A multi-warehouse-oriented inventory dynamic allocation management method

Abstract

The application is particularly a multi-warehouse-oriented inventory dynamic allocation management method, relating to the technical field of inventory allocation management, comprising: based on the global joint state tensor and the time series demand prediction result set, a mixed integer nonlinear programming model is established to couple the constraints of inventory scheduling, transportation vehicle scheduling, path selection and time series scheduling in the same framework. In the application, the four dimensions of inventory scheduling, transportation vehicle scheduling, path selection and time series scheduling are coupled in the same mixed integer nonlinear programming model for joint decision-making, so that the allocation scheme synchronously considers the transportation side constraints such as transportation capacity, vehicle reachable time and goods receiving time window in the generation stage, so that the allocation task is confirmed to have feasible transportation carrying capacity and arrival time when it is generated, thereby overcoming the invalid situation that transportation cannot match the inventory scheme in the traditional step-by-step processing mode.

Description

Technical Field

[0001] This invention relates to the field of inventory transfer management technology, and in particular to a dynamic inventory transfer management method for multiple warehouses. Background Technology

[0002] In the actual operation of multi-warehouse inventory transfers, existing methods typically handle inventory scheduling and transportation scheduling in stages. At the inventory level, the categories and quantities to be transferred are determined first, and then vehicles and routes are independently arranged at the transportation level. This step-by-step approach leads to frequent failures of inventory transfer plans during the execution phase due to insufficient transport capacity, mismatched vehicle types, or untimely delivery. Simultaneously, each warehouse conducts independent demand forecasting, failing to fully consider the demand transmission relationships between warehouses, further exacerbating the deviation of the transfer plan under demand fluctuation scenarios.

[0003] Furthermore, when unexpected events occur during execution, existing methods lack the ability to coordinate and adjust the executed and unexecuted parts, often requiring the original plan to be overturned and replanned, resulting in low execution efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a dynamic inventory allocation management method for multiple warehouses in order to solve the above-mentioned problems.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for dynamic inventory transfer management across multiple warehouses includes: Collect real-time inventory status data of each warehouse, real-time dynamic attribute data of the transportation fleet, and path timeliness data of each allocation route. Then, align and associate them under a unified spatiotemporal coordinate system to generate a global joint state tensor with a three-layer structure of warehouse nodes, transportation nodes, and path edges. Based on the global joint state tensor, a long short-term memory network with an integrated time attention layer is used to predict the demand for each SKU in each warehouse in multiple future time periods, generating a time-series demand prediction result set. Based on the global joint state tensor and the time-series demand prediction result set, a mixed integer nonlinear programming model is established that couples the constraints of four dimensions—inventory scheduling, transportation vehicle scheduling, route selection, and time-series scheduling—within the same framework. The mixed-integer nonlinear programming model is solved by multi-objective optimization to generate multiple sets of non-dominated Pareto optimal joint scheduling strategies; The selected joint scheduling strategy is executed and deviation indicators are continuously monitored. When the deviation exceeds the preset tolerance threshold, rescheduling is triggered.

[0006] Preferably, the collection of real-time inventory status data of each warehouse, real-time dynamic attribute data of the transport fleet, and route timeliness data of each allocation route further includes: The real-time inventory status data includes the real-time inventory quantity of each SKU in each warehouse, safety stock threshold, in-transit replenishment quantity, reserved order occupancy quantity, and remaining shelf life days; the real-time dynamic attribute data includes the current location, remaining transport capacity, in-transit tasks and expected release time, driving speed, fuel consumption cost coefficient, and driver qualification information of each transport vehicle; the route timeliness data includes the expected transport time and confidence interval of each allocation route. The numerical fields in the above data are standardized using Z-score, and the categorical fields are converted into numerical representations using one-hot encoding.

[0007] Preferably, in the long short-term memory network that integrates a time attention layer, the time attention layer is attached to the hidden state sequence of the long short-term memory network and assigns differentiated weights to the hidden states of different historical periods. The temporal attention layer performs a nonlinear transformation on the hidden state at each time step using a projection weight matrix and a bias vector. The result is then mapped to a scalar attention score via a weight vector. The attention score at each time step is then converted into attention weights using a normalization function. The hidden states at each time step are weighted and summed according to the attention weights to generate a context vector. The context vector is then concatenated with the final hidden state and output as the demand prediction mean and confidence interval via a linear mapping layer. During training, actual sales figures for each historical period are used as supervision labels, and the mean squared error loss function is used to update the parameters.

[0008] Preferably, the generation of the time-series demand prediction result set further includes: A graph neural network is used to model the demand relationship between warehouses. The graph neural network uses each warehouse as a node and the historical transfer frequency and geographical distance between warehouses as edge weights to form a warehouse relationship graph. The average demand forecast obtained by each warehouse independently is used as the node feature input. The historical transfer frequency and geographical distance are normalized based on the range before being weighted and merged. The graph neural network outputs updated demand forecast values ​​for each SKU in each warehouse after cross-warehouse demand propagation correction. When the demand forecast for a warehouse surges, the graph neural network propagates the surge signal along the warehouse association graph to neighboring warehouses, generating suggested reserve inventory quantities for neighboring warehouses.

[0009] Preferably, the joint decision variables of the mixed integer nonlinear programming model include: the transfer volume matrix of each SKU between warehouses, the route sequence of each transport vehicle, the loading order and loading volume of each task on each route, and the planned departure time stamp and planned arrival time stamp of each task; wherein, each element in the transfer volume matrix is ​​a non-negative integer, the selection of each node in the route sequence is a zero-one integer variable, and the loading volume is a continuous variable. The constraints of the mixed-integer nonlinear programming model include inventory turnover constraints, transportation resource constraints, and time synchronization constraints. The inventory turnover constraint ensures that the inventory of each SKU in each warehouse is not lower than the safety stock threshold and does not exceed the upper limit of storage capacity at any time section. The inventory deduction time of the transfer task for the source warehouse is the actual loading and departure time of the vehicle corresponding to the task. The transportation resource constraints incorporate the capacity, driving time window, and driving duration compliance requirements of each transport vehicle. When a transport vehicle executes a multi-task loading route between multiple warehouses, the sum of the loading volume of each task shall not exceed the vehicle's remaining capacity.

