Figure 10 This is a functional module diagram of the cross-border commodity regional demand forecasting and distribution system in this invention. Detailed Implementation

[0013] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0014] Example 1: Please see Figure 1 As shown, this embodiment provides a method for regional demand forecasting and warehouse allocation of cross-border commodities, including: S1: Extract features from historical multidimensional data of cross-border commodities to generate positive sales feature vectors and reverse fulfillment feature vectors; construct a reverse state transition Markov chain based on the reverse fulfillment feature vectors and calculate the state transition probability, outputting the expected reverse fulfillment cost matrix.

[0015] Further, step S1 includes the following steps: S11: Obtain historical multidimensional data of cross-border commodities from cross-border logistics terminals and regional e-commerce front-ends; discretize and reduce the dimensionality of the historical multidimensional data of cross-border commodities, and extract the positive sales feature vector and the reverse fulfillment feature vector respectively.

[0016] The cross-border logistics terminal refers to data collection equipment and systems deployed at various nodes of the cross-border logistics chain, including customs electronic declaration systems, international transportation management systems, and overseas warehouse storage management systems. These terminals transmit logistics cost data, customs declaration data, and return / exchange logistics data to this system via standardized application programming interfaces (APIs). The regional e-commerce front-end refers to the front-end system of a cross-border e-commerce platform targeting consumers in each target sales region. This includes product display pages, order management modules, and after-sales service modules. The regional e-commerce front-end transmits sales order data, product return / exchange application data, and user behavior data to this system via data synchronization interfaces. The historical multi-dimensional data for cross-border goods includes two main categories: the first is positive sales dimension data, specifically including historical sales order volume, product unit price, promotional activity markers, seasonal markers, regional population base, and consumption capacity index for each target region; the second is reverse fulfillment dimension data, specifically including product return rate, product exchange rate, customs detention rate, reverse tariff value, return logistics pricing value, and unit price for destroying unsold goods for each target region. The consumption capacity index is obtained from the user profile database of the regional e-commerce front end. The consumption capacity index refers to the dimensionless value obtained by linearly normalizing the average cross-border e-commerce consumption amount of consumers in the target region in the past 12 calendar months. The normalization range is 0 to 1.

[0017] The method for discretizing historical multidimensional data of cross-border commodities is as follows: For continuous numerical variables in the positive sales dimension data, an equal-frequency binning method is used to divide the continuous values ​​into discrete intervals. Specifically, taking historical sales order volume as an example, historical sales order volume samples of all target regions are statistically analyzed over all historical statistical periods. The quartiles of the historical sales order volume samples are calculated, and the 25th, 50th, and 75th percentiles are used as binning boundaries to divide the historical sales order volume into four discrete level intervals, labeled as low demand level, low-to-medium demand level, medium-to-high demand level, and high demand level, respectively. For the product return rate, product exchange rate, and customs detention rate in the reverse fulfillment dimension data, the same equal-frequency binning method is used for discretization. The number of binning intervals is set to three, and the 33rd and 67th percentiles are used as binning boundaries, labeled as low rate level, medium rate level, and high rate level, respectively. The method for dimensionality reduction of discretized historical multidimensional data of cross-border commodities is as follows: Principal component analysis (PCA) is used to linearly reduce the dimensionality of the discretized positive sales dimension data, retaining the top few principal components whose cumulative variance contribution rate reaches a preset variance retention threshold. These retained principal components are then combined into a positive sales feature vector. The preset variance retention threshold is determined based on the information density of the historical sales data of cross-border e-commerce. When the cumulative variance contribution rate reaches the preset variance retention threshold, the retained principal components cover most of the effective information in the original positive sales dimension data. Preferably, the preset variance retention threshold can be set to 0.90. Similarly, PCA is used to linearly reduce the dimensionality of the discretized negative fulfillment dimension data, retaining the top few principal components whose cumulative variance contribution rate reaches a preset variance retention threshold. These retained principal components are then combined into a negative fulfillment feature vector. The dimension of the positive sales feature vector is equal to the number of principal components retained after dimensionality reduction by PCA, and the dimension of the negative fulfillment feature vector is equal to the number of principal components retained after dimensionality reduction by PCA.

[0018] See Figure 2 This is a binned discretized interval diagram of the positive sales dimension data provided in the embodiments of this application. For example... Figure 2As shown in the figure, this diagram visually illustrates the process of discretizing continuous data such as historical sales order volume using the equal-frequency binning method. The figure uses three horizontal dividing lines at the 25th, 50th, and 75th percentiles to divide the continuously fluctuating order volume values ​​into four discrete level intervals: low, low-medium, high-medium, and high. Stepped boundaries indicate the data distribution range of each interval. In cross-border e-commerce scenarios, differences in the basic population base and consumption habits of different regions lead to significant long-tail distributions and seasonal spikes in the original sales data. This binning mechanism, through the principle of frequency balancing, transforms non-stationary original sales volume into standardized level labels, effectively smoothing out data noise caused by short-term promotions or logistics delays. Combined with subsequent principal component dimensionality reduction processing, this structure provides a dimensionally aligned and distributionally stable feature basis for the inverse Markov chain and the full-link feature tensor, improving the signal-to-noise ratio of cross-regional demand feature extraction.

[0019] For example, suppose there are 5 target regions, labeled Region A, Region B, Region C, Region D, and Region E. For a specific cross-border product category, 120 historical sales order records from the past 24 calendar months are retrieved from the regional e-commerce front-end. The quartiles of these 120 historical sales order records are then analyzed: the 25th percentile is 350 orders, the 50th percentile is 720 orders, and the 75th percentile is 1100 orders. Records with fewer than 350 historical sales orders are categorized as low demand; records with 350 or more but less than 720 orders are categorized as low-to-medium demand; records with 720 or more but less than 1100 orders are categorized as medium-to-high demand; and records with 1100 or more orders are categorized as high demand. After dimensionality reduction by principal component analysis, the positive sales dimension data retains 3 principal components, so the positive sales feature vector is a 3-dimensional vector; the negative fulfillment dimension data retains 2 principal components, so the negative fulfillment feature vector is a 2-dimensional vector.

[0020] S12: Construct a reverse state transition Markov chain using reverse performance feature vectors.

[0021] Further, step S12 includes the following steps: S121: Extract the return rate, exchange rate, and customs detention rate of goods in the target area from the reverse fulfillment feature vector.

[0022] The method for parsing from the reverse fulfillment feature vector is as follows: Since the reverse fulfillment feature vector is a low-dimensional representation obtained through principal component analysis (PCA), it is necessary to map the reverse fulfillment feature vector back to the original reverse fulfillment dimension data space through the inverse transformation of PCA, thereby obtaining the reconstructed values ​​of each original feature dimension. Specifically, the reverse fulfillment feature vector is multiplied by the transpose of the principal component loading matrix retained during PCA dimensionality reduction, and then the mean vector of each original feature dimension before dimensionality reduction is added to obtain the reconstructed reverse fulfillment dimension data. From the reconstructed reverse fulfillment dimension data, the values ​​of three feature dimensions are extracted: product return rate, product exchange rate, and customs detention rate. The product return rate refers to the ratio of the number of orders with return requests initiated in the target region within the statistical period to the total number of completed orders. The product exchange rate refers to the ratio of the number of orders with exchange requests initiated in the target region within the statistical period to the total number of completed orders. The customs detention ratio refers to the ratio of the number of cross-border parcels detained by customs in the target area during the statistical period due to customs inspection, tariff disputes, or declaration discrepancies to the total number of shipped parcels.

[0023] S122: Define the discrete state space of the reverse state transition Markov chain, which includes normal receipt state, local return state, cross-border return state, and local destruction state.

[0024] The "normal receipt status" refers to the final state where cross-border goods have been delivered to the target region and the consumer has confirmed receipt without initiating any return or exchange requests. The "local return status" refers to the intermediate state where, after a consumer initiates a return request, the returned goods are received by a local return warehouse in the target region and undergo quality inspection, refurbishment, or restocking. Costs incurred in the local return status include local return warehouse handling fees and depreciation of the goods' value. The "cross-border return status" refers to the state where returned goods cannot be processed locally in the target region and must be returned to the country of origin warehouse via cross-border logistics. Costs incurred in the cross-border return status include return logistics pricing and reverse tariffs. The "local destruction status" refers to the final state where returned or slow-moving goods are destroyed locally in the target region due to reasons such as inability to resell or excessively high return costs. Costs incurred in the local destruction status are the unit price for destroying slow-moving goods.

[0025] The discrete state space is designed based on the actual handling paths that goods may undergo in the reverse logistics chain of cross-border e-commerce. In the cross-border e-commerce scenario, when a shipped product flows back from the consumer to the supply chain system, it will inevitably undergo a sequential transition of one or more of the four states mentioned above. For example, after a product is signed for by a consumer and a return is initiated, it first enters the local return state. If the local return warehouse determines that the product cannot be refurbished, it will be transferred to the cross-border return state or the local destruction state. This state transition process has the Markov property, that is, the next transition of the current state depends only on the current state and is independent of the previous state paths. Therefore, a Markov chain is used for modeling.

