Multi-store cooperative printing order resource dynamic scheduling and distribution method

Abstract

The application belongs to the technical field of resource scheduling, and discloses a printing order resource dynamic scheduling and distribution method for multi-store cooperation; the method comprises the following steps: acquiring topology structure data and logistics communication data of a multi-store network, and constructing a store cooperation relationship graph; collecting node state characteristic vectors of each store in real time, and embedding the node state characteristic vectors into the store cooperation relationship graph to form a dynamic store state graph; inputting the dynamic store state graph into a pre-trained graph neural network model, outputting a cooperative scheduling potential vector of each store, and modeling each store as a scheduling agent; acquiring order attribute data of each to-be-distributed order, independently calculating a local benefit function and a cooperative benefit function by each scheduling agent, generating a cooperative scheduling strategy set, and determining a final execution store of each to-be-distributed order; the application can realize dynamic cooperative scheduling and global optimal distribution of printing order resources in a multi-store network, and improve cross-store load balancing capability and order processing timeliness.

Description

Technical Field

[0001] This invention relates to the field of resource scheduling technology, and more specifically, to a method for dynamic scheduling and allocation of print order resources for multi-store collaboration. Background Technology

[0002] With the rapid development of the digital printing service industry, chain printing store networks have become an important service model to meet the diverse printing needs of enterprises and individuals. In the multi-store operation model, the scheduling and allocation of order resources directly affects service response efficiency and customer satisfaction. Existing printing order scheduling methods mainly include rule-based static allocation methods and optimization algorithm-based centralized scheduling methods. Rule-based static allocation methods usually allocate orders to the nearest store for execution based on the order submission location, which is simple to implement but lacks flexibility. Optimization algorithm-based centralized scheduling methods optimize the allocation of orders globally by constructing a mathematical programming model, which can improve resource utilization efficiency to a certain extent, but the computational complexity is high and it is difficult to adapt to the dynamic changes in store status.

[0003] Further analysis reveals the following shortcomings of the aforementioned methods when dealing with multi-store collaborative scheduling scenarios: Firstly, existing methods treat each store as an independent service node, failing to effectively model the geographical connections, logistics connectivity, and resource complementarity between stores. This results in weak cross-store collaborative scheduling capabilities, making it difficult to dynamically transfer load when some stores experience order backlogs or equipment failures. Secondly, existing methods often employ a centralized decision-making architecture, with a central node uniformly calculating and executing scheduling plans. This presents a single-point bottleneck risk and significant response delays, making it difficult to meet the timeliness requirements of real-time order allocation. Therefore, there is an urgent need for a dynamic scheduling and allocation method for print order resources that can fully leverage store collaborative relationships and support distributed autonomous decision-making.

[0004] In view of this, the present invention proposes a dynamic scheduling and allocation method for printing order resources for multi-store collaboration to solve the above problems. Summary of the Invention

[0005] To overcome the aforementioned shortcomings of the existing technology and achieve the above objectives, the present invention provides the following technical solution: a dynamic scheduling and allocation method for print order resources for multi-store collaboration, comprising:

[0006] Step S1: Obtain the topology data and logistics connectivity data of the multi-store network, and construct a store collaboration relationship diagram based on the topology data and logistics connectivity data;

[0007] Step S2: Collect order backlog data, resource usage data and service response data of each store in real time, and encode them into node status feature vectors of each store. Embed the node status feature vectors into the store collaboration relationship diagram to form a dynamic store status diagram.

[0008] Step S3: Input the dynamic store state graph into the pre-trained graph neural network model, perform neighborhood aggregation on the node state feature vector of each store through the message passing mechanism, output the collaborative scheduling potential vector of each store, and model each store as a scheduling agent based on the collaborative scheduling potential vector.

[0009] Step S4: Obtain the order attribute data of each order to be assigned. Each scheduling agent independently calculates the local revenue function and the collaborative revenue function based on the order attribute data, and reaches the Nash equilibrium solution for order allocation through multiple rounds of game iteration, generating a set of collaborative scheduling strategies.

[0010] Step S5: Determine the final execution store for each order to be assigned based on the collaborative scheduling strategy set, generate a cross-store order routing table, and synchronize the cross-store order routing table to each store.

[0011] Furthermore, methods for obtaining topology data and logistics connectivity data include:

[0012] Obtain the basic information and equipment configuration information of each store in the multi-store network. The basic information of the store includes the store's unique identifier, geographical coordinates, business hours, and service radius. Calculate the comprehensive capacity index of each store based on its equipment configuration information. Calculate the service capacity set of each store based on its equipment configuration information. Summarize the comprehensive capacity index and service capacity set of all stores to obtain the topology data of the multi-store network.

[0013] Any two stores are combined to obtain multiple store combinations; the actual delivery route data of each store combination is obtained, and based on the actual delivery route data of all stores, an actual distance matrix, a delivery time matrix, and a delivery cost matrix are constructed respectively; the straight-line distance between each store combination is calculated based on the geographical coordinates of each store; based on the service radius and straight-line distance of each store combination, a corresponding accessibility identifier is set for each store combination, and a physical accessibility matrix is ​​constructed; based on the business hours of each store combination, the time period overlap is calculated, and a time period overlap matrix is ​​constructed; the actual distance matrix, delivery time matrix, delivery cost matrix, physical accessibility matrix, and time period overlap matrix are integrated to form the logistics connectivity data of the multi-store network.

[0014] Furthermore, methods for constructing store collaboration relationship diagrams include:

[0015] Based on the actual distance matrix, calculate the geographical proximity of each store combination; based on the service capacity set of each store, calculate the capability complementarity of each store combination; based on the delivery time matrix, calculate the timeliness matching degree of each store combination; based on the delivery cost matrix and the comprehensive capacity index of each store, calculate the cost-benefit ratio of each store combination; based on the preset collaboration weights, perform a weighted summation calculation on the geographical proximity, capability complementarity, timeliness matching degree and cost-benefit ratio of the same store combination to obtain the initial collaboration score of each store combination.

[0016] The physical reachability matrix and the time period overlap matrix are used as constraints to correct the initial collaboration score, resulting in a corrected collaboration score for each store combination. The corrected collaboration score for each store combination is then compared with a preset collaboration threshold, and the comparison results are used to determine whether there is a valid collaboration relationship between the two stores corresponding to each store combination.

[0017] Create a node set based on the unique identifier of each store; traverse all stores with valid collaborative relationships and create a set of directed edges based on the corrected collaborative score; use the comprehensive production capacity index and service capability set of each store as the static node attributes of the corresponding node; construct a store collaborative relationship graph based on the node set, the set of directed edges, and the static node attributes.

[0018] Furthermore, methods for generating dynamic store status diagrams include:

[0019] Normalize the order backlog data, resource usage data, and service response data for each store to obtain the order backlog feature vector, resource usage feature vector, and service response feature vector; obtain the current system time and calculate the time period location feature for each store in combination with the store's business hours; concatenate the order backlog feature vector, resource usage feature vector, and service response feature vector for each store with the time period location feature to form the node status feature vector for each store.

[0020] Traverse each node in the store collaboration graph and associate each node with the node state feature vector of the corresponding store; fuse the static node attributes of each node with the node state feature vector to form the complete node feature of each node; calculate the dynamic edge weight of each directed edge in the store collaboration graph based on the node state feature vector of each store; update the static node attributes of each node in the store collaboration graph to the corresponding complete node feature, and update the edge weight of each directed edge to the corresponding dynamic edge weight to form a dynamic store state graph.

[0021] Furthermore, methods for outputting the collaborative scheduling potential vector for each store include:

[0022] Based on the dimensions of the complete node features in the dynamic store status graph, the input layer dimension of the graph neural network model is determined; the network structure of the graph neural network model is constructed, which includes an input layer, multiple graph convolutional layers, activation layers, and an output layer; historical collaborative scheduling records are obtained, and the graph neural network model is pre-trained based on the historical collaborative scheduling records.

[0023] Obtain the complete node features of each node in the dynamic store state graph and input the complete node features as input vectors into the input layer of the graph neural network model; obtain the dynamic edge weights of each directed edge in the dynamic store state graph and construct an adjacency weight matrix; based on the adjacency weight matrix, perform message passing operations in each graph convolutional layer to perform neighborhood aggregation on the complete node features of each node and obtain the high-order aggregated feature vectors of each node.

[0024] The high-order aggregated feature vector of each node is input to the output layer and mapped to the preset output dimension through linear transformation to obtain the collaborative scheduling potential vector of each store; wherein, the collaborative scheduling potential vector includes a first potential component, a second potential component and a third potential component.

[0025] Furthermore, methods for modeling each store as a scheduling agent include:

[0026] For each store, a corresponding scheduling agent is created sequentially, and the attribute parameters of each scheduling agent are initialized according to the collaborative scheduling potential vector. Each scheduling agent includes an agent identifier, agent state, agent capabilities, and agent policy. The agent state is the collaborative scheduling potential vector and attribute parameters of the corresponding store. The agent capabilities are the set of service capabilities of the corresponding store.