[0010] Preferably, the time synchronization constraint includes: The time interval between goods leaving the source warehouse and entering the target warehouse is equal to the sum of the route transportation time and the loading and unloading operation time; multiple tasks on the same vehicle are time-dependent according to the loading and unloading sequence, and the departure time of the later task is not earlier than the unloading completion time of the previous task; the time when the goods arrive at the target warehouse falls within the receiving operation time window of the target warehouse. The transportation resource constraints also include a compatibility matrix, where rows correspond to the transportation attribute categories of each SKU, columns correspond to the qualification categories of each transportation vehicle, and matrix elements are zero or one. When a matrix element is zero, the corresponding SKU and vehicle combination is excluded from the feasible allocation scheme.

[0011] Preferably, the objective function for the multi-objective optimization solution includes four terms: The first objective function is to minimize the total cost, which is the sum of inventory holding cost, stockout penalty cost, allocation and transportation cost, and vehicle turnaround opportunity cost for each period within the planning time domain. All costs are standardized using Z-score before being substituted into the objective function. The second objective function is to maximize the service level, which is represented by minimizing the weighted sum of the number of stockouts and stockout durations of each warehouse in the planning time domain after mean normalization based on the range. At the same time, the order fulfillment rate of each warehouse is constrained to be no less than a preset threshold. The third objective function is to minimize the transportation timeliness deviation, which is represented by minimizing the sum of the absolute values ​​of the differences between the planned arrival timestamp of each allocation task and the center point of the receiving operation time window of the corresponding target warehouse. The fourth objective function is to equalize the utilization rate of transportation resources, which is quantitatively represented by minimizing the variance of the average actual loading rate of all transportation vehicles in the planning time domain.

[0012] Preferably, the multi-objective optimization solution employs a hybrid solution framework that integrates global search and local refinement, and the hybrid solution framework comprises three components: The global search unit uses the improved NSGA-II algorithm to explore the decision variable space globally. It adaptively adjusts the crossover probability and mutation probability according to the distribution density of non-dominated solutions in the current population and outputs a set of candidate solutions on the initial Pareto front. The integer feasibility unit uses the branch and bound method to search for the nearest feasible solution that satisfies the integer constraints in the neighborhood of each candidate solution for the integer variables in the candidate solution set, and outputs a set of feasible candidate solutions after integer constraint correction. The local refinement unit performs neighborhood search on the feasible candidate solution set using two types of search operators based on task exchange and task insertion, and outputs the final Pareto optimal solution set.

[0013] Preferably, the triggering of rescheduling also employs an incremental rolling rescheduling method based on a sliding time window: The decision results of the executed part are locked as fixed constraints. Only for the allocation tasks that have not yet been executed and the transportation tasks that have not yet departed, the joint optimization solution is re-executed based on the currently updated global joint state tensor in the decision variable space of the unexecuted part, so as to generate an updated local scheduling strategy that is continuous with the executed part in time. When a transport vehicle is detected as unable to continue performing its task, the vehicle's unperformed tasks are extracted to the task queue to be assigned. Under stricter time constraints, these tasks are then reassigned to idle vehicles or on-the-road vehicles with sufficient remaining capacity. The additional cost increment generated by emergency dispatch is calculated to update the total cost accounting result.

[0014] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. This invention couples four dimensions—inventory scheduling, transportation vehicle scheduling, route selection, and time-series scheduling—into a single mixed-integer nonlinear programming model for joint decision-making. This allows the allocation plan to simultaneously consider transportation constraints such as capacity, vehicle availability, and delivery time windows during the generation stage. As a result, feasible transportation capacity and arrival time are confirmed when the allocation task is generated, thus overcoming the failure situation where transportation cannot be matched after the inventory plan is generated in the traditional step-by-step processing method.

[0015] 2. This invention models the demand transmission relationship between warehouses using a graph neural network. When the demand in a warehouse surges, the signal propagates along the warehouse association graph to adjacent warehouses, generating a suggested reserve inventory quantity for adjacent warehouses. This enables demand forecasting to reflect the correlation between warehouses and reduces the deviation of allocation plans under demand fluctuation scenarios. Attached Figure Description

[0016] Further details, features, and advantages of this application are disclosed in the following description of exemplary embodiments in conjunction with the accompanying drawings, in which: Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0017] Several embodiments of this application will now be described in more detail with reference to the accompanying drawings to enable those skilled in the art to implement this application. This application may be embodied in many different forms and for various purposes and should not be limited to the embodiments set forth herein. These embodiments are provided to make this application thorough and complete, and to fully convey the scope of this application to those skilled in the art. The embodiments described do not limit this application.

[0018] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It will be further understood that terms such as those defined in commonly used dictionaries shall be interpreted as having a meaning consistent with their meaning in the relevant field and / or the context of this specification, and shall not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0019] Example 1

[0020] Its specific implementation method is combined with the appendix Figure 1 Please provide a detailed explanation.

[0021] In this embodiment, it includes: In the actual operation of multi-warehouse inventory transfers, existing methods typically handle inventory scheduling and transportation scheduling in stages. At the inventory level, the categories and quantities to be transferred are determined first, and then vehicles and routes are independently arranged at the transportation level. This step-by-step approach leads to frequent failures of inventory transfer plans during the execution phase due to insufficient transport capacity, mismatched vehicle types, or untimely delivery. Simultaneously, each warehouse conducts independent demand forecasting, failing to fully consider the demand transmission relationships between warehouses, further exacerbating the deviation of the transfer plan under demand fluctuation scenarios. Furthermore, when unexpected events occur during execution, existing methods lack the ability to coordinate adjustments between executed and unexecuted portions, often requiring the original plan to be scrapped and replanned, resulting in low execution efficiency.

[0022] This embodiment provides a multi-warehouse inventory and transportation joint allocation optimization method, which couples four dimensions—inventory scheduling, transportation vehicle scheduling, route selection, and time-series scheduling—into a single optimization framework for joint decision-making. The execution environment for this method includes: warehouse management systems and their data interfaces deployed in each warehouse, vehicle-mounted positioning terminals covering the transportation fleet, access to a third-party traffic data platform, and a computing server for performing the joint optimization solution.