[0026] S123: Calculate the transition probability matrix between each state in the discrete state space based on the product return rate, product exchange rate, and customs detention rate, and combine them to generate an inverse state transition Markov chain.

[0027] The transition probability matrix is ​​a 4x4 square matrix, with row and column indices corresponding to the normal receipt status, local return status, cross-border return status, and local destruction status, respectively. The element in the i-th row and j-th column of the transition probability matrix represents the probability of transitioning from the i-th state to the j-th state. The transition probability matrix is ​​calculated as follows: The probability of transfer from normal receipt status is calculated as follows: The probability of transferring from normal receipt status to normal receipt status is equal to 1 minus the product return rate minus the product exchange rate, whereby the probability represents the probability that the product was neither returned nor exchanged after being signed for; the probability of transferring from normal receipt status to local return status is equal to the product return rate multiplied by (1 minus the customs detention rate), whereby the probability represents the probability that the returned product was processed in the local return warehouse and was not affected by customs detention; the probability of transferring from normal receipt status to cross-border return status is equal to the product return rate multiplied by the customs detention rate plus half of the product exchange rate, whereby the probability represents the probability that returned products need to be returned across borders due to customs detention and the probability that some exchanged products need to be returned across borders; the probability of transferring from normal receipt status to local destruction status is equal to half of the product exchange rate, whereby the probability represents the probability that the original products in the exchanged products are destroyed on-site in the target area.

[0028] The probability of a transfer from a local return status is calculated as follows: the probability of a local return status transferring to a normal receipt status is equal to the preset local refurbishment success rate. The preset local refurbishment success rate refers to the probability that a returned item can be relisted for sale after quality inspection and refurbishment by the local return warehouse. The preset local refurbishment success rate is obtained based on historical return item refurbishment data from the cross-border e-commerce platform. For example, the preset local refurbishment success rate can be set to 0.35. The probability of a local return status transferring to a cross-border return status is equal to (1 minus the preset local refurbishment success rate) multiplied by 0.6. The probability of a local return status transferring to a local destruction status is equal to (1 minus the preset local refurbishment success rate) multiplied by 0.4. The probability of a local return status transferring to a local return status is 0, indicating that the returned item will not be circulated and retained in the local return warehouse.

[0029] The probability calculation method for transitioning from the cross-border return status is as follows: the cross-border return status is a prerequisite for the absorption status. The probability of transitioning from the cross-border return status to the normal receipt status is 0; the probability of transitioning from the cross-border return status to the local return status is 0; the probability of transitioning from the cross-border return status to the cross-border return status is 1; and the probability of transitioning from the cross-border return status to the local destruction status is 0. This indicates that once the cross-border return status is entered, corresponding costs are incurred and the reverse logistics chain is terminated. The absorption status refers to the termination status of reverse logistics; once entered, there are no further transitions, and the process ends.

[0030] The probability of transfer from the local destruction status is calculated as follows: the probability of the local destruction status being the absorption status, the probability of the local destruction status being transferred to the normal receipt status, the local return status, the cross-border return status, and the local destruction status are 0, 0, 0, and 1, respectively.

[0031] The transition probabilities between the states calculated above are arranged in rows and columns to form a transition probability matrix. The discrete state space and the transition probability matrix are then combined to generate a reverse state transition Markov chain. The data structure of the reverse state transition Markov chain is a directed weighted graph, where nodes correspond to the four states in the discrete state space, and the weights of the directed edges are the corresponding transition probability values ​​in the transition probability matrix. See also... Figure 3This is a directed graph of the reverse state transition Markov chain provided in this application embodiment. As shown in the figure, the graph, in the form of a directed weighted graph, depicts the sequential transition relationship of four core disposal states in the reverse logistics link of cross-border goods. The four circular nodes represent the states of normal receipt, local return, cross-border return, and local destruction, respectively. The arrows connecting the nodes represent the state transition paths, and the arrow weights are the transition probabilities calculated based on the regional return and exchange rate. The absorbing state nodes are configured with self-loops. In actual cross-border fulfillment, returned goods may undergo a multi-stage series process of local quality inspection and refurbishment failure, triggering cross-border repatriation, or on-site destruction. This Markov chain model breaks through the limitations of static calculation of "return rate × single shipping cost". It accurately solves the expected number of stays and absorption probabilities of each path through the basic matrix of the absorbing chain, and incorporates customs inspection fluctuations and overseas warehouse refurbishment success rates into cost extrapolation, thereby outputting a high-precision reverse fulfillment cost expectation matrix.

[0032] For example, suppose the return rate for goods in a target region is 0.12, the exchange rate is 0.08, the customs detention rate is 0.15, and the preset local refurbishment success rate is 0.35. Then, the probability of a normal receipt status transitioning to a normal receipt status is 1 minus 0.12 minus 0.08 equals 0.80; the probability of a normal receipt status transitioning to a local return status is 0.12 multiplied by (1 minus 0.15) equals 0.102; the probability of a normal receipt status transitioning to a cross-border return status is 0.12 multiplied by 0.15 plus 0.08 multiplied by 0.5 equals 0.018 plus 0.04 equals 0.058; and the probability of a normal receipt status transitioning to a local destruction status is 0.08 multiplied by 0.5 equals 0.04. The probability of a local return status being transferred to a normal receipt status is 0.35; the probability of a local return status being transferred to a cross-border return status is (1 minus 0.35) multiplied by 0.6 equals 0.39; the probability of a local return status being transferred to a local destruction status is (1 minus 0.35) multiplied by 0.4 equals 0.26.

[0033] S13: Based on the reverse state transition Markov chain and the transition probability matrix, input the reverse tariff value of the target area, the return logistics pricing value, and the unit price of the unsold goods destruction into the reverse state transition Markov chain to solve the steady-state probability distribution and generate the expected matrix of reverse fulfillment costs.

[0034] The reverse tariff figure is obtained from the customs electronic declaration system in the cross-border logistics terminal, representing the reverse tariff fees payable when returned goods are returned across borders from the target region to the country of origin. The return logistics pricing figure is obtained from the international transportation management system in the cross-border logistics terminal, representing the unit transportation cost of returned goods from the target region to the warehouse in the country of origin. The unit price for the destruction of unsold goods is obtained from the overseas warehouse storage management system in the cross-border logistics terminal, representing the processing cost required to destroy one returned or unsold item locally in the target region.

[0035] The steady-state probability distribution is solved as follows: The transition probability matrix of the inverse state transition Markov chain is decomposed using eigenvalue decomposition. The eigenvectors corresponding to eigenvalues ​​of 1 in the left eigenvector of the transition probability matrix are then normalized so that the sum of all components equals 1, yielding the steady-state probability distribution vector. Each component of the steady-state probability distribution vector corresponds to the long-term residence probability of a state in the discrete state space. Since the cross-border return state and the local destruction state are absorption states, the steady-state probabilities of the normal receipt state and the local return state in the steady-state probability distribution vector approach 0, and the sum of the steady-state probabilities of the cross-border return state and the local destruction state approaches 1. To calculate the expected cost of reaching each absorption state from the normal acceptance state, the basic matrix method of the absorption Markov chain is adopted: the transition probability matrix is ​​split into a transient submatrix and an absorption submatrix. The transient submatrix is ​​a 2x2 submatrix composed of the transition probabilities between the normal acceptance state and the local return state. The absorption submatrix is ​​a 2x2 submatrix composed of the probabilities of transitioning from the normal acceptance state and the local return state to the cross-border return state and the local destruction state. The basic matrix N is calculated as the inverse of (identity matrix minus transient submatrix). The element in the i-th row and j-th column of the basic matrix N represents the expected number of visits to the j-th transient state before absorption, starting from the i-th transient state. The absorption probability matrix B is calculated as the basic matrix N multiplied by the absorption submatrix. The element in the i-th row and j-th column of the absorption probability matrix B represents the probability of being absorbed by the j-th absorption state from the i-th transient state.

[0036] Define a single-transaction cost vector corresponding to each state: the single-transaction cost for the local return state is the preset local return processing unit price, which is obtained based on the return operation fee data in the overseas warehouse management system. For example, the preset local return processing unit price can be set to $8 per item; the single-transaction cost for the cross-border return state is equal to the reverse tariff value plus the return logistics pricing value; the single-transaction cost for the local destruction state is equal to the destruction unit price of unsold goods. The expected cost accumulated in the transient states from the normal receipt state is calculated using the basic matrix N and the single-transaction cost of each transient state. This is then added to the product of the absorption probability matrix B and the single-transaction cost of each absorption state to obtain the total expected reverse fulfillment cost from the normal receipt state. The total expected reverse fulfillment cost for each target region is arranged into a column vector according to the region index, and the column vectors corresponding to different product categories are arranged into rows according to the product category index, generating a reverse fulfillment cost expectation matrix. The number of rows in the reverse fulfillment cost expectation matrix is ​​equal to the total number of product categories, and the number of columns is equal to the total number of target areas. The element in the i-th row and j-th column of the matrix represents the expected reverse fulfillment cost per unit of the i-th product category in the j-th target area.