[0027] The method for initializing attribute parameters based on the collaborative scheduling potential vector is as follows: Calculate the order acceptance willingness and order transfer willingness of each scheduling agent based on the first and second potential components; construct a collaborative neighbor list for each scheduling agent based on the set of directed edges in the dynamic store state graph; calculate the comprehensive scheduling index for each scheduling agent based on the third potential component and the complete node features; integrate the order acceptance willingness, order transfer willingness, collaborative neighbor list, and comprehensive scheduling index corresponding to each scheduling agent to obtain the attribute parameters for each scheduling agent.

[0028] Furthermore, the method for each scheduling agent to independently calculate its local reward function includes:

[0029] For each order to be assigned, all scheduling agents are traversed, and the capability matching degree, capacity adaptation degree, and timeliness feasibility between each scheduling agent and each order to be assigned are calculated in turn. Based on the capability matching degree, capacity adaptation degree, and timeliness feasibility, the local processing adaptation score between each scheduling agent and each order to be assigned is calculated in turn. Based on the order urgency and order complexity in the order attribute data, the order value coefficient of each order to be assigned is calculated. Based on the order acceptance willingness degree and comprehensive scheduling index of each scheduling agent, the local processing willingness score of each scheduling agent is calculated. Based on the local processing adaptation score, the order value coefficient, and the local processing willingness score, the local revenue function value of each scheduling agent for each order to be assigned is calculated.

[0030] Furthermore, the methods for each scheduling agent to independently calculate the cooperative reward function include:

[0031] Obtain the list of collaborating neighbors for the scheduling agent, and iterate through each collaborating neighbor in the list. For each collaborating neighbor, calculate the collaboration compatibility between the scheduling agent and the collaborating neighbor, the neighbor processing adaptation score for the collaborating neighbor in handling orders to be assigned, the collaboration efficiency coefficient between the scheduling agent and the collaborating neighbor, and the neighbor's willingness to accept orders score. Obtain the order transfer willingness of the scheduling agent and use the order transfer willingness as the transfer tendency coefficient. Based on the collaboration compatibility, neighbor processing adaptation score, collaboration efficiency coefficient, neighbor's willingness to accept orders score, and transfer tendency coefficient, calculate the single-neighbor collaboration benefit of the scheduling agent for each collaborating neighbor.

[0032] Traverse all cooperative neighbors, summarize the single-neighbor cooperative benefits of the scheduling agent for all cooperative neighbors, and construct a cooperative benefit vector; obtain the single-neighbor cooperative benefit with the largest value in the cooperative benefit vector and take it as the optimal cooperative benefit; mark the cooperative neighbor corresponding to the optimal cooperative benefit as the optimal transfer target; calculate the product of the optimal cooperative benefit and the order value coefficient to obtain the cooperative benefit function value of the scheduling agent for the order to be assigned.

[0033] Furthermore, methods for achieving Nash equilibrium solutions for order allocation through multiple rounds of game iteration include:

[0034] For each order to be assigned, an order allocation game model is constructed. The game participants in the order allocation game model are all scheduling agents. The policy space of each scheduling agent includes local processing policy and cooperative transfer policy. Based on the local payoff function value and cooperative payoff function value of each scheduling agent, the current policy selection of each scheduling agent is determined from the policy space.

[0035] Define the game iteration process in the order allocation game model as follows: traverse all scheduling agents, calculate the strategy response payoff for each scheduling agent under the corresponding current strategy choice based on the current strategy selection of the optimal transfer target for each scheduling agent; take the strategies in the strategy space corresponding to each scheduling agent that are not the current strategy choice as the evaluation strategy choice; for each scheduling agent, calculate the strategy response payoff under the corresponding evaluation strategy choice and mark it as the evaluation response payoff; compare the strategy response payoff of each scheduling agent with the evaluation response payoff, and determine whether to update the current strategy choice of the scheduling agent to the evaluation strategy choice based on the comparison result;

[0036] For each order allocation game model, the game iteration process is executed cyclically until the iteration termination condition is met; when the iteration termination condition is met, it is determined that the order allocation game has reached a Nash equilibrium solution; the iteration termination condition includes the convergence condition and the maximum iteration condition.

[0037] Furthermore, methods for generating a set of cooperative scheduling strategies include:

[0038] For each order to be assigned, record the current strategy choice of each scheduling agent in the corresponding order allocation game model under the Nash equilibrium solution, and take the scheduling agent with the largest local payoff function value as the recommended execution store for the corresponding order to be assigned; if the local payoff function value of all scheduling agents that choose the local processing strategy is zero, then mark the order source store of the order to be assigned as the recommended execution store.

[0039] For each order to be assigned, a corresponding order scheduling strategy is generated. The order scheduling strategy includes the recommended execution store, execution strategy type, transfer path, and expected revenue. The execution strategy type includes local execution and collaborative transfer. The order scheduling strategies of all orders to be assigned are aggregated to construct a collaborative scheduling strategy set.

[0040] The technical effects and advantages of this invention's dynamic scheduling and allocation method for print order resources in multi-store collaboration are as follows:

[0041] By acquiring topological and logistical connectivity data of multi-store networks, and comprehensively considering multi-dimensional collaborative evaluation indicators such as geographical proximity, capability complementarity, timeliness matching, and cost-effectiveness among stores, and combining constraints such as physical accessibility and time period overlap, a store collaboration relationship diagram that accurately reflects the feasibility and benefits of collaborative scheduling between stores is constructed. Compared to existing technologies that treat each store as an independent service node, this approach can effectively mine and model the geographical connections, logistical connectivity, and resource complementarity among stores, providing a solid data foundation and decision-making basis for cross-store collaborative scheduling, thereby achieving accurate modeling and quantitative representation of store collaboration relationships.

[0042] By collecting real-time order backlog data, resource usage data, and service response data from each store, and encoding these data into node status feature vectors, which are then embedded into the store collaboration graph, a dynamic store status graph reflecting the real-time operational status of the stores is formed. Simultaneously, edge weights are dynamically updated based on differences in capacity load and order acceptance capacity coefficients between stores, allowing the collaboration graph to adjust in real-time according to changes in store status. Compared to the lack of flexibility in existing static allocation methods, this approach can promptly detect dynamic changes in store status. When a store experiences order backlog or equipment failure, it can quickly respond and dynamically transfer the load, thus achieving real-time perception and dynamic updating of store status.

[0043] By inputting a dynamic store state graph into a pre-trained graph neural network model, the node state feature vectors of each store are aggregated using a message passing mechanism to output a collaborative scheduling potential vector that integrates multi-hop neighbor node information. This collaborative scheduling potential vector can quantitatively characterize the comprehensive ability of a store to participate in collaborative scheduling under the current network state from multiple dimensions, such as order receiving potential, order transfer potential, and resource sharing potential. Compared with existing methods that make scheduling decisions based on only a single indicator, this method can deeply explore the structural position and neighborhood state of stores in the collaborative network, providing a more comprehensive and accurate capability assessment for subsequent intelligent scheduling decisions.

[0044] Each store is modeled as a scheduling agent with independent decision-making capabilities. Each scheduling agent independently calculates its local and collaborative revenue functions based on order attribute data, and reaches a Nash equilibrium solution for order allocation through multiple rounds of game iteration. The Nash equilibrium solution ensures that, assuming all scheduling agents choose the optimal response strategy, no scheduling agent can improve its own revenue by unilaterally changing its strategy, thus achieving globally stable optimal allocation under a distributed decision-making architecture. Compared with existing centralized scheduling methods, which have the risk of single-point bottlenecks and large response delays, the distributed game decision-making mechanism allows each store to perform decision calculations in parallel, improving the system's scalability and real-time response capabilities.

[0045] Based on the game equilibrium results, a set of collaborative scheduling strategies is generated, including recommended execution stores, execution strategy types, transfer paths, and expected returns. Furthermore, a cross-store order routing table sorted by order urgency is generated. The order allocation results are synchronized to each store's terminal system via the enterprise resource management system's message push module, achieving a complete closed loop from strategy generation to execution. Compared to existing methods that struggle to quickly distribute scheduling results, this approach provides a complete order routing and synchronization mechanism, ensuring that scheduling strategies are promptly and accurately communicated to each execution store. This effectively improves service response efficiency and customer satisfaction, thereby achieving the systematic generation and efficient execution of order scheduling strategies. Attached Figure Description

[0046] Figure 1 This is a flowchart of the dynamic scheduling and allocation method for print order resources for multi-store collaboration according to Embodiment 1 of the present invention. Detailed Implementation

[0047] 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.

[0048] Example 1

[0049] Please see Figure 1 As shown in this embodiment, the method for dynamic scheduling and allocation of printing order resources for multi-store collaboration includes:

[0050] Step S1: Obtain the topology data and logistics connectivity data of the multi-store network, and construct a store collaboration relationship diagram based on the topology data and logistics connectivity data.