[0023] A multi-warehouse inventory and transportation joint allocation optimization method according to an embodiment of the present invention includes the following steps: Step 1: Collect multi-source heterogeneous data and generate a global joint state tensor.

[0024] Through the data interfaces of the warehouse management systems of each warehouse, real-time inventory levels, safety stock thresholds, in-transit replenishment quantities, reserved order occupancy, and remaining shelf-life days for each SKU in each warehouse are collected, forming a real-time inventory status matrix for each warehouse. Simultaneously, data on the current location, remaining capacity, in-transit tasks and estimated release time, travel speed, and fuel cost coefficient of each transport vehicle in the transportation fleet are collected, forming a real-time dynamic attribute set of transportation resources. Furthermore, road traffic conditions between warehouses are obtained through a third-party traffic data platform, and combined with the receiving operation time windows of each warehouse, the estimated transportation time for each allocation route is calculated, forming a route timeliness dataset.

[0025] Among the three types of data mentioned above, numerical fields such as real-time inventory, in-transit replenishment quantity, reserved order occupancy, remaining shelf life days, remaining transport capacity, driving speed, fuel consumption cost coefficient, and estimated transportation time are standardized using Z-score to eliminate the impact of different dimensions on subsequent tensor calculations; categorical fields such as road traffic status are converted into numerical representations using one-hot encoding.

[0026] The three types of data are correlated and aligned in a unified spatiotemporal coordinate system to generate a global joint state tensor with a three-layer structure including warehouse nodes, transportation nodes, and path edges. This global joint state tensor serves as the unified data input for subsequent steps.

[0027] It should be noted that the attribute information for each transport vehicle mentioned above also includes driver qualification information. Driver qualification information is used to identify whether each transport vehicle possesses specific types of transport capabilities, such as cold chain transport qualifications or hazardous materials transport qualifications. Driver qualification information participates in the compatibility matching between transport resources and allocation tasks in subsequent steps.

[0028] It should be noted that the above estimated transportation time also includes a confidence interval. The confidence interval is determined based on the congestion index in road traffic conditions, road closure information, and weather influence factors, and is used to characterize the range of uncertainty in transportation time.

[0029] Step 2: Forecast the future demand for each SKU in each warehouse.

[0030] Based on historical sales data from each warehouse within the global joint state tensor, and incorporating promotional plans, holiday factors, external weather data, and inventory turnover cycles as auxiliary features, a Long Short-Term Memory (LSTM) network with an integrated temporal attention layer is employed to predict the sales demand of each SKU in each warehouse over multiple future time periods. The LSM network's input layer receives multidimensional temporal feature sequences for each SKU in each warehouse, while the output layer outputs the mean demand prediction and confidence interval for each SKU in each warehouse over future time periods. During training, actual sales figures from each historical time period are used as supervision labels, and the mean squared error loss function is employed, with parameters updated using the Adam optimization algorithm.

[0031] It should be noted that the aforementioned time attention layer is attached to the hidden state sequence of the Long Short-Term Memory network, assigning differentiated weights to the hidden states of different historical periods. This allows the model to adaptively focus on historical period information that is highly relevant to the current prediction period when generating the prediction output. Let... For the first The hidden states at each time step are used to calculate the attention weights in the temporal attention layer. for: ; in, For the first Attention score at each step, The total number of time steps in the time-series feature sequence. To provide the index for traversing each time step in the summation operation, Let be the projection weight matrix of the hidden states in the temporal attention layer. This is the bias vector for the temporal attention layer. To map the projection results to a weight vector of scalar scores, Represents an exponential function. Indicates transpose, the above , , All three are learnable parameters. Weighted context vector After being concatenated with the final hidden state, the output, along with the mean and confidence interval of the demand forecast, is obtained through a linear mapping layer.

[0032] Based on the mean demand forecast and confidence interval of each SKU in each warehouse, and combined with the expected transportation time of each transfer route, the expected inventory consumption rate and expected replenishment demand time of each warehouse in each time period are calculated, and the time series demand forecast result set of each warehouse is generated.

[0033] In this embodiment, to capture the demand transmission relationship between warehouses, a graph neural network is used to model the demand correlation between warehouses based on independent forecasts from each warehouse. The graph neural network constructs a warehouse association graph with each warehouse as a node and historical transfer frequency and geographical distance between warehouses as edge weights. The average demand forecast obtained from independent forecasts by each warehouse is used as the node feature input. The historical transfer frequency and geographical distance are normalized based on the range before being used as edge weights, ensuring they are within the same numerical range before weighted merging. The output layer of the graph neural network is a fully connected layer, outputting the updated demand forecast values ​​for each SKU in each warehouse after cross-warehouse demand propagation correction. During training, the actual sales volume of each warehouse in historical periods is used as the supervision label, and the mean squared error loss function is used, with parameters updated using the Adam optimization algorithm. When a surge in demand forecast occurs in a warehouse, the graph neural network propagates this surge signal along the warehouse association graph to adjacent warehouses, generating suggested reserved inventory levels for those adjacent warehouses.

[0034] In this embodiment, to provide a basis for the advance allocation of transportation resources, the expected scale and time distribution of transportation demand among warehouses in the future are predicted based on historical order delivery data, regional consumption habits, and seasonal variation patterns, generating logistics transportation demand forecast results. These logistics transportation demand forecast results, along with the time-series demand forecast results for each warehouse, serve as inputs for subsequent joint optimization.

[0035] In this embodiment, to enable a conservative strategy in subsequent decision-making processes when prediction uncertainty is high, confidence scores are output for each type of prediction result. A lower confidence score indicates a higher risk of prediction bias. These confidence scores are used as penalty coefficients for corresponding constraints in the subsequent optimization model, reducing the risk of decision-making errors due to prediction bias.

[0036] Step 3: Establish a joint optimization model that couples inventory and transportation in time and space.

[0037] Based on the global joint state tensor and the time-series demand forecast result set, a unified mixed-integer nonlinear programming model is established. The mixed-integer nonlinear programming model couples the constraints of four dimensions—inventory scheduling, transportation vehicle scheduling, route selection, and time-series scheduling—within the same framework.