[0037] For example, suppose the reverse tariff for a target region is $5 per item, the return logistics price is $12 per item, the unit price for destroying unsold goods is $3 per item, and the preset local return processing price is $8 per item. The transient submatrix is ​​a 2x2 matrix, with the first row and first column having a value of 0.80, the first row and second column having a value of 0.102, the second row and first column having a value of 0.35, and the second row and second column having a value of 0. The identity matrix minus the transient submatrix results in the first row and first column having a value of 0.20, the first row and second column having a value of -0.102, the second row and first column having a value of -0.35, and the second row and second column having a value of 1. Inverting this matrix yields the fundamental matrix N. The absorber submatrix has a value of 0.058, the first row and second column having a value of 0.04, the second row and first column having a value of 0.39, and the second row and second column having a value of 0.26. The absorption probability matrix B equals the basic matrix N multiplied by the absorption submatrix. The single cost for a cross-border return is $5 plus $12, equaling $17, while the single cost for a local destruction is $3. The total expected reverse fulfillment cost starting from the normal acceptance state equals the product of the first row of the basic matrix N and the single cost vector of the transient state, plus the product of the first row of the absorption probability matrix B and the single cost vector of the absorption state.

[0038] Specifically, the core function of step S1 is to incorporate multiple cost factors in the cross-border e-commerce reverse logistics chain into a unified Markov chain state transition framework, achieving systematic and dynamic quantification of reverse fulfillment costs. Compared to the static calculation method of directly multiplying the return rate by the cost of a single return, the state transition mechanism established in step S1 reveals the inherent linkage between various reverse cost factors: taking the customs detention ratio as an example, this parameter not only directly determines the probability of transitioning from the normal receipt state to the cross-border return state, but also indirectly affects the probability distribution of subsequent failed refurbishment shipments flowing to the cross-border return state and the local destruction state by changing the probability of entering the local return state. When the customs detention ratio changes abruptly within the statistical period, its impact will be synchronously transmitted to all downstream states along the transition probability matrix, causing the cost weights of reverse tariff values, return logistics pricing values, and the unit price of unsold goods destruction to be redistributed in a coordinated manner, rather than being calculated individually. This multi-factor synergistic characteristic ensures that any local mutation in a single reverse parameter will not distort the global cost accounting, guaranteeing the robustness of the expected reverse fulfillment cost matrix in scenarios with frequent changes in the cross-border regulatory environment. Furthermore, the Markov chain fundamental matrix method, by accurately calculating the expected number of visits from the transient state to each absorbed state, compresses the multi-stage sequential cost accumulation process of returned goods undergoing local quality inspection and refurbishment, refurbishment failure, and then transfer to cross-border returns or local destruction into a single total expected reverse fulfillment cost value. This provides dimensionally aligned and physically meaningful reverse cost input for the tensor splicing operation in step S2. Without the explicit modeling of the multi-stage state transition path in step S1, step S2 would not obtain a matrix input that reflects the heterogeneity of reverse fulfillment costs in each target region. The objective function of step S3 would systematically overestimate the warehouse operation benefits of categories with high return rates, causing warehouse allocation decisions to deviate from the optimal solution across the entire chain.

[0039] S2: Concatenate the positive sales feature vector and the reverse fulfillment cost expectation matrix into a full-link feature tensor. Use the support vector regression algorithm to calculate the regional demand of the full-link feature tensor and generate a dynamic mapping table for full-link revenue prediction.

[0040] Further, step S2 includes the following steps: S21: Perform dimension alignment calculations on the vector dimension of the positive sales feature vector and the matrix dimension of the reverse fulfillment cost expectation matrix to obtain aligned positive features and aligned reverse matrices.

[0041] The dimension alignment calculation method is as follows: The positive sales feature vector generated in step S11 is a one-dimensional vector organized by target region. Each target region corresponds to one positive sales feature vector, and the dimension of the positive sales feature vector is equal to the number of principal components retained after dimensionality reduction by principal component analysis of the positive sales dimension data. The reverse fulfillment cost expectation matrix generated in step S13 is a two-dimensional matrix with the number of rows equal to the total number of product categories and the number of columns equal to the total number of target regions. To enable tensor concatenation between the positive sales feature vector and the reverse fulfillment cost expectation matrix, the positive sales feature vector needs to be expanded into a two-dimensional matrix with the same number of rows as the reverse fulfillment cost expectation matrix. Specifically, for the positive sales feature vector corresponding to each target region, the total number of product categories is copied along the row direction to generate a two-dimensional matrix with the number of rows equal to the total number of product categories and the number of columns equal to the dimension of the positive sales feature vector. This two-dimensional matrix is ​​denoted as the aligned positive feature. No dimension transformation is performed on the reverse fulfillment cost expectation matrix; it is directly denoted as the aligned reverse matrix. The number of rows in the aligned positive feature is equal to the total number of product categories, and the number of columns is equal to the dimension of the positive sales feature vector. The number of rows in the aligned inverse matrix is ​​equal to the total number of product categories, and the number of columns is equal to the total number of target regions.

[0042] S22: Concatenate the aligned forward features and the aligned inverse matrix along the feature dimension to generate the full-link feature tensor.

[0043] The tensor concatenation method is as follows: Aligned positive features and aligned inverse matrices are horizontally concatenated along the column direction, that is, each column of the aligned positive features is connected end-to-end with each column of the aligned inverse matrix, generating a two-dimensional matrix with the number of rows equal to the total number of product categories and the number of columns equal to the dimension of the positive sales feature vector plus the total number of target regions. This two-dimensional matrix is ​​denoted as the end-to-end feature tensor. Each row of the end-to-end feature tensor corresponds to a product category. The first few columns of each row are the values ​​of the aligned positive features, and the last few columns are the expected reverse fulfillment cost per unit for the corresponding product category in each target region from the aligned inverse matrix. The end-to-end feature tensor integrates the positive sales dimension and the reverse fulfillment cost dimension into a unified feature representation, enabling subsequent support vector regression algorithms to simultaneously perceive positive demand signals and reverse cost signals. See also Figure 4 This is a horizontally stitched structure diagram of the end-to-end feature tensor provided in the embodiments of this application. For example... Figure 4As shown in the figure, this diagram illustrates the fusion process of the positive sales feature vector and the reverse fulfillment cost expectation matrix in terms of feature dimensions. The left-aligned positive feature matrix is ​​expanded from the original one-dimensional vector along the product category dimension, maintaining consistency in sales trends across multiple categories; the right-aligned reverse matrix fully preserves the expected reverse cost per unit in each region. The two are connected horizontally in the column direction, forming a full-link feature tensor with the number of rows equal to the total number of product categories and the number of columns equal to the sum of the feature dimensions and the total number of regions. In cross-border operations, high-volume regions are often accompanied by high return rates and complex tariffs, resulting in strong coupling between positive and reverse signals. This tensor structure breaks down data separation barriers, enabling subsequent support vector regression algorithms to simultaneously perceive market heat and fulfillment losses in a unified high-dimensional space, accurately capturing nonlinear interaction patterns, and laying a structured foundation for dynamic mapping of regional demand.

[0044] S23: Initialize the Gaussian radial basis kernel function parameters and penalty coefficients for the support vector regression algorithm.

[0045] The support vector regression algorithm is a nonlinear regression algorithm based on the kernel method. It maps input features to a high-dimensional regenerating kernel Hilbert space, constructing a linear regression hyperplane in the high-dimensional space to achieve nonlinear fitting in the original space. The mathematical expression of the Gaussian radial basis function is: in and Let be any two sample row vectors in the full-link feature tensor. The parameters are Gaussian radial basis kernel function parameters. This is the square of the Euclidean distance between two sample row vectors. (Gaussian radial basis function parameters) Control the width of the kernel function. The larger the kernel size, the stronger the locality of the kernel function, and the more refined the model fits the training samples, but the generalization ability may be reduced. A smaller kernel size results in a stronger global effect of the kernel function, leading to a smoother model fit, but potentially underfitting. Gaussian radial basis function parameters. The method for determining the parameter is as follows: A 5-fold cross-validation method is used to traverse and search the preset candidate parameter set to minimize the mean squared error of the cross-validation. The preset parameter candidate set determines the search center based on the reciprocal of the feature dimension in the end-link feature tensor. For example, the Gaussian radial basis function parameters... The penalty coefficient can be set to the reciprocal of the number of columns in the full-link feature tensor. The penalty coefficient is denoted as C. The penalty coefficient C controls the model's tolerance for training error; a larger C indicates a lower tolerance for training error and a more rigorous fit, while a smaller C indicates a higher tolerance for training error. The penalty coefficient C is determined using the 5-fold cross-validation method, searching through a pre-defined set of candidate penalty coefficients for the C value that minimizes the mean squared error of the cross-validation. For example, the penalty coefficient C can be set to 10.