[0051] Methods for obtaining topology data of multi-store networks include:

[0052] The store management module of the enterprise resource management system obtains the basic information of each store in the multi-store network. The basic information of the store includes the store's unique identifier, store's geographical coordinates, store's business hours, and store's service radius. Among them, the store's unique identifier is used to uniquely identify and index each store; the store's geographical coordinates include the longitude and latitude values ​​of the store's location; the store's business hours include the store's daily start and end times; and the store's service radius is the maximum distance range within which the store can provide door-to-door delivery services.

[0053] The equipment configuration information for each store is obtained through the equipment management module of the enterprise resource management system. The equipment configuration information includes a list of printing equipment and equipment specifications. The list of printing equipment records the equipment types of all printing equipment configured in the store, such as black and white laser printers, color laser printers, inkjet printers, large format printers, and special material printers. The equipment specifications include the single-page printing time, supported paper size set, supported material type set, and maximum number of pages printed in a single print for each printing device.

[0054] Based on the equipment configuration information of each store, the comprehensive capacity index of each store is calculated. Specifically, each printing device in the store's printing equipment list is traversed, and the ratio of unit time to the corresponding single-page printing time of each printing device is calculated to obtain the number of pages produced per unit time for each printing device. A corresponding capacity weight is set for each type of equipment, and the capacity weight is pre-set by those skilled in the art based on the service value of each type of equipment. The number of pages produced per unit time for all printing devices in the same store is weighted and summed based on the capacity weight to obtain the weighted capacity value of each store. The start time and end time of the store's business hours are obtained, and the difference between the end time and the start time is calculated to obtain the daily business hours of each store. The product of the weighted capacity value and the daily business hours is calculated to obtain the comprehensive capacity index of each store. The comprehensive capacity index is used to reflect the maximum theoretical order processing capacity of the store in a single working day. It should be noted that the units (such as seconds, minutes, hours, etc.) of unit time, single-page printing time, and daily business hours are all the same.

[0055] Based on the equipment configuration information of each store, the service capability set of each store is calculated. Specifically, each printing device in the store's printing equipment list is traversed to obtain the device type, supported paper size set, and supported material type set for each printing device. The device types of all printing devices in the same store are merged and deduplicated to obtain the store's available device type set. The supported paper size sets of all printing devices in the same store are merged and deduplicated to obtain the store's available paper size set. The supported material type sets of all printing devices in the same store are merged and deduplicated to obtain the store's available material type set. The available device type set, available paper size set, and available material type set are integrated to form the service capability set of each store. The service capability set is used to determine whether a store has the ability to process a specific order.

[0056] The comprehensive production capacity indicators and service capabilities are integrated to form the store characteristic data of each store; the store characteristic data of all stores are summarized to obtain the topology data of the multi-store network.

[0057] Methods for obtaining logistics connectivity data for multi-store networks include:

[0058] Any two stores are combined to obtain multiple store combinations. The actual delivery route data for each store combination is obtained through the application programming interface (API) of a third-party logistics service platform. This data includes the actual delivery distance, estimated delivery time, and basic delivery cost. The actual delivery distance is the actual transportation distance after considering the road network; the estimated delivery time is the delivery time predicted by the logistics service platform based on historical delivery data and real-time traffic conditions; and the basic delivery cost is the standard charge for this delivery route. Based on the actual delivery route data for all stores, an actual distance matrix, a delivery time matrix, and a delivery cost matrix are constructed.

[0059] Based on the geographical coordinates of each store, the straight-line distance between each store combination is calculated using the Haversine formula. The Haversine formula is a well-known technique in this field, and its specific process will not be elaborated upon here. The physical reachability of each store combination is determined based on its service radius and straight-line distance, and a corresponding reachability flag is set. Specifically, any two stores in a store combination are marked as the source store and the target store, respectively. The service radius of the source store is obtained, and the straight-line distance is compared with the service radius. If the straight-line distance between stores is less than or equal to the service radius, the source store is determined to be physically reachable from the target store, and the corresponding reachability flag is set to 1. If the straight-line distance between stores is greater than the service radius, the source store is determined to be physically unreachable from the target store, and the corresponding reachability flag is set to 0. A physical reachability matrix is ​​constructed based on all reachability flags; this physical reachability matrix is ​​an asymmetric matrix.

[0060] Based on the operating hours of each store, the time period overlap for each store combination is calculated. Specifically, the start and end times of the operating hours of the source and target stores are obtained. The larger of the start and end times of the source and target stores is taken as the overlap start time. The smaller of the end and end times of the source and target stores is taken as the overlap end time. If the overlap end time is greater than the overlap start time, the difference between the overlap end time and the overlap start time is calculated to obtain the overlap duration. If the overlap end time is less than or equal to the overlap start time, the overlap duration is set to zero. The average daily operating hours of the source and target stores are calculated to obtain the average operating hours. The ratio of the overlap duration to the average operating hours is calculated to obtain the time period overlap. The time period overlap is used to evaluate the degree of time window matching when coordinating scheduling between two stores. Based on all time period overlaps, a time period overlap matrix is ​​constructed.

[0061] The actual distance matrix, delivery time matrix, delivery cost matrix, physical reach matrix, and time period overlap matrix are integrated to form the logistics connectivity data of the multi-store network.

[0062] Methods for constructing store collaboration graphs based on topological data and logistics connectivity data include:

[0063] Based on the actual distance matrix, calculate the geographical proximity of each store combination; specifically, obtain the actual delivery distance with the largest value in the actual distance matrix and use it as the maximum delivery distance; calculate the ratio of the actual delivery distance between the source store and the target store to the maximum delivery distance, and subtract the calculated result from one to obtain the geographical proximity; where, the larger the geographical proximity, the closer the two stores are geographically, and the more suitable they are for collaborative scheduling.

[0064] Based on the service capability set of each store, the capability complementarity of each store combination is calculated. Specifically, the available equipment type sets of the source store and the target store are obtained, and the number of elements in the union and intersection of the two available equipment type sets are calculated. The difference between the number of elements in the union and the number of elements in the intersection is calculated and then divided by the number of elements in the union to obtain the equipment complementarity coefficient. The available paper specifications and available material types sets of the source store and the target store are obtained, and the paper complementarity coefficient and material complementarity coefficient are calculated using the same method as for calculating the equipment complementarity coefficient. Corresponding complementarity weights are set for the equipment complementarity coefficient, paper complementarity coefficient, and material complementarity coefficient. The complementarity weights are pre-set by those skilled in the art based on the importance of each complementarity coefficient. The capability complementarity is calculated by weighted summation of the equipment complementarity coefficient, paper complementarity coefficient, and material complementarity coefficient based on the complementarity weights to obtain the capability complementarity. The capability complementarity is used to measure the degree of difference in service capabilities between the two stores. The higher the capability complementarity, the better the two stores can compensate for each other's capability shortcomings.

[0065] Based on the delivery time matrix, the timeliness matching degree of each store combination is calculated. Specifically, a timeliness constraint threshold is preset, which represents the maximum delivery time that can be tolerated by the coordinated scheduling between stores. The estimated delivery time between the source store and the target store in the delivery time matrix is ​​obtained. If the estimated delivery time is less than or equal to the timeliness constraint threshold, the difference between the timeliness constraint threshold and the estimated delivery time is calculated and then divided by the timeliness constraint threshold to obtain the timeliness matching degree. If the estimated delivery time is greater than the timeliness constraint threshold, the timeliness matching degree is set to zero. The timeliness constraint threshold is preset by those skilled in the art based on actual business needs.

[0066] Based on the delivery cost matrix and the comprehensive capacity index of each store, the cost-benefit ratio of each store combination is calculated. Specifically, the basic delivery cost between the source store and the target store in the delivery cost matrix is ​​obtained; the comprehensive capacity index of the target store is obtained, and the ratio of the basic delivery cost to the comprehensive capacity index is calculated to obtain the unit capacity delivery cost; the ratio of all basic delivery costs in the delivery cost matrix to the corresponding comprehensive capacity index of the target store is calculated, and the maximum value is obtained to obtain the maximum unit capacity delivery cost; the ratio of the unit capacity delivery cost to the maximum unit capacity delivery cost is calculated, and the result is subtracted to obtain the cost-benefit ratio; the cost-benefit ratio is used to evaluate the economic rationality of transferring orders to the target store.

[0067] Geographic proximity, capability complementarity, timeliness matching, and cost-effectiveness ratio are collectively referred to as collaborative evaluation indicators. A corresponding collaborative weight is set for each collaborative evaluation indicator. The collaborative weight is preset by those skilled in the art based on the actual business scenario. Based on the collaborative weight, the geographic proximity, capability complementarity, timeliness matching, and cost-effectiveness ratio of the same store combination are weighted and summed to obtain the initial collaborative score of each store combination.