[0038] Step 3 may specifically include: Step 3.1, define joint decision variables.

[0039] Define the following decision variables: the allocation matrix of each SKU between warehouses, the route sequence of each transport vehicle, the loading order and loading quantity of each task on each route, and the planned departure and arrival timestamps of each task. The elements in the allocation matrix are non-negative integers, the nodes in the route sequence are zero- or one-integer variables, and the loading quantity is a continuous variable.

[0040] Step 3.2: Establish inventory turnover constraints.

[0041] Establish dynamic inventory balance constraint equations for each warehouse. These equations ensure that, at any given time point, the inventory level of each SKU in each warehouse is not lower than the safety stock threshold and does not exceed the maximum storage capacity. Simultaneously, they constrain the amount of inventory transferred from each warehouse to not exceed the available surplus at that point in time.

[0042] It should be noted that the aforementioned available inventory refers to the effective inventory portion of each SKU in each warehouse after excluding the quantity already occupied by orders and the quantity en route. Unlike existing methods that statically validate available inventory after deducting safety stock, this step aligns transportation timeliness and vehicle arrival time with the inventory deduction node. Specifically, the inventory deduction point for a transfer task in the source warehouse is the actual loading and departure time of the vehicle corresponding to that task, not the generation time of the transfer plan. This approach ensures that the inventory status remains consistent with the actual execution progress.

[0043] Step 3.3: Establish transportation resource constraints.

[0044] The constraints include the transport capacity, driving time window, driving time compliance requirements, and route options of each transport vehicle. A joint allocation constraint is established between vehicles, routes, and allocation volume. Specifically, this constraint stipulates that a transport vehicle can execute multi-task loading routes between multiple warehouses, and the sum of the loading volumes for each task must not exceed the vehicle's remaining transport capacity; it also constrains the driver's continuous driving time to not exceed the compliance limit.

[0045] It should be noted that the aforementioned multi-task loading path refers to a circular or chain-like path in which a transport vehicle sequentially passes through multiple warehouse nodes, performing pickup or unloading operations at different nodes. For example, a vehicle can sequentially perform multiple transfer tasks in the order of "pick up from warehouse A, unload from warehouse B, pick up from warehouse C, and unload from warehouse D".

[0046] Step 3.4: Establish time synchronization constraints.

[0047] Establish temporal dependency constraints between allocation tasks. These constraints include three aspects: First, the time interval between goods leaving the source warehouse and entering the target warehouse is equal to the sum of the route transportation time and the loading and unloading operation time; second, multiple tasks on the same vehicle form a temporal dependency according to the loading and unloading sequence, with the departure time of the later task not earlier than the unloading completion time of the previous task; third, the arrival time of the goods at the target warehouse falls within the receiving operation time window of that target warehouse.

[0048] In this embodiment, to ensure that SKUs with special transportation requirements match the type attributes of transport vehicles, a compatibility matrix is ​​added to the transportation resource constraints. The rows of the compatibility matrix correspond to the transportation attribute categories of each SKU, and the columns correspond to the qualification categories of each transport vehicle. Matrix elements are zero or one, indicating whether the SKU is allowed to be transported by that vehicle. When a matrix element is zero, the corresponding SKU and vehicle combination is excluded from feasible allocation schemes; when a matrix element is one, the corresponding allocation combination can be included in the solution. For example, the row corresponding to cold chain goods has a zero value in the column corresponding to vehicles without temperature control capabilities, thus excluding incompatible allocation schemes.

[0049] Step 4: Solve the joint optimization model for multiple objectives and generate a scheduling strategy.

[0050] The mixed-integer nonlinear programming model established in step 3 is solved by multi-objective optimization to obtain multiple sets of non-dominated Pareto optimal joint scheduling strategies.

[0051] Step 4 may specifically include: Step 4.1: Define multiple optimization objective functions.

[0052] Define the following four objective functions: The primary objective function is to minimize the total cost. Let the planning time domain be... ,in To determine the total number of time periods in the planning time domain, the objective function for total cost is: ; in, For time period index, For the first Inventory holding costs during the period For the first The cost of stockout penalties during certain periods For the first The time-slot allocation and transportation costs (including fuel costs, toll fees, and vehicle depreciation costs). For the first The opportunity cost of vehicle turnover during a given period. All costs mentioned above are expressed in a uniform currency unit and are standardized using Z-score before being substituted into the objective function to eliminate the impact of differences in the order of magnitude of each cost item on the weighted summation result.

[0053] The second objective function is to maximize the service level. This is quantified by minimizing the weighted sum of the number of stockouts and their duration for each warehouse within the planning time domain. ; in, For the first The cumulative number of stockouts in each warehouse during the time period. For the first Cumulative stockout duration for each warehouse during the time period (unit: hours). and These are the corresponding weighting coefficients. Because... (times) and Due to the different units of measurement (hours), mean normalization based on the range is applied separately before weighted summation to normalize them to the same numerical range before weighted merging. Simultaneously, the order fulfillment rate of each warehouse within the planned time domain is constrained to not be lower than a preset threshold. That is, each warehouse in The percentage of valid order fulfillment periods within the period shall not be less than ,in This is the preset lower limit for order fulfillment rate.

[0054] The third objective function is to minimize the transportation timeliness deviation. Let the set of allocation tasks be... ,in The first The, the The first to the second An allocation task. The total number of tasks to be allocated. Tasks The planned arrival timestamp is The center point of the receiving operation time window for the target warehouse is ,but: ; in, For allocating task indexes, For the task The planned arrival timestamp For the task The center point of the corresponding target warehouse receiving operation time window.

[0055] The fourth objective function is to equalize the utilization rate of transportation resources. Let the set of transportation vehicles be... ,in The first Vehicle, No. Vehicle to the first A transport vehicle, The total number of transport vehicles. For transport vehicle assembly The number of elements. Vehicles The average actual loading rate within the planning time domain was , If the load factor of all vehicles is the average, then: ; in, For transport vehicle indexing, For vehicles The average actual loading rate within the planning time domain. This represents the average load factor for all vehicles. The goal is to minimize this variance to prevent some vehicles from being overloaded while others remain idle.