[0046] S24: Input the full-link feature tensor into the initialized support vector regression algorithm, calculate the functional distance from the full-link feature tensor to the optimal hyperplane of the support vector regression algorithm, and output the regional demand prediction value.

[0047] The optimal hyperplane is determined as follows: the support vector regression algorithm determines the optimal hyperplane parameters by solving the following convex quadratic optimization problem: minimizing half the square of the L2 norm of the weight vector plus the penalty coefficient C multiplied by the sum of the slack variables of all training samples. The constraint is that the absolute value of the difference between the actual output value and the hyperplane prediction value of each training sample is less than or equal to the insensitive loss parameter plus the corresponding slack variable. The insensitive loss parameter defines a tubular region centered on the hyperplane. The prediction error within the tubular region is not included in the loss function. The insensitive loss parameter is determined based on the standard deviation of the training sample output values. For example, the insensitive loss parameter can be set to one-tenth of the standard deviation of the training sample output values. The functional distance is the signed distance from each sample row vector in the full-link feature tensor to the optimal hyperplane in the high-dimensional space after being mapped by the Gaussian radial basis function. The signed distance is converted into the regression prediction value in the original space through inverse mapping, which is the regional demand prediction value. The data structure for the regional demand forecast is a one-dimensional vector. The vector length equals the total number of target regions multiplied by the total number of product categories. Each element represents the predicted demand quantity for the corresponding product category within a preset forecast period in the corresponding target region. The preset forecast period is determined based on the cross-border e-commerce replenishment cycle; for example, the preset forecast period can be set to 14 calendar days. See also... Figure 5This figure illustrates the support vector regression insensitive tubular region constraint diagram provided in this application embodiment. As shown, the diagram visualizes the hyperplane construction mechanism of the support vector regression algorithm. The solid central line represents the optimal regression hyperplane. Samples within the tube do not generate prediction loss, while samples outside the tube are quantified by introducing slack variables through vertical short lines. Historical data from cross-border e-commerce is often affected by promotional stockouts or customs clearance delays, resulting in measurement noise. This tubular region design provides a fault-tolerant buffer for the model, allowing a certain range of prediction deviations to be excluded from the objective function, effectively suppressing overfitting to abnormal order fluctuations. Combined with the nonlinear mapping of the Gaussian kernel function, this mechanism ensures a globally convex optimization unique solution for medium-sized samples while improving the model's generalization robustness to cross-cycle demand fluctuations.

[0048] S25: Calculate the expected net revenue per unit of goods in each target region based on the regional demand forecast, the pricing of goods sold forward, and the expected cost values ​​in the expected matrix of reverse fulfillment costs.

[0049] The pricing of goods sold in the forward sales are obtained from the product pricing database on the regional e-commerce front end, representing the current selling price of each product category in each target region. The expected net profit per unit is calculated as follows: for each product category and each target region combination, the expected reverse fulfillment cost per unit in the corresponding target region is subtracted from the forward sales price. The expected net profit per unit is obtained by subtracting the expected reverse fulfillment cost per unit in the corresponding product category from the expected reverse fulfillment cost matrix. The data structure of the expected net profit per unit is a two-dimensional matrix, with the number of rows equal to the total number of product categories and the number of columns equal to the total number of target regions. The element in the i-th row and j-th column of the matrix represents the expected net profit of selling one unit of the i-th product category in the j-th target region.

[0050] For example, suppose a product category in region A is priced at $50 for direct sales, and the corresponding element in the expected reverse fulfillment cost matrix is ​​$7.2. Then, the expected net profit per unit is $50 minus $7.2, equaling $42.8. The same product category in region B is priced at $48 for direct sales, and the corresponding element in the expected reverse fulfillment cost matrix is ​​$15.6. Then, the expected net profit per unit is $48 minus $15.6, equaling $32.4.

[0051] S26: Map the expected net revenue per unit of goods in each target region to the three-dimensional coordinate nodes of the target region, and generate a dynamic mapping table for full-link revenue forecast.

[0052] The three-dimensional coordinate nodes are defined as follows: a three-dimensional coordinate space is constructed using the product category index as the first coordinate axis, the target region index as the second coordinate axis, and the prediction time period index as the third coordinate axis. Each three-dimensional coordinate node is uniquely determined by three coordinate values: the product category index, the target region index, and the prediction time period index. The expected net profit per unit of product and the predicted regional demand value are bound as attribute values ​​for each three-dimensional coordinate node. The data structure of the end-to-end revenue prediction dynamic mapping table is a three-dimensional array. The length of the first dimension is equal to the total number of product categories, the length of the second dimension is equal to the total number of target regions, and the length of the third dimension is equal to the number of prediction time periods. Each array element contains two attribute fields: the expected net profit per unit of product field and the predicted regional demand value field. The number of prediction time periods is determined based on the planning time domain of the warehouse allocation decision. For example, if the planning time domain is 56 calendar days and the preset prediction period is 14 calendar days, then the number of prediction time periods is 4.

[0053] See Figure 6 This is a data node structure diagram of the end-to-end predictive dynamic mapping table provided in this application embodiment. As shown in the figure, the diagram constructs a three-dimensional coordinate system with the commodity category index as the X-axis, the target region index as the Z-axis, and the prediction time period index as the Y-axis. At each discrete node where the space intersects, two core fields, the expected net profit per unit commodity and the predicted regional demand value, are bound by leader lines, demonstrating the data topology in the multi-dimensional grid. Cross-border warehousing needs to take into account the dynamic changes of category differences, regional distribution, and rolling time windows. This three-dimensional node structure upgrades the discrete two-dimensional prediction results into a time-series, structured dynamic mapping table, enabling the subsequent mixed-integer programming solver to extract constraint parameters by dimensional slicing with low complexity, adapting to the periodic decay law of storage capacity and inventory moisture, and providing a clear data access interface for multi-period rolling optimization.

[0054] Specifically, the core function of step S2 is to fuse the expected reverse fulfillment cost matrix and the positive sales feature vector output from step S1 into a unified end-to-end feature tensor. This is achieved through the insensitive tubular region constraint mechanism of the support vector regression algorithm, simultaneously considering both positive demand signals and reverse cost signals in regional demand modeling. The tensor concatenation operation merges the originally separate positive sales dimension and reverse fulfillment cost dimension into a single row vector in the feature space. This allows the Gaussian radial basis function to simultaneously perceive the joint contribution of positive sales feature differences and reverse cost differences to sample similarity when calculating the Euclidean distance between any two sample row vectors, capturing the nonlinear interaction between the two types of features. It is noteworthy that the tubular region defined by the insensitive loss parameter, after introducing the reverse fulfillment cost dimension, exhibits a filtering effect exceeding the conventional expectation of simply smoothing positive sales noise caused by promotional fluctuations or logistics delays. Specifically, in the end-to-end feature tensor, abnormally high sales volume and abnormally high reverse fulfillment costs often coexist in the same sample row vector. These samples have a significantly larger Euclidean distance from normal samples in the feature space, making them more likely to be pushed outside the tubular region boundary. Therefore, they are included in the penalty term as slack variables rather than directly affecting the hyperplane fitting result. This mechanism objectively enhances the model's resistance to samples with "high sales volume accompanied by large-scale abnormal returns," ensuring that regional demand predictions are not significantly shifted by extreme positive and negative coupling data within local abnormal transaction cycles. Simultaneously, the convex optimization characteristics of the support vector regression algorithm guarantee the uniqueness of the global optimal solution under medium-sized training samples, avoiding the prediction instability problem caused by local minima in deep neural networks. The three-dimensional array structure of the end-to-end revenue prediction dynamic mapping table allows step S3 to directly extract constraint parameters by slicing according to three dimensions: product category, target region, and prediction time period, ensuring that data integration with mixed-integer programming equations requires no additional conversion. Without the full-link feature fusion and support vector regression prediction in step S2, the objective function in step S3 will not be able to accurately reflect the true expected profit level of each product category in each target region, and the profit maximization objective of the warehouse allocation decision will lose its practical meaning due to the lack of input data and the inverse cost dimension.

[0055] S3: Construct a mixed-integer programming equation with the objective function of maximizing the expected total revenue based on the dynamic mapping table of full-link revenue prediction. Use the branch and bound algorithm to solve the mixed-integer programming equation and output the global optimal allocation decision feature set.

[0056] Further, step S3 includes the following steps: S31: Extract the distribution sequence of expected net revenue per unit of commodity in the target region from the dynamic mapping table of end-to-end revenue forecast.