[0068] Using the physical reachability matrix and time period overlap matrix as constraints, the initial collaboration score is corrected to obtain the corrected collaboration score for each store combination. Specifically, the reachability identifier of the source store to the target store in the physical reachability matrix is ​​obtained. If the reachability identifier is 0, the corresponding initial collaboration score is set to zero, indicating that the two stores do not have the basic conditions for collaborative scheduling. If the reachability identifier is 1, the time period overlap between the source store and the target store in the time period overlap matrix is ​​obtained, and the product of the initial collaboration score and the time period overlap is calculated to obtain the corrected collaboration score. The corrected collaboration score is used to comprehensively reflect the feasibility and benefits of collaborative scheduling between the two stores.

[0069] The corrected collaboration score for each store combination is compared with a preset collaboration threshold, which is set by a person skilled in the art based on actual business needs. If the corrected collaboration score is greater than or equal to the collaboration threshold, it is determined that there is a valid collaboration relationship between the two stores. If the corrected collaboration score is less than the collaboration threshold, it is determined that there is no valid collaboration relationship between the two stores.

[0070] Create a node set based on the unique identifier of each store; each node in the node set corresponds to a store, and the identifier of the node is the unique identifier of the corresponding store. Traverse all stores with valid collaborative relationships and create a set of directed edges based on the adjusted collaborative score; the starting point of each directed edge in the set of directed edges is the node corresponding to the source store, the ending point of the directed edge is the node corresponding to the target store, and the edge weight of the directed edge is the adjusted collaborative score of the corresponding store combination. Use the comprehensive capacity index and service capacity set of each store as the static node attributes of the corresponding node; the static node attributes are used to represent the inherent service capacity and theoretical capacity limit of the store. Construct a store collaborative relationship graph based on the node set, the set of directed edges, and the static node attributes.

[0071] Step S2: Collect order backlog data, resource usage data and service response data of each store in real time, and encode them into node status feature vectors of each store. Embed the node status feature vectors into the store collaboration relationship graph to form a dynamic store status graph.

[0072] Methods for collecting order backlog data from various stores in real time include:

[0073] Through the order management module of the enterprise resource management system, the pending order queue of each store can be obtained in real time. The pending order queue contains all order records that have been received but have not yet been printed. Each order record includes the order receipt time, order deadline, number of pages to be printed, order paper specifications, order material type, and order equipment requirements.

[0074] The system counts the number of order records in the pending order queue for each store to obtain the backlog of orders for each store; it sums the number of printed pages for all order records in the same store to obtain the total backlog of pages for each store; it obtains the current system time (i.e., the current actual time recorded by the system), calculates the difference between the order deadline and the current system time for each order record to obtain the remaining delivery time for each order; it presets an emergency time threshold, marking orders with a remaining delivery time less than the emergency time threshold as emergency orders, and not marking orders with a remaining delivery time greater than or equal to the emergency time threshold; it counts the number of emergency orders for each store to obtain the number of emergency orders for each store; the emergency time threshold is preset by those skilled in the art based on actual business needs.

[0075] Calculate the ratio of the total backlog of pages to the overall capacity index for each store to obtain the capacity load rate of each store; calculate the difference between the current system time and the order receipt time of each order record to obtain the waiting time of each order; calculate the average waiting time of all orders in the same store to obtain the average waiting time of each store.

[0076] The backlog of orders, total backlog pages, number of urgent orders, capacity utilization rate and average waiting time for each store are integrated to form the order backlog data for each store.

[0077] Methods for collecting real-time resource usage data from each store include:

[0078] The equipment management module of the Enterprise Resource Management System (ERP) acquires the real-time equipment status identifiers for each store. These identifiers mark the operational status of each printer, including idle, working, under maintenance, and faulty. The system counts the number of printers in each store with status identifiers of idle, working, under maintenance, or faulty, yielding the numbers of idle, working, and unavailable printers. Idle printers are those that are currently idle, working printers are those that are in operation, and unavailable printers are those that are under maintenance or faulty. The total number of printers in each store is calculated. The ratio of working printers to total printers in each store is calculated to obtain the equipment utilization rate. The ratio of unavailable printers to total printers in each store is calculated to obtain the equipment failure rate. Finally, the ratio of idle printers to total printers in each store is calculated to obtain the equipment idle rate.

[0079] Through the consumables management module of the enterprise resource management system, the consumables status information of each store is obtained in real time. The consumables status information includes the remaining toner percentage and the paper inventory quantity. The average remaining toner percentage of all printing equipment in each store is calculated to obtain the average toner balance of each store. The ratio of the paper inventory quantity to the total backlog of pages is calculated to obtain the paper guarantee coefficient of each store.

[0080] Through the personnel management module of the enterprise resource management system, the on-duty personnel information of each store can be obtained in real time. The on-duty personnel information includes the skill level of all employees on duty. The skill level refers to the result of the enterprise's quantitative representation of the employee's skill level based on the employee's job ability, operational proficiency, business qualifications and other dimensions. Different skill weights are set for different skill levels, and the skill levels of all employees on duty in the same store are weighted and summed based on the skill weights to obtain the comprehensive human resource index of each store.

[0081] The resource utilization data for each store is compiled by integrating the equipment utilization rate, equipment failure rate, equipment idle rate, average toner balance, paper availability coefficient, and comprehensive manpower index.

[0082] Methods for collecting real-time service response data from various stores include:

[0083] The order management module of the enterprise resource management system retrieves the completed order records for each store within a preset statistical time window. The completed order records include the order receipt time, order completion time, order deadline, number of pages completed, and customer rating. The statistical time window is preset by those skilled in the art based on actual business needs.

[0084] Calculate the difference between the order completion time and the order receipt time for each completed order record to obtain the actual processing time; calculate the mean and standard deviation of the actual processing time for all completed order records for the same store to obtain the average processing time and processing time fluctuation for each store; mark orders with completion times less than or equal to the order deadline as on-time orders and count the number of on-time orders for each store; count the number of completed order records for each store to obtain the total number of historical orders; calculate the ratio of the number of on-time orders to the total number of historical orders for each store to obtain the on-time delivery rate for each store; calculate the mean of customer ratings for all completed order records for the same store to obtain the average customer rating for each store.

[0085] The average processing time, processing time fluctuation, on-time delivery rate, and average customer rating for each store are integrated to form the service response data for each store.

[0086] Methods for encoding node state feature vectors include:

[0087] For each type of data in the order backlog data for each store, normalization is performed separately, and the data are concatenated to form the order backlog feature sub-vector for each store; for each type of data in the resource usage data for each store, normalization is performed separately, and the data are concatenated to form the resource usage feature sub-vector for each store; for each type of data in the service response data for each store, normalization is performed separately, and the data are concatenated to form the service response feature sub-vector for each store.

[0088] Based on the store's operating hours and the current system time, calculate the time period location feature for each store. Specifically, calculate the difference between the current system time and the start time of business to obtain the operating time; calculate the ratio of the operating time to the daily operating time to obtain the business progress ratio, which is used as the time period location feature; concatenate the order backlog feature sub-vector, resource usage feature sub-vector, and service response feature sub-vector of each store with the time period location feature to form the node status feature vector of each store.

[0089] Methods for generating dynamic store status diagrams include:

[0090] The process iterates through each node in the store collaboration graph, associating each node with the node state feature vector of its corresponding store. It then fuses the static node attributes and node state feature vectors of each node to form the complete node features. Specifically, it obtains the comprehensive capacity index from the static node attributes and normalizes it to obtain the standard capacity index; it obtains the service capability set from the static node attributes and encodes it as a service capability feature vector; it concatenates the standard capacity index with the service capability feature vector to obtain the static attribute feature vector; and it concatenates the node state feature vector with the static attribute feature vector to form the complete node feature. Features; the encoding method for the service capability feature vector is as follows: A global capability index table containing all equipment types, paper specifications, and material types is pre-constructed; the service capability set of each store is traversed, and if a capability in the global capability index table exists in the service capability set, the feature value at the corresponding position is set to 1; otherwise, it is set to 0, thus obtaining the service capability feature vector. For example, the global capability index table includes five capabilities: color printer, black and white printer, A4 paper, A3 paper, and coated paper; the service capability set of store A is {black and white printer, A4 paper, coated paper}, then the service capability feature vector of store A is: ;

[0091] Based on the node state feature vector of each store, the dynamic edge weight of each directed edge in the store collaboration graph is calculated. Specifically, the node corresponding to the starting point of the directed edge is marked as the starting node, and the node corresponding to the ending point of the directed edge is marked as the ending node. The difference between the capacity load rate of the starting node and the capacity load rate of the ending node is calculated to obtain the load difference. The product of the equipment idle rate and the on-time delivery rate of the ending node is calculated to obtain the order acceptance capacity coefficient. The corrected collaboration score corresponding to the directed edge is used as the static edge weight. The product of the load difference, the order acceptance capacity coefficient, and the static edge weight is calculated to obtain the dynamic edge weight. If the dynamic edge weight is less than zero, it is set to zero.