[0056] Step 4.2: Solve the problem using a hybrid solution framework.

[0057] To address the high-dimensionality of the aforementioned mixed-integer nonlinear programming model, a hybrid solution framework integrating global search and local refinement is employed. This framework comprises three units: a global search unit, an integer feasibility unit, and a local refinement unit.

[0058] The global search unit employs an improved NSGA-II algorithm to globally explore the decision variable space. The improved NSGA-II algorithm introduces an adaptive crossover and mutation probability adjustment strategy based on the standard NSGA-II algorithm. It automatically adjusts the crossover and mutation probabilities according to the distribution density of non-dominated solutions in the current population: increasing the mutation probability to expand the search range when population diversity is insufficient, and decreasing the mutation probability to maintain stable convergence when the population distribution is uniform. The input to the global search unit consists of the decision variables, the initial population, and four objective functions defined in step 3; the output is the set of candidate solutions on the initial Pareto front.

[0059] The integer feasibility unit performs feasibility processing on the integer variables in each candidate solution output by the global search unit. For the non-negative integer variables in the allocation matrix and the zero- and one-integer variables in the path sequence, the branch and bound method is used to search for the nearest feasible solution that satisfies the integer constraints in the neighborhood of each candidate solution. The input of the integer feasibility unit is the set of candidate solutions on the initial Pareto front, and the output is the set of feasible candidate solutions after integer constraint correction.

[0060] The local refinement unit performs a neighborhood search on each feasible candidate solution after integer feasibility processing. The neighborhood search employs two types of search operators: task swapping and task insertion. The task swapping operator exchanges transfer tasks between two different vehicles, while the task insertion operator moves a task from one vehicle to the path sequence of another vehicle. The input to the local refinement unit is the set of feasible candidate solutions, and the output is the final Pareto optimal solution set after local optimization.

[0061] The data transfer relationship between the three components is as follows: the global search unit generates the initial Pareto front and passes it to the integer feasible unit. The integer feasible unit performs integer constraint correction on each candidate solution and then passes it to the local refinement unit. The local refinement unit outputs the final Pareto optimal solution set.

[0062] Step 4.3: Generate the Pareto optimal policy set.

[0063] Based on the final Pareto optimal solution set, multiple sets of non-dominated joint scheduling strategies are generated. Each strategy set includes the allocation quantity of each SKU between warehouses, the route sequence and loading scheme of each transport vehicle, and the planned departure and arrival times of each task. Each strategy set is labeled with its score on four objective functions, and the Pareto optimal strategy set is output.

[0064] It should be noted that the Pareto optimal strategy set contains multiple strategy sets rather than a single strategy, and each strategy set has its own emphasis on the four objective functions. Users can select a strategy set from the Pareto optimal strategy set as the execution plan based on their current operational priorities.

[0065] In this embodiment, to avoid excessive compression of timeliness for edge warehouses or long-cycle delivery tasks during the global optimization process, differentiated weights are assigned to each allocation task during the multi-objective solution process. Specifically, based on the emergency allocation response time of each warehouse and the timeliness sensitivity level of each SKU, differentiated weight values ​​are assigned to the sub-items corresponding to each allocation task in the second and third objective functions. For tasks with longer delivery cycles and stricter timeliness requirements, higher weight values ​​are assigned, ensuring that the optimization solution process prioritizes the service level and timeliness performance of such tasks.

[0066] Step 5: Execute the scheduling strategy and perform deviation detection.

[0067] A set of strategies selected from the Pareto optimal strategy set will be distributed to each warehouse management system and transportation fleet dispatching system for execution. During execution, the following indicators will be continuously monitored through real-time data feedback from vehicle positioning terminals, warehouse operation terminals, and the order management system: the deviation between actual and predicted inventory in each warehouse, the deviation between the actual location and planned route of each transportation vehicle, and the deviation between actual travel time and planned delivery time. When the deviation of any indicator exceeds a preset tolerance threshold, a rescheduling trigger signal will be generated.

[0068] It should be noted that the preset tolerance thresholds are set separately for different monitoring indicators. The tolerance threshold for inventory deviation is expressed as a proportion of the safety stock threshold for each SKU, the tolerance threshold for location deviation is expressed as a proportion of the planned route mileage, and the tolerance threshold for timeliness deviation is expressed as a proportion of the receiving operation time window width for each task. Each threshold can be adjusted independently according to the operational strategy.

[0069] In this embodiment, to avoid overturning the entire plan and replanning when execution deviations occur, an incremental rolling rescheduling method based on a sliding time window is adopted. When a rescheduling trigger signal is received, only the allocation tasks that have not yet been executed and the transportation tasks that have not yet departed within the planned time window are locally updated. Specifically, the decision results of the executed part are locked as fixed constraints. In the decision variable space of the unexecuted part, based on the currently updated global joint state tensor, the local optimization solutions of steps 3 and 4 are re-executed to generate an updated local scheduling strategy. The updated local scheduling strategy maintains temporal continuity with the executed part, avoiding contradictions between the new plan and the executed arrangements.

[0070] In this embodiment, to address specific events such as sudden vehicle malfunctions, an emergency dispatch process is added to the incremental rolling rescheduling. When a transport vehicle is detected as unable to continue its task, its unfinished tasks are extracted to a task queue. Under stricter time constraints, these tasks are then reassigned to idle vehicles or on-the-road vehicles with sufficient remaining capacity. Simultaneously, the additional cost increment resulting from the emergency dispatch is calculated, and the total cost calculation is updated.

[0071] In this embodiment, to enable the scheduling strategy to adapt to long-term changes in the external environment, an offline simulation learning method is used to continuously update the model parameters. Using planned and actual values ​​from historical execution data as samples, simulation playback is performed in an offline environment to analyze the distribution of causes of various deviations. Based on this, the objective function weight parameters of the hybrid solution framework in step 4 and the boundary condition parameters of the mixed integer nonlinear programming model in step 3 are updated.