[0057] The extraction method is as follows: traverse all three-dimensional coordinate nodes in the dynamic mapping table of end-to-end revenue prediction, read the unit product expected net revenue field value and the regional demand prediction value field value of each three-dimensional coordinate node, and sort the unit product expected net revenue field values ​​of the same product category in the same target region for all prediction time periods in ascending order according to the prediction time period index to generate a unit product expected net revenue distribution sequence. The data structure of the unit product expected net revenue distribution sequence is a three-dimensional array, where the first dimension index corresponds to the product category, the second dimension index corresponds to the target region, and the third dimension index corresponds to the prediction time period. The array elements are the unit product expected net revenue values. Simultaneously, regional demand prediction values ​​are extracted to form a regional demand prediction value distribution sequence, which has the same three-dimensional array structure as the unit product expected net revenue distribution sequence.

[0058] S32: Obtain real-time inventory values, maximum capacity thresholds, and forward delivery logistics costs for each regional warehouse.

[0059] The real-time inventory value is obtained from the inventory data interface of the overseas warehouse storage management system, representing the current available inventory quantity of each product category in each regional warehouse. The maximum capacity threshold is obtained from the warehouse configuration information of the overseas warehouse storage management system, representing the maximum storage capacity limit of each regional warehouse. The forward shipping logistics cost value is obtained from the freight quotation interface of the international transportation management system, representing the forward logistics cost per item shipped from each originating warehouse to each target regional warehouse. The data structure of the forward shipping logistics cost value is a two-dimensional matrix, where the row index corresponds to the originating warehouse, the column index corresponds to the target regional warehouse, and the matrix elements are the forward logistics cost per item from the originating warehouse to the target regional warehouse.

[0060] S33: Calculate the total revenue by multiplying the expected net revenue distribution sequence per unit by the quantity of goods shipped from different warehouses, and calculate the total logistics cost by multiplying the quantity of goods shipped from different warehouses by the forward shipping logistics cost. Subtract the total logistics cost from the total revenue as the objective function to maximize the expected total revenue.

[0061] The warehouse-based shipment quantity variable is a decision variable in a mixed-integer programming equation. Its data structure is a three-dimensional integer array. The first dimension corresponds to the product category, the second dimension to the starting warehouse, and the third dimension to the target region warehouse. Array elements represent the planned shipment quantity of the corresponding product category from the starting warehouse to the target region warehouse, and these planned shipment quantities are non-negative integers. The total revenue is calculated by triple summing over all product categories, all target regions, and all forecast time periods. The summation term is the product of the corresponding element in the expected net revenue distribution sequence for each unit of product multiplied by the smaller value between the planned shipment quantity for the target region warehouse and the corresponding element in the regional demand forecast distribution sequence. The smaller value is chosen because when the planned shipment quantity exceeds the regional demand forecast, the excess cannot generate effective sales; therefore, the effective sales quantity is the smaller of the planned shipment quantity and the regional demand forecast. The total logistics cost is calculated by summing the costs for all product categories, all originating warehouses, and all target area warehouses. The summation term is the product of the corresponding element in the warehouse shipment quantity variable multiplied by the unit shipping cost from the originating warehouse to the target area warehouse in the forward shipping logistics cost value. The objective function is defined as the total revenue minus the total logistics cost, with the optimization direction being maximization.

[0062] S34: Set the real-time inventory value and the maximum capacity threshold as linear constraints of the objective function, and combine the objective function and linear constraints to construct a mixed integer programming equation.

[0063] The linear constraints include the following three categories: The first category is the starting warehouse inventory constraint, where, for each combination of starting warehouse and each product category, the sum of the quantities shipped from the starting warehouse to all target area warehouses for that product category is less than or equal to the real-time inventory value of that product category in the starting warehouse; the second category is the target area warehouse capacity constraint, where, for each target area warehouse, the sum of the quantities shipped from all starting warehouses to the target area warehouse for all product categories plus the current real-time inventory value of the target area warehouse is less than or equal to the maximum capacity threshold of the target area warehouse; the third category is the non-negative integer constraint, where all quantities shipped from each warehouse take the value of a non-negative integer. The objective function is then combined with the above three categories of linear constraints to construct a mixed-integer programming equation.

[0064] S35: Solve mixed integer programming equations using the branch and bound algorithm.

[0065] Further, step S35 includes the following steps: S351: Remove the integer constraints on the warehouse delivery quantity variable in the mixed integer programming equation to obtain a linear programming relaxation problem.

[0066] The method for removing integer constraints is as follows: the range of values ​​for the warehouse shipment quantity variable is broadened from non-negative integers to non-negative real numbers, while the remaining objective functions and linear constraints remain unchanged. The linear programming relaxation problem is a standard linear programming problem, and the objective function value of its optimal solution is an upper bound of the objective function value of the optimal solution to the mixed-integer programming equation.

[0067] S352: The simplex algorithm is used to solve the linear programming relaxation problem to obtain an initial fractional solution; based on the initial fractional solution, the warehouse shipment quantity variable is rounded down and up to generate left and right branch nodes. See also Figure 7 This is a branch-and-prune tree structure diagram of integer programming provided in this application embodiment. As shown in the figure, this diagram depicts the decision tree evolution process of the branch-and-bound algorithm for solving mixed integer programming equations. Each child node solves the relaxation subproblem and calculates the upper bound. If the upper bound is lower than the current integer feasible solution, pruning is triggered until all integer leaf nodes are traversed. Cross-border transfers involve full container shipments, the quantity must be a non-negative integer, and are subject to the combined influence of multi-warehouse capacity and freight constraints. This branch-and-prune mechanism avoids heuristic algorithms from getting trapped in local suboptimal conditions. By eliminating invalid combination searches through bounding, it compresses the time spent solving in high-dimensional space, ensuring that the transfer scheme achieves optimal benefits under strict physical constraints.

[0068] The solution process of the simplex algorithm is as follows: An initial feasible basis is constructed for the linear programming relaxation problem. The objective function value is monotonically increased by gradually replacing the basic variables until no further improvement is possible, at which point the optimal solution is output. The initial fractional solution is the optimal solution vector of the linear programming relaxation problem, and each element in the initial fractional solution may be a non-integer real value. A non-integer variable representing the quantity of goods shipped to the warehouse is selected from the initial fractional solution, and its value is denoted as f. The floor operation constrains the upper bound of the value of the quantity of goods shipped to the warehouse to the largest integer not exceeding f. This upper bound constraint is added to the original linear programming relaxation problem to generate the sub-linear programming problem corresponding to the left branch node. The floor operation constrains the lower bound of the value of the quantity of goods shipped to the warehouse to the smallest integer not less than f. This lower bound constraint is added to the original linear programming relaxation problem to generate the sub-linear programming problem corresponding to the right branch node.

[0069] S353: Recursively traverse the left and right branch nodes, compare the function boundary values ​​of the left and right branch nodes, remove non-optimal branch nodes whose function boundary values ​​are lower than the current optimal solution, until all traversed nodes satisfy the integer constraint conditions, and extract the node values ​​that satisfy the integer constraint conditions as the global optimal partitioning decision feature set.

[0070] The recursive traversal method is as follows: For each left and right branch node, the simplex algorithm is used to solve the corresponding sub-linear programming problem, obtaining the optimal solution and corresponding objective function value for each branch node. The function bound value is the optimal objective function value of the sub-linear programming problem corresponding to each branch node, and the function bound value is the upper bound of the objective function values ​​of all integer feasible solutions under that branch node. If the function bound value of a branch node is lower than or equal to the objective function value of the currently found optimal integer feasible solution, then the branch node and all its child nodes are pruned, and no further branching is performed on the branch node. If all warehouse delivery quantity variables in the optimal solution of a branch node are integers, then the optimal solution of the branch node is an integer feasible solution. If the objective function value of the integer feasible solution is greater than the objective function value of the current optimal integer feasible solution, then the current optimal integer feasible solution is updated. The recursive traversal terminates when all unpruned branch nodes have been traversed and integer feasibility has been determined. The values ​​of all warehouse delivery quantity variables in the final current optimal integer feasible solution are extracted as the global optimal warehouse decision feature set. The data structure of the global optimal warehouse allocation decision feature set is a set of key-value pairs. The key of each key-value pair is a triple composed of the product category index, the starting warehouse identifier, and the target area warehouse identifier. The value of each key-value pair is the corresponding planned number of shipments.