[0092] The static node attributes of each node in the store collaboration relationship graph are updated to the corresponding complete node features, and the edge weight of each directed edge is updated to the corresponding dynamic edge weight, forming a dynamic store state graph.

[0093] Step S3: Input the dynamic store state graph into the pre-trained graph neural network model, perform neighborhood aggregation on the node state feature vectors of each store through the message passing mechanism, output the collaborative scheduling potential vector of each store, and model each store as a scheduling agent based on the collaborative scheduling potential vector.

[0094] Methods for constructing pre-trained graph neural network models include:

[0095] Based on the dimension of the complete node features in the dynamic store status graph, the input layer dimension of the graph neural network model is determined. Specifically, the complete node features of any store are obtained, the number of elements in the complete node features is counted to obtain the node feature dimension, and the node feature dimension is used as the input layer dimension of the graph neural network model.

[0096] A graph neural network model is constructed, comprising an input layer, multiple graph convolutional layers, activation layers, and an output layer. The graph convolutional layers are used to implement message passing and neighborhood aggregation operations. The activation layers employ the ReLU activation function to introduce nonlinear transformations. The output layer generates a cooperative scheduling potential vector. The number of graph convolutional layers and the hidden dimension of each layer are preset, both by those skilled in the art based on actual business needs. The output dimension of the output layer is also preset, determined by those skilled in the art based on the required information richness to be represented by the cooperative scheduling potential vector. The output dimension of the output layer determines the dimension of the cooperative scheduling potential vector.

[0097] Historical collaborative scheduling records are obtained, and a graph neural network model is pre-trained based on these records. Specifically, the historical collaborative scheduling records contain complete node features, dynamic edge weights, order transfer records, and collaborative effect scores for each store within a historical period. Order transfer records include the source store, target store, and the number of transferred orders. The collaborative effect score is a quantitative value of the collaborative scheduling effect calculated based on the actual processing time of transferred orders, on-time delivery rate, and customer ratings. Using the complete node features and dynamic edge weights of each store within the historical period as training input, the graph neural network model outputs a collaborative scheduling potential vector for each store. For each order transfer record, the collaborative scheduling potential vectors of the source store and target store are obtained, and the dot product of the two collaborative scheduling potential vectors is calculated to obtain the predicted collaborative score. The predicted collaborative score is compared with the corresponding collaborative effect score, and the loss value is calculated using the mean squared error loss function. The loss value is minimized using the backpropagation algorithm to optimize the parameter weights of the graph neural network model, resulting in a pre-trained graph neural network model.

[0098] It should be noted that both the backpropagation algorithm and the mean squared error loss function are well-known techniques in this field, and the specific process will not be elaborated on here.

[0099] Methods for neighborhood aggregation of node state feature vectors for each store include:

[0100] Obtain the complete node features of each node in the dynamic store state graph, and use these complete node features as input vectors to the input layer of the graph neural network model; obtain the dynamic edge weights of each directed edge in the dynamic store state graph, and construct an adjacency weight matrix; where the i-th node in the adjacency weight matrix... Line number The element of the column is the first The node points to the first The dynamic edge weights corresponding to the directed edges of each node are zero if there is no directed edge between two nodes.

[0101] In each graph convolutional layer, message passing is performed to aggregate the complete node features of each node into a neighborhood, resulting in a high-order aggregated feature vector for each node. Specifically, each node in the dynamic store state graph is traversed, and each node is treated as the current node. All neighboring nodes of the current node are obtained. A neighboring node is a node connected to the current node by a directed edge, including nodes pointing to the current node and nodes pointed to by the current node. The complete node features of each neighboring node are obtained, and the dynamic edge weights between the current node and each neighboring node are obtained based on the adjacency weight matrix. For each neighboring node, the product of the complete node features and the corresponding dynamic edge weights is calculated to obtain the weighted neighbor features. The weighted neighbor features of the current node are then calculated. The algorithm calculates and obtains the aggregated neighbor features of the current node. It then concatenates the node feature vector of the current node with the aggregated neighbor features to obtain a concatenated feature vector. This concatenated feature vector is input to the linear transformation layer of the graph convolutional layer, where it is multiplied by matrix multiplication and added to the bias term to obtain the transformed feature vector. The transformed feature vector is then input to the activation layer, where it undergoes a non-linear transformation using the ReLU activation function to obtain the output feature vector of the current node in the current graph convolutional layer. This output feature vector is used as the input feature vector of the current node in the next graph convolutional layer. After passing through all graph convolutional layers, a higher-order aggregated feature vector is obtained for each node. This higher-order aggregated feature vector incorporates information from multi-hop neighbor nodes, reflecting the structural position and neighborhood state of the store within the collaborative network.

[0102] Methods for outputting the collaborative scheduling potential vector of each store include:

[0103] The high-order aggregated feature vector of each node is input to the output layer and mapped to a preset output dimension through linear transformation to obtain the collaborative scheduling potential vector of each store. The collaborative scheduling potential vector is a multi-dimensional feature representation obtained by deep aggregation of the store's current state and its neighborhood collaborative relationships through a graph neural network. It is used to quantify the store's comprehensive ability to participate in collaborative scheduling under the current network state. The collaborative scheduling potential vector contains multiple potential components, each corresponding to a different dimension of collaborative capability representation. Specifically, the first potential component in the collaborative scheduling potential vector represents the store's order receiving potential, reflecting the store's ability to receive orders transferred from other stores; the second potential component represents the store's order transfer potential, reflecting the store's tendency to transfer orders to other stores; and the third potential component represents the store's resource sharing potential, reflecting the store's ability to participate in cross-store resource coordination.

[0104] Methods for modeling each store as a scheduling agent include:

[0105] For each store, a corresponding scheduling agent is created sequentially, and the attribute parameters of each scheduling agent are initialized according to the collaborative scheduling potential vector. Specifically, each scheduling agent includes an agent identifier, agent state, agent capabilities, and agent policy. The agent identifier is the unique identifier of the corresponding store; the agent state is the collaborative scheduling potential vector and attribute parameters of the corresponding store; the agent capabilities are the set of service capabilities of the corresponding store; and the agent policy is used to store the decision rules of the scheduling agent later. It should be noted that each scheduling agent has independent decision-making capabilities and can make autonomous decisions and engage in game-theoretic interactions based on order attribute data. The method for initializing the attribute parameters according to the collaborative scheduling potential vector is as follows:

[0106] Based on the collaborative scheduling potential vector, calculate the order acceptance willingness and order transfer willingness of each scheduling agent; specifically, obtain the first potential component in the collaborative scheduling potential vector and use it as the order acceptance willingness of the scheduling agent; obtain the second potential component in the collaborative scheduling potential vector and use it as the order transfer willingness of the scheduling agent; wherein, the order acceptance willingness is used to evaluate the scheduling agent's enthusiasm for accepting transferred orders, and the order transfer willingness is used to evaluate the scheduling agent's enthusiasm for transferring local orders.

[0107] Based on the set of directed edges in the dynamic store state graph, a list of cooperative neighbors for each scheduling agent is constructed. Specifically, the set of directed edges in the dynamic store state graph is traversed to obtain all directed edges with the current store's corresponding node as the starting or ending point. The other end node of the directed edge is marked as a cooperative neighbor, and the corresponding store's unique identifier is added to the list of cooperative neighbors. At the same time, the dynamic edge weight of each directed edge is recorded and associated with the corresponding cooperative neighbor to obtain a list of cooperative neighbors with edge weights. The list of cooperative neighbors is used to determine the scope of game interaction between scheduling agents.

[0108] Based on the collaborative scheduling potential vector and the characteristics of the complete node, the comprehensive scheduling index of each scheduling agent is calculated. Specifically, the capacity load rate in the characteristics of the complete node is obtained, and the remaining capacity ratio is obtained by subtracting the capacity load rate from the remaining capacity. The third potential component in the collaborative scheduling potential vector is obtained and used as the resource sharing potential. The product of the remaining capacity ratio and the resource sharing potential is calculated to obtain the comprehensive scheduling index of each scheduling agent. The comprehensive scheduling index is used to evaluate the comprehensive priority of the scheduling agent in participating in collaborative scheduling.

[0109] The order acceptance willingness, order transfer willingness, collaborative neighbor list, and comprehensive scheduling index of each scheduling agent are integrated to obtain the attribute parameters of each scheduling agent.

[0110] Step S4: Obtain the order attribute data of each order to be assigned. Each scheduling agent independently calculates the local revenue function and the collaborative revenue function based on the order attribute data, and reaches the Nash equilibrium solution for order allocation through multiple rounds of game iteration, generating a set of collaborative scheduling strategies.