[0072] Example 2

[0073] A regional FMCG distribution network needs to conduct cross-warehouse transfers of inventory across its four regional warehouses (Warehouse A, B, C, and D) before the 20XX promotional season, and coordinate a fleet of transport vehicles to execute the transfers. The transferred product categories include three SKUs: ambient temperature beverages (SKU-A), cold chain dairy products (SKU-B), and snack foods (SKU-C). SKU-B is a cold chain product, requiring transport vehicles to have cold chain certification. The fleet currently has five transport vehicles (vehicles 1 to 5), with vehicles 3 and 5 possessing cold chain certification. The planning timeframe covers seven future time periods (each corresponding to one day).

[0074] Step 1: Global Joint Status Acquisition and Standardization

[0075] The data interfaces of each warehouse management system synchronously collect inventory status. Taking SKU-A as an example, Warehouse A has a real-time inventory of 1240 units, a safety stock threshold of 300 units, 200 units in transit for replenishment, 180 units in reserved orders, and 42 days remaining on the shelf life. Meanwhile, Vehicle 1 is currently near Warehouse A, with remaining capacity of 8.2 tons, an estimated release time of 18:00 on the same day for its in-transit task, a travel speed of 72 km / h, and a fuel cost coefficient of 1.35 yuan / km. The traffic platform returns a congestion index of 0.62 for the route from Warehouse A to Warehouse B, with no current road closures and a weather impact factor of 0.08. Based on this, the estimated transportation time is 4.3 hours, with a confidence interval of 3.9 to 5.1 hours.

[0076] After one-hot encoding, the road traffic status field is converted to [1, 0, 0], [0, 1, 0], and [0, 0, 1] for "smooth traffic", "light congestion", and "severe congestion", respectively. Numerical fields are standardized using Z-scores: a real-time inventory of 1240 items corresponds to a standardized value of 1.24, and an estimated transportation time of 4.3 hours corresponds to a standardized value of 0.87. The above data are aligned and correlated in a unified spatiotemporal coordinate system, forming a global joint state tensor containing warehouse node layers, transportation node layers, and path edge layers.

[0077] Table 1. Raw data and standardized results of SKU-A inventory status for each warehouse

[0078] In Table 1, the available inventory of warehouses B and D is negative, indicating that the current available inventory is insufficient and needs to be transferred from warehouse A or warehouse C. This signal is directly fed into the global joint state tensor, serving as the basic input for demand forecasting in step 2 and optimization modeling in step 3.

[0079] Step 2: Time-series demand forecasting

[0080] Taking SKU-A in Warehouse B as an example, the input layer of the Long Short-Term Memory (LSTM) network receives historical sales sequences from the past 28 time periods, while incorporating promotional plans (a discount event starts in time period 5), holiday factors (time periods 6 and 7 are weekends), local weather forecasts (rain is expected in time period 3), and inventory turnover cycle (historical average is 5.2 days) as auxiliary features. The time attention layer calculates attention weights for the hidden states of the 28 historical time steps. The time steps with the highest weights are concentrated in time steps 22 to 28 (i.e., the most recent week) and time steps 8 to 14 (corresponding to the previous promotional cycle), indicating that the model adaptively focuses on recent trends and similar promotional history. After concatenating the weighted context vector with the final hidden state, the output is the mean and confidence interval of demand forecasts for the next 7 time periods.

[0081] The graph neural network uses four warehouses as nodes, with edge weights calculated using normalized weights of historical transfer frequency and geographical distance. The normalized historical transfer frequency between warehouse A and warehouse B is 0.78, and the normalized geographical distance is 0.31, resulting in a weighted edge weight of 0.61. When warehouse B experiences a predicted surge in demand in period 5, the graph neural network propagates this signal along the association graph to warehouse D (edge ​​weight 0.48), generating suggested reserve inventory quantities of 85 units for warehouse D in periods 5 and 120 units in periods 6.

[0082] Table 2: Demand Forecast Results for SKU-A in Warehouse B for the Next 7 Periods (Excerpt)

[0083] On day 3, the confidence score dropped to 0.76, reflecting the uncertainty of the impact of rainy weather on sales forecasts; on day 5, demand surged to 287 units during the promotion period, and the confidence score dropped to 0.68. This score will be used as the penalty coefficient input for the corresponding constraint in step 3, prompting the optimization model to adopt a more conservative allocation strategy.

[0084] Step 3: Joint Optimization Modeling

[0085] Based on the global joint state tensor and the time-series demand prediction results shown in Table 2, a mixed-integer nonlinear programming model is established.

[0086] In step 3.1, the transfer quantity matrix defines the number of transfers of each SKU between warehouses. For example, the quantity of SKU-A transferred from warehouse A to warehouse B. The variable is a non-negative integer. In the path sequence, the decision variable is whether vehicle 1 passes through warehouse A node. For zero- and one-integer variables, the actual load is... It is a continuous variable.

[0087] In step 3.2, taking warehouse B on day 1 as an example, the dynamic inventory balance constraint verification is as follows: Beginning inventory is 318 units, plus 200 units in transit replenishment, minus the daily reserved inventory of 95 units, and further minus the average demand forecast of 142 units, resulting in ending inventory of 281 units. This is below the safety stock threshold of 300 units, requiring a transfer to be triggered. After excluding the already occupied quantity, the available quantity for transfer from warehouse A on day 1 is 760 units. The inventory deduction point corresponds to the vehicle loading and departure point, not the time the plan is generated.

[0088] In step 3.3, the compatibility matrix confirms that SKU-B (cold chain dairy products) has a value of 0 in the corresponding columns of vehicle 1, vehicle 2, and vehicle 4, and a value of 1 in the corresponding columns of vehicle 3 and vehicle 5, thereby excluding the scheme of non-cold chain vehicles transporting SKU-B.

[0089] In step 3.4, taking the task of "retrieving SKU-B from warehouse A and unloading from warehouse B" performed by vehicle 3 as an example, the departure timestamp is set to 08:00 on day 1, the route transportation time is 4.3 hours, the loading and unloading operation time is 0.5 hours, and the planned arrival time is 13:18 on day 1, which falls within the receiving time window of warehouse B from 08:00 to 17:00, thus satisfying the time synchronization constraint.