[0071] Specifically, the core function of step S3 is to transform the dynamic mapping table of end-to-end revenue prediction output in step S2 into a mixed-integer programming equation with the objective of maximizing the expected total revenue. A branch-and-bound algorithm is then used to ensure the output of the globally optimal warehouse allocation decision while strictly satisfying inventory and capacity constraints. The objective function defines the effective number of sold items as the smaller value between the warehouse shipment quantity variable and the regional demand forecast. This approach mathematically mandates that the planned shipment quantity does not exceed the predicted demand, thus eliminating the possibility of ineffective inventory backlog due to overstocking being included in the objective function's revenue term. Three types of linear constraints constrain the feasible domain of the decision variables from three dimensions: the initial warehouse inventory limit, the target region warehouse capacity limit, and the non-negative integer nature of the shipment quantity. These three constraints work together to ensure that the feasible solution space strictly corresponds to the physical operational boundary of cross-border warehousing and allocation. In particular, the non-negative integer constraint requires that all warehouse shipment quantity variables take non-negative integer values, which is completely consistent with the physical operation characteristics of the target region warehouse actually performing full-case picking and outbound operations, avoiding the problem of unexecutable solutions due to decimal numbers in continuous relaxation solutions. The branch and bound algorithm, through systematic branching and bounding pruning of the linear programming relaxation problem, ensures that all integer feasible solutions are traversed. It pre-prunes suboptimal branches using the function bounds of each branch node, guaranteeing that the final output globally optimal warehouse allocation decision feature set has a strict global optimality theoretical guarantee, rather than the local near-optimal solution provided by heuristic algorithms. Without the mixed-integer programming modeling and branch and bound solution in step S3, step S4 will not obtain the globally optimized integer allocation quantity configuration. The allocation quantity in the pre-shipment instruction will lack optimality guarantee, potentially leading to overstocking in some regional warehouses and understocking in others, resulting in a loss of revenue across the entire supply chain.

[0072] S4: Analyze the global optimal warehouse allocation decision feature set to obtain the allocation quantity and the shortest logistics route configuration, generate a pre-shipment instruction sequence based on the allocation quantity and the shortest logistics route configuration, and execute the pre-shipment operation of goods.

[0073] Further, step S4 includes the following steps: S41: Perform key-value pair reading operations on the global optimal warehouse allocation decision feature set to extract the starting warehouse identifier, target area warehouse identifier, and allocation quantity from the global optimal warehouse allocation decision feature set.

[0074] The key-value pair reading operation is performed as follows: traverse all key-value pairs in the global optimal warehouse allocation decision feature set. For each key-value pair, parse the first element of the triplet key as the product category index, parse the second element of the triplet key as the starting warehouse identifier, parse the third element of the triplet key as the target area warehouse identifier, and read the value of the key-value pair as the allocation quantity. The starting warehouse identifier is the unique code of the starting warehouse in the warehouse management system. The target area warehouse identifier is the unique code of the target area warehouse in the warehouse management system. The allocation quantity is the value of the corresponding warehouse shipment quantity variable in the current optimal integer feasible solution obtained in step S35, representing the planned shipment number of the corresponding product category from the starting warehouse to the target area warehouse. Key-value pairs with an allocation quantity of 0 are not included in the processing scope of subsequent steps; only key-value pairs with an allocation quantity greater than 0 are processed.

[0075] S42: Query the directed graph of the cross-border logistics network and use the Dijkstra algorithm to calculate the shortest logistics route configuration between the starting warehouse identifier and the target area warehouse identifier.

[0076] The data structure of the directed graph of the cross-border logistics network is a directed weighted graph. The set of nodes in the graph includes all originating warehouses, all transit hubs, and all target area warehouses. Directed edges indicate the existence of available logistics transportation routes between two nodes, and the weight of the directed edge is the single-item transportation time of the logistics transportation route, with the single-item transportation time in calendar days. The directed graph of the cross-border logistics network is obtained from the network configuration module of the international transportation management system. The network configuration module maintains all available transportation routes and their timeliness data in the cross-border logistics chain.

[0077] The Dijkstra algorithm is used to calculate the shortest logistics route configuration as follows: The node corresponding to the starting warehouse identifier is set as the source node, and the node corresponding to the target warehouse identifier is set as the target node. The shortest path distance of the source node is initialized to 0, and the shortest path distance of all other nodes is positive infinity. An unvisited node set is created, adding all nodes in the directed graph of the cross-border logistics network to the unvisited node set. An iterative process is executed: In each iteration, the node with the smallest shortest path distance from the unvisited node set is selected as the current processing node, and then removed from the unvisited node set. All adjacent nodes of the current processing node are traversed. For each adjacent node, the path distance from the source node to the adjacent node via the current processing node is calculated. This path distance is equal to the shortest path distance of the current processing node plus the weight of the directed edge from the current processing node to the adjacent node. If the path distance is less than the currently recorded shortest path distance of the adjacent node, the shortest path distance of the adjacent node is updated to the path distance, and the predecessor node of the adjacent node is recorded as the current processing node. The iteration process is repeated until the target node is removed from the set of unvisited nodes or the set of unvisited nodes is empty. Starting from the target node, the process backtracks to the source node based on the predecessor node records. All node identifiers and directed edge identifiers along the backtracking path are arranged in order from the source node to the target node to generate the shortest logistics route configuration. The data structure of the shortest logistics route configuration is an ordered list, where each element is a tuple. The first element of the tuple is the identifier of a node along the route, and the second element is the identifier of the next segment of the logistics route starting from that node.

[0078] See Figure 8 This is a schematic diagram of the Dijkstra shortest logistics time routing network provided in this application embodiment. As shown in the figure, the graph constructs a cross-border logistics network topology using a directed weighted graph. Nodes cover the originating warehouse, transit hubs, and target regional warehouses, and directed edges represent available transportation routes. This routing optimization model breaks through the limitations of single-mode operation, dynamically matching the fastest link in the current international transportation network during the warehouse allocation decision-making stage. This effectively compresses the pre-positioning and transit cycle, reduces the risk of regional stockouts and capital occupation caused by transportation delays, and ensures the efficient transformation of the optimal warehouse allocation plan into physical fulfillment.

[0079] For example, assuming the starting warehouse is identified as WH-CN-SZ and the target warehouse is identified as WH-DE-FRA, the directed graph of the cross-border logistics network contains the following paths: from WH-CN-SZ via transit hub HUB-HK to HUB-AMS and then to WH-DE-FRA, with timeframes of 1 day, 8 days, and 2 days respectively, for a total timeframe of 11 days; from WH-CN-SZ via transit hub HUB-SH to HUB-HAM and then to WH-DE-FRA, with timeframes of 2 days, 10 days, and 1 day respectively, for a total timeframe of 13 days. The shortest logistics route output by Dijkstra's algorithm is configured as an ordered list: the first element is (WH-CN-SZ, logistics route L1), the second element is (HUB-HK, logistics route L2), the third element is (HUB-AMS, logistics route L3), and the fourth element is (WH-DE-FRA, empty), corresponding to a total transportation timeframe of 11 days.

[0080] S43: Combine and encapsulate the starting warehouse identifier, target area warehouse identifier, transfer quantity, and shortest logistics route configuration according to the standard data exchange protocol to generate a pre-shipment instruction sequence.

[0081] The standard data exchange protocol is a data communication format specification agreed upon between the warehouse management system and the logistics management system. This standard data exchange protocol defines the field structure, field types, and field order of instruction messages. The generation method for the pre-shipment instruction sequence is as follows: For each key-value pair with a transfer quantity greater than 0, a pre-shipment instruction message is created. This pre-shipment instruction message includes the following fields: a unique instruction number field, a unique identifier generated using a combination of a timestamp and a random number; a product category index field, the first element of the triplet key of the corresponding key-value pair; a starting warehouse identifier field, the starting warehouse identifier extracted in step S41; a target area warehouse identifier field, the target area warehouse identifier extracted in step S41; a transfer quantity field, the transfer quantity extracted in step S41; a logistics route field, the serialized string of the shortest logistics route configuration calculated in step S42; and an instruction generation timestamp field, the current system time. All pre-shipment instruction messages are arranged in ascending order according to the unique instruction number field and combined to form the pre-shipment instruction sequence. See also... Figure 9This is a standard encapsulation structure diagram of the pre-shipment instruction message fields provided in this application embodiment. As shown in the figure, this diagram defines the standard message format for the warehouse management system to issue transfer instructions to automated terminals. The message uses a fixed-width horizontal block, encapsulating seven fields from left to right: unique instruction number, product category index, starting warehouse identifier, target area warehouse identifier, transfer quantity, logistics route, and instruction generation timestamp. In the final execution stage of the supply chain, the digital layer optimization results need to be converted into physical layer automated instructions. This standardized structure shields the underlying protocol differences between warehouse control terminals from different manufacturers, directly driving location picking, label printing, and outbound barcode scanning through structured fields. The message queue ensures high concurrency and low latency delivery, while the timestamp and number fields provide data anchors for inventory write-back and trajectory tracking, achieving a seamless closed loop from algorithm decision-making to physical fulfillment.

[0082] S44: Send the pre-shipment instruction sequence to the warehouse automation control terminal, and then parse the pre-shipment instruction sequence and execute the pre-shipment product placement operation through the warehouse automation control terminal.