[0111] Methods for obtaining order attribute data for each order to be assigned include:

[0112] From the pending order queues of each store, filter out the order records that have not yet been assigned to a store for execution and mark them as pending orders; each pending order includes a unique order identifier, order receipt time, order deadline, number of pages to be printed, order paper specifications, order material type, order equipment requirements, and the order originating store; among which, the order originating store is the store that initially received the order;

[0113] Based on the order deadline and the current system time, calculate the remaining delivery time for each order to be assigned; based on the remaining delivery time and a preset emergency time threshold, calculate the order urgency for each order to be assigned; specifically, if the remaining delivery time is less than or equal to zero, the order urgency is set to the maximum value of 1; if the remaining delivery time is greater than zero and less than the emergency time threshold, calculate the difference between the emergency time threshold and the remaining delivery time, and then divide it by the emergency time threshold to obtain the order urgency; if the remaining delivery time is greater than or equal to the emergency time threshold, the order urgency is set to zero.

[0114] Based on the number of pages printed, paper specifications, material type, and equipment requirements, the order complexity of each order to be assigned is calculated. Specifically, a specification complexity coefficient is set for different paper specifications, a material complexity coefficient is set for different material types, and an equipment complexity coefficient is set for different equipment requirements. The specification complexity coefficient, material complexity coefficient, and equipment complexity coefficient for each order to be assigned are obtained. The product of the specification complexity coefficient, material complexity coefficient, and equipment complexity coefficient is calculated to obtain the comprehensive complexity coefficient. A logarithmic transformation is performed on the number of pages printed to obtain the page number complexity factor. The product of the comprehensive complexity coefficient and the page number complexity factor is calculated to obtain the order complexity. Each complexity coefficient is preset by those skilled in the art based on actual business needs.

[0115] The unique identifier of each pending order, order receipt time, order deadline, number of pages printed, paper specifications, material type, equipment requirements, store of origin, urgency, and complexity are integrated to form the order attribute data for each pending order.

[0116] Methods for each scheduling agent to independently calculate its local reward function include:

[0117] For each order to be assigned, all scheduling agents are traversed, and the capability matching degree, capacity adaptation degree, and timeliness feasibility between each scheduling agent and each order to be assigned are calculated in turn. Based on the capability matching degree, capacity adaptation degree, and timeliness feasibility, the local processing adaptation score between each scheduling agent and each order to be assigned is calculated in turn. Specifically:

[0118] The system acquires the capabilities of the scheduling agent, determines whether the paper specifications of the order to be assigned exist in the available paper specifications set of the service capability set, and sets the paper matching flag to 1 if it exists, otherwise to 0; determines whether the material type of the order to be assigned exists in the available material types set of the service capability set, and sets the material matching flag to 1 if it exists, otherwise to 0; determines whether the equipment requirements of the order to be assigned exist in the available equipment types set of the service capability set, and sets the equipment matching flag to 1 if it exists, otherwise to 0; and calculates the product of the paper matching flag, material matching flag, and equipment matching flag to obtain the capability matching degree. If the capability matching degree is 0, it means that the scheduling agent does not have the capability to process the order to be assigned.

[0119] Obtain the comprehensive capacity index and capacity load rate of the store corresponding to the scheduling agent; calculate and subtract the capacity load rate to obtain the remaining capacity ratio; obtain the number of printed pages of the orders to be assigned, calculate the ratio of the number of printed pages of the orders to the comprehensive capacity index to obtain the order capacity ratio; if the order capacity ratio is less than or equal to the remaining capacity ratio, calculate the difference between the remaining capacity ratio and the order capacity ratio, and then divide it by the remaining capacity ratio to obtain the capacity fit; if the order capacity ratio is greater than the remaining capacity ratio, set the capacity fit to zero.

[0120] The system obtains the average processing time of the corresponding store for the scheduling agent and the number of completed pages for all completed order records. It then calculates the average number of completed pages for all completed order records to obtain the historical average number of pages. The system calculates the ratio of the number of printed pages for the pending orders to the historical average number of pages, multiplies this ratio by the average processing time to obtain the estimated processing time, and compares this estimated processing time with the remaining delivery time for the pending orders. If the estimated processing time is less than or equal to the remaining delivery time, the system calculates the difference between the remaining delivery time and the estimated processing time, divides this difference by the remaining delivery time, and obtains the timeliness feasibility. If the estimated processing time is greater than the remaining delivery time, the timeliness feasibility is set to zero.

[0121] Corresponding adaptation weights are set for capability matching degree, capacity adaptability degree, and timeliness feasibility, and the local processing adaptation score is obtained by weighted summation of capability matching degree, capacity adaptability degree, and timeliness feasibility based on the adaptation weights; wherein, each adaptation weight is preset by those skilled in the art according to actual business needs.

[0122] Based on the urgency and complexity of the orders to be assigned, the order value coefficient of each order is calculated. Specifically, corresponding value weights are set for the urgency and complexity of the orders, and these value weights are preset by those skilled in the art based on actual business needs. The order value coefficient is obtained by weighted summation of the urgency and complexity of the orders based on the value weights.

[0123] Based on the order acceptance willingness and comprehensive scheduling index of the scheduling agent, calculate the local processing willingness score for each scheduling agent; specifically, obtain the order acceptance willingness and comprehensive scheduling index from the corresponding attribute parameters of the scheduling agent, and calculate the product of the order acceptance willingness and comprehensive scheduling index to obtain the local processing willingness score.

[0124] Based on the local processing adaptation score, order value coefficient, and local processing willingness score, the local revenue function value for each scheduling agent for each order to be assigned is calculated. Specifically, all scheduling agents and orders to be assigned are combined and traversed to obtain multiple matching combinations. Each matching combination includes one scheduling agent and one order to be assigned, and each matching combination is different. For each matching combination, the product of the corresponding local processing adaptation score, order value coefficient, and local processing willingness score is calculated to obtain the local revenue function value for the corresponding scheduling agent for the corresponding order to be assigned in each matching combination. The local revenue function value is used to quantitatively evaluate the overall revenue of the scheduling agent in processing the order to be assigned locally.

[0125] Methods for each scheduling agent to independently calculate the cooperative benefit function include:

[0126] Obtain the list of cooperative neighbors for the scheduling agent, and iterate through each cooperative neighbor in the list. For each cooperative neighbor, calculate the cooperative compatibility between the scheduling agent and the cooperative neighbor. Specifically, obtain the cooperative scheduling potential vectors of the scheduling agent and the cooperative neighbor, calculate the cosine similarity between the two cooperative scheduling potential vectors, and obtain the cooperative compatibility. The cooperative compatibility is used to evaluate the degree of matching between the two scheduling agents in cooperative scheduling. The method for calculating the cosine similarity is a well-known technique in this field, and the specific process will not be elaborated here.

[0127] For each collaborating neighbor, the same method as calculating the local processing adaptation score is used to calculate the neighbor processing adaptation score for the collaborating neighbor to process the order to be assigned. The difference is that when calculating the timeliness feasibility of the collaborating neighbor, the delivery time of the order transfer needs to be considered separately. Specifically, the estimated delivery time between the store corresponding to the scheduling agent and the store corresponding to the collaborating neighbor is obtained, the estimated delivery time is deducted from the remaining delivery time, and then the timeliness feasibility is calculated.

[0128] For each collaborating neighbor, calculate the collaboration efficiency coefficient between the scheduling agent and the collaborating neighbor; specifically, obtain the collaboration edge weights between the scheduling agent and the collaborating neighbor based on the dynamic edge weights recorded in the collaborating neighbor list; obtain the basic delivery cost between the store corresponding to the scheduling agent and the store corresponding to the collaborating neighbor based on the delivery cost matrix; calculate the reciprocal of the basic delivery cost and normalize it to obtain the delivery cost coefficient; calculate the product of the collaboration edge weights and the delivery cost coefficient to obtain the collaboration efficiency coefficient.

[0129] For each collaborative neighbor, obtain the corresponding order acceptance willingness level and comprehensive scheduling index, and calculate the product of the order acceptance willingness level and comprehensive scheduling index to obtain the neighbor's order acceptance willingness score; obtain the order transfer willingness level of the scheduling agent, and use the order transfer willingness level as the transfer tendency coefficient;

[0130] Based on the collaboration compatibility, neighbor processing adaptation score, collaboration efficiency coefficient, neighbor order acceptance willingness score, and transfer tendency coefficient, the single-neighbor collaboration benefit of the scheduling agent for each collaborative neighbor is calculated; specifically, the single-neighbor collaboration benefit is obtained by multiplying the collaboration compatibility, neighbor processing adaptation score, collaboration efficiency coefficient, neighbor order acceptance willingness score, and transfer tendency coefficient.