[0090] Table 3 Compatibility Matrix (SKU and Vehicle Qualification Matching)

[0091] Step 4: Multi-objective solution and strategy generation

[0092] In step 4.1, taking day 1 of the planning time domain as an example, warehouse A transfers 400 units of SKU-A to warehouse B, with inventory holding costs... The cost is 182 yuan, and the penalty cost for out-of-stock items is [amount missing]. The cost is 0 yuan (sufficient inventory after allocation), and the allocation transportation cost is [not specified]. The opportunity cost of vehicle turnover is 1260 yuan (including fuel, toll fees, and depreciation). The cost is 320 yuan. All costs, after Z-score standardization, are input into the first objective function. In the third objective function, vehicle 3 is scheduled to arrive at warehouse B at 13:18, which is the center point of the receiving time window. The timeliness deviation is 12:30. It lasts for 48 minutes.

[0093] In step 4.2, the global search unit searches the decision variable space for 5 vehicles, 4 warehouses, 3 SKUs, and 7 time periods, with an initial population size of 200 candidate solutions. After 50 generations of evolution, it outputs 80 candidate solutions on the initial Pareto front. The integer feasibility unit corrects the continuous relaxation values ​​of the allocation matrix in each candidate solution (e.g., the relaxation value of SKU-A allocated from warehouse A to warehouse B is 397.6 pieces) to integer values ​​(398 pieces) using the branch and bound method. The local refinement unit performs task exchange and task insertion search for each feasible candidate solution. For example, it inserts the SKU-C allocation task from warehouse C to warehouse D undertaken by vehicle 2 into the path of vehicle 4, increasing the loading rate of vehicle 4 from 0.51 to 0.73, while releasing vehicle 2 to undertake the emergency replenishment task of SKU-A. Finally, it outputs 48 Pareto optimal solutions.

[0094] Step 4.3 Generate a Pareto optimal policy set, where policy P1 focuses on minimizing total cost, policy P2 focuses on maximizing service level, and policy P3 achieves equilibrium among the four objectives.

[0095] Table 4 Comparison of key objective scores for Pareto optimal strategy sets

[0096] The operations team prioritizes ensuring the smooth operation of the overall promotional season and selects strategy P2 for execution.

[0097] Step 5: Dynamic Monitoring and Rescheduling

[0098] After strategy P2 was distributed to the warehouse management systems and fleet dispatch systems, the vehicle positioning terminals continuously transmitted vehicle locations. On the third day of execution, vehicle 3 encountered rainfall, which reduced its speed. The actual transport time reached 6.6 hours, exceeding the planned time by 4.3 hours, with a deviation of 2.3 hours and a deviation rate of 53.5%. This exceeded the preset timeliness tolerance threshold (25% of the 9-hour receiving time window, i.e., 2.25 hours), triggering a rescheduling signal.

[0099] After incremental rolling rescheduling is initiated, the results of the allocation tasks executed on days 1 and 2 are locked as fixed constraints, and only tasks that have not yet departed on days 3 to 7 are re-optimized. The updated global joint state tensor incorporates the delay status of vehicle 3 and the current actual inventory of warehouse B (reduced to 176 units after two days of consumption). Based on the updated tensor, the local optimizations in steps 3 and 4 are re-executed, transferring the original SKU-A replenishment task (350 units) from warehouse C to warehouse B for vehicle 3 on day 3 to vehicle 1 (with remaining capacity of 9.1 tons, currently located near warehouse C), generating an updated local scheduling strategy.

[0100] Table 5 Comparison of key parameters before and after rescheduling.

[0101] In the updated local strategy, vehicle 1 arrives at 14:45 after accepting the task, still within the receiving time window of warehouse B (08:00 to 17:00), thus maintaining temporal continuity. The additional cost increment of 340 yuan is included in the total cost calculation. The offline simulation module records samples of deviations caused by this rainfall, which are used to update the objective function weight parameters corresponding to the weather influence factors in the hybrid solution framework of step 4.

[0102] Throughout the implementation process, the data starts from the inventory status matrix and path timeliness data collected in step 1. Step 2 generates the time-series demand and confidence score for each warehouse through demand forecasting. The confidence score is used as a penalty coefficient and input into the joint optimization model in step 3. The compatibility matrix and time synchronization constraints in the model ensure that the allocation plan is feasible for transportation during the generation stage. Step 4 outputs the Pareto optimal strategy set through the hybrid solution framework. Step 5 compares the real-time back data with the planned value and triggers incremental rescheduling, which only updates the unexecuted parts locally, so that the data flow throughout the process remains logically consistent and temporally continuous between each step.

[0103] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

[0104] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0105] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for dynamic inventory transfer management across multiple warehouses, characterized in that, include: Collect real-time inventory status data of each warehouse, real-time dynamic attribute data of the transportation fleet, and path timeliness data of each allocation route. Then, align and associate these data in a unified spatiotemporal coordinate system to generate a global joint state tensor with a three-layer structure including warehouse nodes, transportation nodes, and path edges. Based on the global joint state tensor, a long short-term memory network with an integrated time attention layer is used to predict the demand for each SKU in each warehouse in multiple future time periods, generating a time-series demand prediction result set. Based on the global joint state tensor and the time-series demand prediction result set, a mixed integer nonlinear programming model is established that couples the constraints of four dimensions—inventory scheduling, transportation vehicle scheduling, route selection, and time-series scheduling—within the same framework. The joint decision variables of the mixed integer nonlinear programming model include: the transfer volume matrix of each SKU between warehouses, the route sequence of each transport vehicle, the loading order and loading volume of each task on each route, and the planned departure time stamp and planned arrival time stamp of each task; among them, each element in the transfer volume matrix is ​​a non-negative integer, the selection of each node in the route sequence is a zero-one integer variable, and the loading volume is a continuous variable. The constraints of the mixed-integer nonlinear programming model include inventory turnover constraints, transportation resource constraints, and time synchronization constraints. The inventory turnover constraint ensures that the inventory of each SKU in each warehouse is not lower than the safety stock threshold and does not exceed the upper limit of storage capacity at any time section. The inventory deduction time of the transfer task for the source warehouse is the actual loading and departure time of the vehicle corresponding to the task. The transportation resource constraints include the capacity, driving time window, and driving time compliance requirements of each transportation vehicle. When a transportation vehicle executes a multi-task loading route between multiple warehouses, the sum of the loading volume of each task shall not exceed the vehicle's remaining capacity. The mixed-integer nonlinear programming model is solved by multi-objective optimization to generate multiple sets of non-dominated Pareto optimal joint scheduling strategies; The selected joint scheduling strategy is executed and deviation indicators are continuously monitored. When the deviation exceeds the preset tolerance threshold, rescheduling is triggered.