[0083] The warehouse automation control terminal is an automated sorting and shipping control system deployed in each starting warehouse, including an automated sorting line controller, automatic labeling equipment, and outbound barcode scanning equipment. The pre-shipment instruction sequence is issued as follows: each pre-shipment instruction message in the sequence is pushed to the warehouse automation control terminal corresponding to the starting warehouse identifier via a message queue through the instruction issuance interface of the warehouse management system. The warehouse automation control terminal parses the pre-shipment instruction sequence as follows: it pulls the pre-shipment instruction messages one by one from the message queue, parses the product category index field to determine the product category to be picked, parses the transfer quantity field to determine the number of items to be picked, and parses the logistics route field to determine the carrier and waybill template corresponding to the first segment of the logistics route. Based on the analysis results, the warehouse automation control terminal drives the automated sorting line to pick the specified categories and quantities of goods from the corresponding storage locations. An automatic labeling device affixes a shipping label containing logistics routing information to each item. Each item is then scanned one by one by the outbound barcode scanner to confirm its release, completing the pre-shipment process. After the pre-shipment is complete, the warehouse automation control terminal sends outbound confirmation data back to the warehouse management system. The warehouse management system then updates the real-time inventory value of the corresponding starting warehouse based on the outbound confirmation data.

[0084] Specifically, the core function of step S4 is to transform the globally optimal warehouse allocation decision feature set output in step S3 into a sequence of pre-shipment instructions that can be directly parsed and executed by the warehouse automation control terminal, thus achieving a complete closed loop from the optimal decision at the digital layer to the physical layer's merchandise allocation action. In the globally optimal warehouse allocation decision feature set output in step S3, the value of the warehouse shipment quantity variable is guaranteed to be an integer number by the non-negative integer constraint. This integer characteristic strictly corresponds to the physical operation unit of the warehouse automation control terminal that drives the automated sorting line by item and performs outbound scanning confirmation by item. This allows the optimal integer solution at the digital layer to be executed directly and unambiguously by the physical layer equipment without introducing any rounding or truncation operations in the instruction conversion stage. The Dijkstra algorithm uses the single-item delivery time of each segment of the directed graph of the cross-border logistics network as the edge weight to solve for the shortest path. The output shortest logistics route configuration is serialized and written into the logistics route field of the pre-shipment instruction message. The warehouse automation control terminal can determine the carrier and waybill template corresponding to the first logistics segment by parsing this field, driving the automatic labeling equipment to generate a logistics waybill containing complete transit route information. This ensures that goods flow along the optimal time-efficiency path in the cross-border logistics network, reducing the risk of stockouts in regional warehouses due to transportation delays. The pre-shipment instruction message uses a standard data exchange protocol to encapsulate seven structured fields, enabling the instruction message to be uniformly parsed by warehouse automation control terminals from different manufacturers, masking differences in underlying device protocols. After the pre-shipment operation is completed, the warehouse automation control terminal sends outbound confirmation data back to the warehouse management system. The warehouse management system updates the real-time inventory value of the corresponding starting warehouse accordingly, ensuring that the real-time inventory value obtained in step S1 in the next prediction cycle accurately reflects the current inventory status, providing a reliable data foundation for the dynamic iterative optimization of steps S1 to S4. Without the logistics route optimization and instruction execution closed loop in step S4, the globally optimal warehouse allocation decision feature set output in step S3 will remain at the numerical level and cannot be transformed into actual commodity allocation actions. The entire warehouse allocation prediction method will not be able to produce actual supply chain operation benefit improvement effects.

[0085] For example, the following provides a complete workflow example of steps S1 to S4 above. Assume a cross-border e-commerce company operates three product categories, labeled as category P1, category P2, and category P3, and has two starting warehouses, labeled as WH-CN-SZ and WH-CN-SH, respectively. It sells to three target regions, labeled as region DE, region US, and region JP, respectively, and has three corresponding target region warehouses labeled as WH-DE-FRA, WH-US-LAX, and WH-JP-TKY, respectively.

[0086] In step S11, historical multi-dimensional data of cross-border goods for the past 24 calendar months are obtained from the regional e-commerce front-end. Category P1 has an average monthly sales order volume of 800 units in region DE, with a selling price of $50, a return rate of 0.12%, an exchange rate of 0.08%, and a customs detention rate of 0.15. Category P1 has an average monthly sales order volume of 1200 units in region US, with a selling price of $55, a return rate of 0.18%, an exchange rate of 0.10%, and a customs detention rate of 0.05. Category P1 has an average monthly sales order volume of 600 units in region JP, with a selling price of $52, a return rate of 0.08%, an exchange rate of 0.04%, and a customs detention rate of 0.10. Principal component analysis (PCA) was performed on the positive sales data to reduce dimensionality, retaining the top three principal components with a cumulative variance contribution rate of 0.90. This generated positive sales feature vectors for category P1 in the three regions, with each vector having a dimension of 3. Similarly, PCA was performed on the negative fulfillment data to reduce dimensionality, retaining the top two principal components. This generated negative fulfillment feature vectors for category P1 in the three regions, with each vector having a dimension of 2.

[0087] In step S12, taking product category P1 in the US region as an example, the product return rate is 0.18, the product exchange rate is 0.10, the customs detention rate is 0.05, and the preset local refurbishment success rate is 0.35. The probability of transferring from normal receipt status to normal receipt status is 1 minus 0.18 minus 0.10 equals 0.72; the probability of transferring from normal receipt status to local return status is 0.18 multiplied by (1 minus 0.05) equals 0.171; the probability of transferring from normal receipt status to cross-border return status is 0.18 multiplied by 0.05 plus 0.10 multiplied by 0.5 equals 0.009 plus 0.05 equals 0.059; the probability of transferring from normal receipt status to local destruction status is 0.10 multiplied by 0.5 equals 0.05.

[0088] In step S13, the reverse tariff for product category P1 in the US is $3 per item, the return logistics price is $15 per item, the unit price for destroying slow-moving goods is $2 per item, and the preset local return processing price is $8 per item. The single cost for a cross-border return is $3 plus $15, which equals $18. The total expected reverse fulfillment cost starting from the normal receipt state is calculated using the Markov chain fundamental matrix method. The transient submatrix is: row 1, column 1 = 0.72, row 1, column 2 = 0.171, row 2, column 1 = 0.35, row 2, column 2 = 0. The identity matrix minus the transient submatrix is: row 1, column 1 = 0.28, row 1, column 2 = -0.171, row 2, column 1 = -0.35, row 2, column 2 = 1. The determinant of the matrix is ​​0.28 multiplied by 1 minus (-0.171) multiplied by (-0.35) equals 0.28 minus 0.05985 equals 0.22015. The matrix N in row 1, column 1 equals 1 divided by 0.22015, which is approximately 4.542; the matrix N in row 1, column 2 equals 0.171 divided by 0.22015, which is approximately 0.777. The single cost of a local return in the transient state is $8. The expected cost accumulated in the transient state from the normal receipt state is equal to N in row 1, column 1 multiplied by 0 plus N in row 1, column 2 multiplied by 8, which equals 0.777 multiplied by 8, which equals approximately $6.22. The first row of the absorption probability matrix B is equal to the first row of the basic matrix N multiplied by the absorber submatrix. The absorber submatrix has the following values: first row, first column: 0.059; first row, second column: 0.05; second row, first column: 0.39; second row, second column: 0.26. The first row, first column of B equals 4.542 multiplied by 0.059 plus 0.777 multiplied by 0.39, which equals 0.268 plus 0.303, approximately 0.571. The first row, second column of B equals 4.542 multiplied by 0.05 plus 0.777 multiplied by 0.26, which equals 0.227 plus 0.202, approximately 0.429. The expected cost of reaching the absorption state from the normal acceptance state is 0.571 multiplied by 18 plus 0.429 multiplied by 2, which equals 10.278 plus 0.858, approximately $11.14. The total expected reverse fulfillment cost for product category P1 in region US is approximately $6.22 plus $11.14, which equals approximately $17.36. The element in the category P1 row and region US column of the expected reverse fulfillment cost matrix is ​​denoted as 17.36.

[0089] In step S25, the forward sales price of product category P1 in region US is $55, the corresponding element in the reverse fulfillment cost expectation matrix is ​​$17.36, and the expected net profit per unit is $37.64, which is $55 minus $17.36.

[0090] In steps S33 to S35, it is assumed that the forward shipping logistics cost from the starting warehouse WH-CN-SZ to the target area warehouse WH-US-LAX is $6 per item, and the predicted regional demand for product category P1 in region US is 1150 items. After solving the branch and bound algorithm, the global optimal warehouse allocation decision feature set is output, and the number of product category P1 transferred from WH-CN-SZ to WH-US-LAX is 1150 items.

[0091] In step S42, the Dijkstra algorithm calculates the shortest logistics route configuration from WH-CN-SZ to WH-US-LAX as follows: WH-CN-SZ via HUB-HK via HUB-LAX to WH-US-LAX, with a total transportation time of 12 days.

[0092] In step S44, the warehouse automation control terminal receives the pre-shipment instruction message, picks 1150 items from the category P1 storage location in the WH-CN-SZ warehouse, affixes the logistics label containing HUB-HK transfer information, scans the code to confirm the outbound shipment, and completes the pre-shipment operation of category P1 to region US.