[0131] Traverse all cooperative neighbors and summarize the single-neighbor cooperative benefits of the scheduling agent for all cooperative neighbors to construct a cooperative benefit vector. Each element in the cooperative benefit vector corresponds to the single-neighbor cooperative benefit of a cooperative neighbor. Obtain the single-neighbor cooperative benefit with the largest value in the cooperative benefit vector and use it as the optimal cooperative benefit. Mark the cooperative neighbor corresponding to the optimal cooperative benefit as the optimal transfer target. Calculate the product of the optimal cooperative benefit and the order value coefficient to obtain the cooperative benefit function value of the scheduling agent for the order to be assigned. The cooperative benefit function value is used to quantitatively evaluate the comprehensive benefit of the scheduling agent in transferring the order to be assigned to the optimal transfer target.

[0132] Methods for achieving Nash equilibrium solutions for order allocation through multi-round game iterations include:

[0133] For each order to be assigned, an order allocation game model is constructed. The participants in the order allocation game model are all scheduling agents, and each scheduling agent's policy space includes a local processing policy and a cooperative transfer policy. Based on the local payoff function value and the cooperative payoff function value of each scheduling agent, the current policy selection of each scheduling agent is determined from the policy space. Specifically, the local payoff function value and the cooperative payoff function value of each scheduling agent are compared. If the local payoff function value is greater than or equal to the cooperative payoff function value, the current policy selection of the scheduling agent is set to the local processing policy; if the local payoff function value is less than the cooperative payoff function value, the current policy selection of the scheduling agent is set to the cooperative transfer policy. Here, the local processing policy indicates that the scheduling agent chooses to process the order to be assigned locally, and the cooperative transfer policy indicates that the scheduling agent chooses to transfer the order to be assigned to the optimal transfer target for processing.

[0134] Define the iterative process in the order allocation game model as follows: Traverse all scheduling agents; based on the current policy choice of each scheduling agent for the optimal transition target, calculate the policy response payoff for each agent under the corresponding current policy choice; identify the policies in the policy space corresponding to each scheduling agent that are not currently chosen as the evaluation policy choices; for each scheduling agent, calculate the policy response payoff under the corresponding evaluation policy choice and mark it as the evaluation response payoff; compare the policy response payoff of each scheduling agent with the evaluation response payoff; if the policy response payoff is greater than or equal to the evaluation response payoff, do not proceed with the current policy choice of the corresponding scheduling agent. The strategy is updated; if the policy response benefit is less than the evaluated response benefit, the current policy selection of the corresponding scheduling agent is updated to the corresponding evaluated policy selection. Specifically, if the scheduling agent selects the local processing strategy, the policy response benefit is the local benefit function value; if the scheduling agent selects the cooperative transfer strategy, it is necessary to determine the current policy selection of the optimal transfer target; if the current policy selection of the optimal transfer target is the local processing strategy and the capability matching degree of the optimal transfer target is 1, the corresponding policy response benefit is the cooperative benefit function value; if the current policy selection of the optimal transfer target is the cooperative transfer strategy or the capability matching degree of the optimal transfer target is 0, the corresponding policy response benefit is zero.

[0135] For each order allocation game model, the game iteration process is executed cyclically until the iteration termination condition is met. When the iteration termination condition is met, it is determined that the order allocation game has reached a Nash equilibrium solution. The iteration termination condition includes a convergence condition and a maximum iteration condition. The convergence condition is that all scheduling agents have not changed their strategies in the current iteration round, that is, the current strategy selection of all scheduling agents has not been updated. The maximum iteration condition is that the number of iteration rounds reaches the preset maximum number of iterations, which is preset by those skilled in the art according to actual business needs. It should be understood that the Nash equilibrium solution refers to a stable state in which all scheduling agents choose the optimal response strategy and no scheduling agent can improve its own revenue by unilaterally changing its strategy.

[0136] Methods for generating a set of cooperative scheduling policies include:

[0137] For each order to be assigned, record the current strategy choice of each scheduling agent in the corresponding order allocation game model under the Nash equilibrium solution, and take the scheduling agent with the largest local payoff function value as the recommended execution store for the corresponding order to be assigned; if the local payoff function value of all scheduling agents that choose the local processing strategy is zero, then mark the order source store of the order to be assigned as the recommended execution store.

[0138] For each order to be assigned, a corresponding order scheduling strategy is generated. The order scheduling strategy includes a unique order identifier, a recommended execution store, an execution strategy type, a transfer path, and expected revenue. The execution strategy type includes local execution and collaborative transfer. Specifically, if the recommended execution store is the same as the order's originating store, the execution strategy type is set to local execution, the transfer path is set to empty, and the local revenue function value of the scheduling agent corresponding to the recommended execution store is used as the expected revenue. If the recommended execution store is different from the order's originating store, the execution strategy type is set to collaborative transfer; the order's originating store is used as the starting point of the transfer path, and the recommended execution store is used as the ending point of the transfer path; the local revenue function value of the scheduling agent corresponding to the recommended execution store is used as the expected revenue.

[0139] The order scheduling strategies for all pending orders are aggregated to construct a set of collaborative scheduling strategies.

[0140] Step S5: Determine the final execution store for each order to be assigned based on the collaborative scheduling strategy set, generate a cross-store order routing table, and synchronize the cross-store order routing table to each store.

[0141] Iterate through each order scheduling strategy in the collaborative scheduling strategy set, obtain the recommended execution store for each order scheduling strategy, and use it as the final execution store for the corresponding order to be assigned; generate a cross-store order routing table based on all order scheduling strategies in the collaborative scheduling strategy set; each routing record in the cross-store order routing table corresponds to an order scheduling strategy, and the routing record contains a unique order identifier, the order originating store, the final execution store, the execution strategy type, the transfer path, and the expected revenue; all routing records in the cross-store order routing table are sorted in descending order according to the urgency of the corresponding order to be assigned, that is, the routing record with higher order urgency is ranked first;

[0142] The system iterates through each route record in the cross-store order routing table, retrieving the corresponding order to be assigned based on the unique order identifier in the route record. If the execution strategy type in the route record is collaborative transfer, the corresponding order to be assigned is removed from the pending order queue of the order originating store and added to the pending order queue of the final executing store. If the execution strategy type in the route record is local execution, the corresponding order to be assigned is retained in the pending order queue of the order originating store. The order allocation results of this scheduling are pushed to the corresponding store terminal systems via the message push module of the enterprise resource management system. Each store terminal system executes the printing job of each order to be assigned sequentially according to its corresponding pending order queue.

[0143] This embodiment acquires topology data and logistics connectivity data of a multi-store network, comprehensively considers multi-dimensional collaborative evaluation indicators such as geographical proximity, capability complementarity, timeliness matching, and cost-effectiveness between stores, and combines constraints such as physical accessibility and time period overlap to construct a store collaboration relationship diagram that accurately reflects the feasibility and benefits of collaborative scheduling between stores. Compared with the existing technology that treats each store as an independent service node, this embodiment can effectively mine and model the geographical associations, logistics connectivity, and resource complementarity between stores, providing a solid data foundation and decision-making basis for cross-store collaborative scheduling, thereby achieving accurate modeling and quantitative representation of store collaboration relationships.

[0144] By collecting real-time order backlog data, resource usage data, and service response data from each store, and encoding these data into node status feature vectors, which are then embedded into the store collaboration graph, a dynamic store status graph reflecting the real-time operational status of the stores is formed. Simultaneously, edge weights are dynamically updated based on differences in capacity load and order acceptance capacity coefficients between stores, allowing the collaboration graph to adjust in real-time according to changes in store status. Compared to the lack of flexibility in existing static allocation methods, this approach can promptly detect dynamic changes in store status. When a store experiences order backlog or equipment failure, it can quickly respond and dynamically transfer the load, thus achieving real-time perception and dynamic updating of store status.

[0145] By inputting a dynamic store state graph into a pre-trained graph neural network model, the node state feature vectors of each store are aggregated using a message passing mechanism to output a collaborative scheduling potential vector that integrates multi-hop neighbor node information. This collaborative scheduling potential vector can quantitatively characterize the comprehensive ability of a store to participate in collaborative scheduling under the current network state from multiple dimensions, such as order receiving potential, order transfer potential, and resource sharing potential. Compared with existing methods that make scheduling decisions based on only a single indicator, this method can deeply explore the structural position and neighborhood state of stores in the collaborative network, providing a more comprehensive and accurate capability assessment for subsequent intelligent scheduling decisions.

[0146] Each store is modeled as a scheduling agent with independent decision-making capabilities. Each scheduling agent independently calculates its local and collaborative revenue functions based on order attribute data, and reaches a Nash equilibrium solution for order allocation through multiple rounds of game iteration. The Nash equilibrium solution ensures that, assuming all scheduling agents choose the optimal response strategy, no scheduling agent can improve its own revenue by unilaterally changing its strategy, thus achieving globally stable optimal allocation under a distributed decision-making architecture. Compared with existing centralized scheduling methods, which have the risk of single-point bottlenecks and large response delays, the distributed game decision-making mechanism allows each store to perform decision calculations in parallel, improving the system's scalability and real-time response capabilities.