2. The method for dynamic inventory transfer management for multiple warehouses according to claim 1, characterized in that, The collection of real-time inventory status data for each warehouse, real-time dynamic attribute data for the transportation fleet, and route timeliness data for each allocation route also includes: The real-time inventory status data includes the real-time inventory quantity of each SKU in each warehouse, safety stock threshold, in-transit replenishment quantity, reserved order occupancy quantity, and remaining shelf life days; the real-time dynamic attribute data includes the current location, remaining transport capacity, in-transit tasks and expected release time, driving speed, fuel consumption cost coefficient, and driver qualification information of each transport vehicle; the route timeliness data includes the expected transport time and confidence interval of each allocation route. The numerical fields in the above data are standardized using Z-score, and the categorical fields are converted into numerical representations using one-hot encoding.

3. The method for dynamic inventory transfer management for multiple warehouses according to claim 1, characterized in that, In a long short-term memory network that integrates a temporal attention layer, the temporal attention layer is attached to the hidden state sequence of the long short-term memory network and assigns differentiated weights to the hidden states of different historical periods. The temporal attention layer performs a nonlinear transformation on the hidden state at each time step using a projection weight matrix and a bias vector. The result is then mapped to a scalar attention score via a weight vector. The attention score at each time step is then converted into attention weights using a normalization function. The hidden states at each time step are weighted and summed according to the attention weights to generate a context vector. The context vector is then concatenated with the final hidden state and output as the demand prediction mean and confidence interval via a linear mapping layer. During training, actual sales figures for each historical period are used as supervision labels, and the mean squared error loss function is used to update the parameters.

4. The method for dynamic inventory transfer management for multiple warehouses according to claim 1, characterized in that, The generation of the time-series demand forecast result set also includes: A graph neural network is used to model the demand relationship between warehouses. The graph neural network uses each warehouse as a node and the historical transfer frequency and geographical distance between warehouses as edge weights to form a warehouse relationship graph. The average demand forecast obtained by each warehouse independently is used as the node feature input. The historical transfer frequency and geographical distance are normalized based on the range before being weighted and merged. The graph neural network outputs updated demand forecast values ​​for each SKU in each warehouse after cross-warehouse demand propagation correction. When the demand forecast for a warehouse surges, the graph neural network propagates the surge signal along the warehouse association graph to adjacent warehouses, generating suggested reserve inventory quantities for adjacent warehouses.

5. The method for dynamic inventory transfer management for multiple warehouses according to claim 1, characterized in that, Time synchronization constraints include: The time interval between goods leaving the source warehouse and entering the target warehouse is equal to the sum of the route transportation time and the loading and unloading operation time; multiple tasks on the same vehicle are time-dependent according to the loading and unloading sequence, and the departure time of the later task is not earlier than the unloading completion time of the previous task; the time when the goods arrive at the target warehouse falls within the receiving operation time window of the target warehouse. The transportation resource constraints also include a compatibility matrix, where rows correspond to the transportation attribute categories of each SKU, columns correspond to the qualification categories of each transportation vehicle, and matrix elements are zero or one. When a matrix element is zero, the corresponding SKU and vehicle combination is excluded from the feasible allocation scheme.

6. The method for dynamic inventory transfer management for multiple warehouses according to claim 1, characterized in that, The objective function for multi-objective optimization includes four terms: The first objective function is to minimize the total cost, which is the sum of inventory holding cost, stockout penalty cost, allocation and transportation cost, and vehicle turnaround opportunity cost for each period within the planning time domain. All costs are standardized using Z-score before being substituted into the objective function. The second objective function is to maximize the service level, which is represented by minimizing the weighted sum of the number of stockouts and stockout durations of each warehouse in the planning time domain after mean normalization based on the range. At the same time, the order fulfillment rate of each warehouse is constrained to be no less than a preset threshold. The third objective function is to minimize the transportation timeliness deviation, which is represented by minimizing the sum of the absolute values ​​of the differences between the planned arrival timestamp of each allocation task and the center point of the receiving operation time window of the corresponding target warehouse. The fourth objective function is to equalize the utilization rate of transportation resources, which is quantitatively represented by minimizing the variance of the average actual loading rate of all transportation vehicles in the planning time domain.

7. The method for dynamic inventory allocation management for multiple warehouses according to claim 1, characterized in that, The multi-objective optimization solution employs a hybrid solution framework that integrates global search and local refinement. This hybrid solution framework comprises three components: The global search unit uses the improved NSGA-II algorithm to explore the decision variable space globally. It adaptively adjusts the crossover probability and mutation probability according to the distribution density of non-dominated solutions in the current population and outputs a set of candidate solutions on the initial Pareto front. The integer feasibility unit uses the branch and bound method to search for the nearest feasible solution that satisfies the integer constraints in the neighborhood of each candidate solution for the integer variables in the candidate solution set, and outputs a set of feasible candidate solutions after integer constraint correction. The local refinement unit performs neighborhood search on the feasible candidate solution set using two types of search operators based on task exchange and task insertion, and outputs the final Pareto optimal solution set.

8. The method for dynamic inventory transfer management for multiple warehouses according to claim 1, characterized in that, When rescheduling is triggered, an incremental rolling rescheduling method based on a sliding time window is also used: The decision results of the executed part are locked as fixed constraints. Only for the allocation tasks that have not yet been executed and the transportation tasks that have not yet departed, the joint optimization solution is re-executed based on the currently updated global joint state tensor in the decision variable space of the unexecuted part, so as to generate an updated local scheduling strategy that is continuous with the executed part in time. When a transport vehicle is detected as unable to continue performing its task, the vehicle's unperformed tasks are extracted to the task queue to be assigned. Under stricter time constraints, these tasks are then reassigned to idle vehicles or on-the-road vehicles with sufficient remaining capacity. The additional cost increment generated by emergency dispatch is calculated to update the total cost accounting result.

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