[0093] Example 2: This embodiment, based on Embodiment 1, provides a cross-border commodity regional demand forecasting and warehousing system, such as... Figure 10 As shown, it includes: Data feature extraction and reverse cost quantification module: used to extract features from historical multidimensional data of cross-border commodities to generate positive sales feature vectors and reverse fulfillment feature vectors, construct reverse state transition Markov chains based on the reverse fulfillment feature vectors and calculate state transition probabilities, and output the expected reverse fulfillment cost matrix; The end-to-end revenue prediction mapping module is used to concatenate the positive sales feature vector and the reverse fulfillment cost expectation matrix into an end-to-end feature tensor, and use the support vector regression algorithm to calculate the regional demand of the end-to-end feature tensor to generate an end-to-end revenue prediction dynamic mapping table. Global allocation decision optimization module: It is used to construct a mixed integer programming equation with the objective function of maximizing the expected total revenue based on the dynamic mapping table of the end-to-end revenue prediction, solve the mixed integer programming equation using the branch and bound algorithm, and output the global optimal allocation decision feature set; The pre-schedule execution control module is used to parse the global optimal warehouse allocation decision feature set to obtain the allocation quantity and the shortest logistics route configuration, generate a pre-shipment instruction sequence based on the allocation quantity and the shortest logistics route configuration, and execute the pre-shipment operation of goods.

Claims

1. A method for regional demand forecasting and warehousing allocation of cross-border commodities, characterized in that, include: Feature extraction is performed on historical multidimensional data of cross-border commodities to generate positive sales feature vectors and negative fulfillment feature vectors; The return rate, exchange rate, and customs detention rate of goods in the target area are extracted from the reverse fulfillment feature vector; a discrete state space is defined, which includes normal receipt state, local return state, cross-border return state, and local destruction state; the transition probability matrix between each state in the discrete state space is calculated based on the return rate, exchange rate, and customs detention rate, and the matrix is ​​combined to generate a reverse state transition Markov chain; The cross-border return status and the local destruction status are absorption statuses. The transition probability matrix is ​​split into a transient sub-matrix and an absorption sub-matrix. The basic matrix N is calculated. The basic matrix N is equal to the inverse matrix of the matrix obtained by subtracting the transient sub-matrix from the identity matrix. The absorption probability matrix B is calculated as the basic matrix N multiplied by the absorption sub-matrix. The expected cost accumulated in the transient states from the normal acceptance state is calculated using the basic matrix N and the single cost of each transient state. This is then added to the absorption probability matrix B and the single cost of each absorption state to obtain the total expected reverse fulfillment cost from the normal acceptance state. The total expected reverse fulfillment cost of each target area is arranged into a column vector according to the area index, and the column vectors corresponding to different product categories are arranged into rows according to the product category index to generate the expected reverse fulfillment cost matrix. The positive sales feature vector and the reverse fulfillment cost expectation matrix are dimensionally aligned. For the positive sales feature vector corresponding to each target region, the total number of product categories is copied along the row direction to generate aligned positive features. The reverse fulfillment cost expectation matrix is ​​not dimensionally transformed and is denoted as aligned reverse matrix. The aligned positive features and aligned reverse matrix are horizontally concatenated along the column direction to generate the full-link feature tensor. The support vector regression algorithm is used to calculate the regional demand of the full-link feature tensor to obtain the regional demand prediction value. For each combination of product category and target region, the expected reverse fulfillment cost per unit in the corresponding target region is subtracted from the forward sales product price. The expected net profit per unit of product is obtained. A three-dimensional coordinate node is constructed using the product category index, target region index and prediction time period index. The expected net profit per unit of product and the regional demand prediction value are mapped to the three-dimensional coordinate node to generate a dynamic mapping table for full-link revenue prediction. Based on the dynamic mapping table for full-link revenue prediction, a mixed integer programming equation with the objective function of maximizing the expected total revenue is constructed. The branch and bound algorithm is used to solve the mixed integer programming equation and output the global optimal allocation decision feature set. The global optimal warehouse allocation decision feature set is analyzed to obtain the allocation quantity and the shortest logistics route configuration. Based on the allocation quantity and the shortest logistics route configuration, a pre-shipment instruction sequence is generated to execute the pre-shipment operation of goods.

2. The cross-border commodity regional demand forecasting and warehousing method according to claim 1, characterized in that, The process of extracting features from historical multidimensional data of cross-border commodities to generate positive sales feature vectors and negative fulfillment feature vectors includes: Historical multidimensional data of the cross-border goods are obtained from cross-border logistics terminals and regional e-commerce front-ends; The historical multidimensional data of cross-border commodities is discretized and dimensionality reduced to extract the positive sales feature vector and the negative fulfillment feature vector.

3. The cross-border commodity regional demand forecasting and warehousing method according to claim 1, characterized in that, The generation of the reverse fulfillment cost expectation matrix also includes: The steady-state probability distribution of the transition probability matrix of the reverse state transition Markov chain is solved.

4. The cross-border commodity regional demand forecasting and warehousing method according to claim 1, characterized in that, The step of using the support vector regression algorithm to calculate the regional demand of the end-link feature tensor includes: Initialize the parameters and penalty coefficients of the Gaussian radial basis function; The function distance of the optimal hyperplane is calculated in the support vector regression algorithm after the full-link feature tensor is initialized. The functional distance is converted into a regional demand forecast value through inverse mapping.

5. The cross-border commodity regional demand forecasting and warehousing method according to claim 1, characterized in that, The construction of a mixed-integer programming equation with the objective function of maximizing expected total revenue based on the dynamic mapping table for end-to-end revenue prediction includes: Extract the distribution sequence of expected net revenue per unit of commodity and the numerical distribution sequence of regional demand forecasts; Obtain real-time inventory values, maximum capacity thresholds, and forward delivery logistics costs for warehouses in each region; The total revenue value is calculated using the expected net revenue distribution sequence of the unit commodity and the warehouse shipment quantity variable, and the total logistics cost value is calculated using the warehouse shipment quantity variable and the forward shipment logistics cost value. The objective function that maximizes the expected total revenue is constructed by subtracting the total logistics cost from the total revenue value.

6. The cross-border commodity regional demand forecasting and warehousing method according to claim 5, characterized in that, The method of solving the mixed integer programming equation using the branch and bound algorithm includes: Removing the integer constraints on the quantity of goods shipped from different warehouses yields a linear programming relaxation problem. The simplex algorithm is used to solve the linear programming relaxation problem to obtain an initial fractional solution, and left and right branch nodes are generated based on the initial fractional solution. The process involves recursively traversing each branch node, eliminating non-optimal branches until the integer constraint condition is met, and extracting the node values ​​that meet the condition as the global optimal warehouse allocation decision feature set.

7. The cross-border commodity regional demand forecasting and warehousing method according to claim 1, characterized in that, The process of analyzing the global optimal warehouse allocation decision feature set to obtain the allocation quantity and shortest logistics route configuration includes: The global optimal warehouse allocation decision feature set is used to perform key-value pair reading operations to extract the starting warehouse identifier, the target area warehouse identifier, and the allocation quantity; The cross-border logistics network directed graph is queried, and the Dijkstra algorithm is used to calculate the shortest logistics route configuration between the starting warehouse identifier and the target area warehouse identifier.

8. The cross-border commodity regional demand forecasting and warehousing method according to claim 7, characterized in that, The step of generating a pre-shipment instruction sequence based on the allocation quantity and the shortest logistics route configuration, and executing the pre-shipment product distribution operation, includes: The starting warehouse identifier, target area warehouse identifier, transfer quantity, and shortest logistics route configuration are combined and encapsulated according to a standard data exchange protocol to generate a pre-shipment instruction sequence. The pre-shipment instruction sequence is sent to the warehouse automation control terminal, which then parses and drives automated equipment to perform product picking, labeling, and barcode scanning for outbound operations.

9. A cross-border commodity regional demand forecasting and distribution system, characterized in that, To implement the method according to any one of claims 1 to 8, comprising: The data feature extraction and reverse cost quantification module is used to extract features from historical multidimensional data of cross-border commodities to generate positive sales feature vectors and reverse fulfillment feature vectors. Based on the reverse fulfillment feature vectors, a reverse state transition Markov chain is constructed and the state transition probability is calculated. The reverse fulfillment cost expectation matrix is ​​then output. The end-to-end revenue prediction mapping module is used to concatenate the positive sales feature vector and the reverse fulfillment cost expectation matrix into an end-to-end feature tensor, and use the support vector regression algorithm to calculate the regional demand of the end-to-end feature tensor to generate an end-to-end revenue prediction dynamic mapping table. The global allocation decision optimization module is used to construct a mixed integer programming equation with the objective function of maximizing the expected total revenue based on the dynamic mapping table of the end-to-end revenue prediction, solve the mixed integer programming equation using the branch and bound algorithm, and output the global optimal allocation decision feature set. The pre-schedule execution control module is used to parse the global optimal warehouse allocation decision feature set to obtain the allocation quantity and the shortest logistics route configuration, generate a pre-shipment instruction sequence based on the allocation quantity and the shortest logistics route configuration, and execute the pre-shipment operation of goods.

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