[0147] Based on the game equilibrium results, a set of collaborative scheduling strategies is generated, including recommended execution stores, execution strategy types, transfer paths, and expected returns. Furthermore, a cross-store order routing table sorted by order urgency is generated. The order allocation results are synchronized to each store's terminal system via the enterprise resource management system's message push module, achieving a complete closed loop from strategy generation to execution. Compared to existing methods that struggle to quickly distribute scheduling results, this approach provides a complete order routing and synchronization mechanism, ensuring that scheduling strategies are promptly and accurately communicated to each execution store. This effectively improves service response efficiency and customer satisfaction, thereby achieving the systematic generation and efficient execution of order scheduling strategies.

[0148] Example 2

[0149] This application also provides an electronic device. The electronic device may include one or more processors and one or more memories. The memories store computer-readable code that, when executed by the one or more processors, can perform the dynamic scheduling and allocation method for print order resources for multi-store collaboration as described above.

[0150] The method according to the embodiments of this application can also be implemented using the architecture of the electronic device shown in this application. The electronic device may include a bus, one or more CPUs, ROM, RAM, a communication port connected to a network, input / output, a hard disk, etc. The storage device in the electronic device, such as ROM or hard disk, may store the dynamic scheduling and allocation method for print order resources for multi-store collaboration provided in this application. Furthermore, the electronic device may also include a user interface. Of course, the architecture shown in this application is merely exemplary; when implementing different devices, one or more components in the electronic device shown in this application may be omitted according to actual needs.

[0151] Example 3

[0152] Please refer to the accompanying drawings. One embodiment of this application discloses a computer-readable storage medium. The computer-readable storage medium stores computer-readable instructions. When the computer-readable instructions are executed by a processor, the dynamic scheduling and allocation method for print order resources for multi-store collaboration, as described in the above-described embodiments of this application, can be performed. The storage medium includes, but is not limited to, volatile memory and / or non-volatile memory. Volatile memory may include, for example, random access memory (RAM) and cache memory. Non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc.

[0153] Furthermore, according to embodiments of this application, the processes described in the above-referenced flowcharts can be implemented as computer software programs. For example, this application provides a non-transitory machine-readable storage medium storing machine-readable instructions that can be executed by a processor to perform instructions corresponding to the method steps provided in this application, such as a dynamic scheduling and allocation method for print order resources for multi-store collaboration. When this computer program is executed by a central processing unit (CPU), it performs the functions defined in the method of this application.

[0154] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0155] All formulas in this manual are dimensionless and calculated numerically. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters and thresholds in the formulas are set by those skilled in the art according to the actual situation.

[0156] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for dynamic scheduling and allocation of printing order resources for multi-store collaboration, characterized in that, include: Step S1: Obtain the topology data and logistics connectivity data of the multi-store network, and construct a store collaboration relationship diagram based on the topology data and logistics connectivity data; wherein, the topology data includes the comprehensive capacity indicators and service capability set of each store; the logistics connectivity data includes the actual distance matrix, delivery time matrix, delivery cost matrix, physical reachability matrix and time period overlap matrix; Methods for constructing store collaboration diagrams include: Based on the actual distance matrix, calculate the geographical proximity of each store combination; based on the service capacity set of each store, calculate the capability complementarity of each store combination; based on the delivery time matrix, calculate the timeliness matching degree of each store combination; based on the delivery cost matrix and the comprehensive capacity index of each store, calculate the cost-benefit ratio of each store combination; based on the preset collaboration weights, perform a weighted summation calculation on the geographical proximity, capability complementarity, timeliness matching degree and cost-benefit ratio of the same store combination to obtain the initial collaboration score of each store combination. The physical reachability matrix and the time period overlap matrix are used as constraints to correct the initial collaboration score, resulting in a corrected collaboration score for each store combination. The corrected collaboration score for each store combination is then compared with a preset collaboration threshold, and the comparison results are used to determine whether there is a valid collaboration relationship between the two stores corresponding to each store combination. Obtain the unique identifier of each store and create a node set based on the unique identifier; traverse all stores with valid collaborative relationships and create a directed edge set based on the corrected collaborative score; use the comprehensive capacity index and service capability set of each store as the static node attributes of the corresponding node; construct a store collaborative relationship graph based on the node set, the directed edge set, and the static node attributes. Step S2: Collect order backlog data, resource usage data and service response data of each store in real time, and encode them into node status feature vectors of each store. Embed the node status feature vectors into the store collaboration relationship diagram to form a dynamic store status diagram. Step S3: Input the dynamic store state graph into the pre-trained graph neural network model, perform neighborhood aggregation on the node state feature vector of each store through the message passing mechanism, output the collaborative scheduling potential vector of each store, and model each store as a scheduling agent based on the collaborative scheduling potential vector. Step S4: Obtain the order attribute data of each order to be assigned. Each scheduling agent independently calculates the local revenue function and the collaborative revenue function based on the order attribute data, and reaches the Nash equilibrium solution for order allocation through multiple rounds of game iteration, generating a set of collaborative scheduling strategies. Step S5: Determine the final execution store for each order to be assigned based on the collaborative scheduling strategy set, generate a cross-store order routing table, and synchronize the cross-store order routing table to each store.

2. The method for dynamic scheduling and allocation of print order resources for multi-store collaboration as described in claim 1, characterized in that, Methods for obtaining topology data and logistics connectivity data include: Obtain the basic information and equipment configuration information of each store in the multi-store network. The basic information of the store includes the store's unique identifier, geographical coordinates, business hours, and service radius. Calculate the comprehensive capacity index of each store based on its equipment configuration information. Calculate the service capacity set of each store based on its equipment configuration information. Summarize the comprehensive capacity index and service capacity set of all stores to obtain the topology data of the multi-store network. Any two stores are combined to obtain multiple store combinations; the actual delivery route data of each store combination is obtained, and based on the actual delivery route data of all stores, an actual distance matrix, a delivery time matrix, and a delivery cost matrix are constructed respectively; the straight-line distance between each store combination is calculated based on the geographical coordinates of each store; based on the service radius and straight-line distance of each store combination, a corresponding accessibility identifier is set for each store combination, and a physical accessibility matrix is ​​constructed; based on the business hours of each store combination, the time period overlap is calculated, and a time period overlap matrix is ​​constructed; the actual distance matrix, delivery time matrix, delivery cost matrix, physical accessibility matrix, and time period overlap matrix are integrated to form the logistics connectivity data of the multi-store network.

3. The method for dynamic scheduling and allocation of print order resources for multi-store collaboration as described in claim 2, characterized in that, Methods for generating dynamic store status diagrams include: Normalize the order backlog data, resource usage data, and service response data for each store to obtain the order backlog feature vector, resource usage feature vector, and service response feature vector; obtain the current system time and calculate the time period location feature for each store in combination with the store's business hours; concatenate the order backlog feature vector, resource usage feature vector, and service response feature vector for each store with the time period location feature to form the node status feature vector for each store. Traverse each node in the store collaboration graph and associate each node with the node state feature vector of the corresponding store; fuse the static node attributes of each node with the node state feature vector to form the complete node feature of each node; calculate the dynamic edge weight of each directed edge in the store collaboration graph based on the node state feature vector of each store; update the static node attributes of each node in the store collaboration graph to the corresponding complete node feature, and update the edge weight of each directed edge to the corresponding dynamic edge weight to form a dynamic store state graph.

4. The method for dynamic scheduling and allocation of print order resources for multi-store collaboration as described in claim 3, characterized in that, Methods for outputting the collaborative scheduling potential vector of each store include: Based on the dimensions of the complete node features in the dynamic store status graph, the input layer dimension of the graph neural network model is determined; the network structure of the graph neural network model is constructed, which includes an input layer, multiple graph convolutional layers, activation layers, and an output layer; historical collaborative scheduling records are obtained, and the graph neural network model is pre-trained based on the historical collaborative scheduling records. Obtain the complete node features of each node in the dynamic store state graph and input the complete node features as input vectors into the input layer of the graph neural network model; obtain the dynamic edge weights of each directed edge in the dynamic store state graph and construct an adjacency weight matrix; based on the adjacency weight matrix, perform message passing operations in each graph convolutional layer to perform neighborhood aggregation on the complete node features of each node and obtain the high-order aggregated feature vectors of each node. The high-order aggregated feature vector of each node is input to the output layer and mapped to the preset output dimension through linear transformation to obtain the collaborative scheduling potential vector of each store; wherein, the collaborative scheduling potential vector includes a first potential component, a second potential component and a third potential component.

5. The method for dynamic scheduling and allocation of print order resources for multi-store collaboration as described in claim 4, characterized in that, Methods for modeling each store as a scheduling agent include: For each store, a corresponding scheduling agent is created sequentially, and the attribute parameters of each scheduling agent are initialized according to the collaborative scheduling potential vector. Each scheduling agent includes an agent identifier, agent state, agent capabilities, and agent policy. The agent state is the collaborative scheduling potential vector and attribute parameters of the corresponding store. The agent capabilities are the set of service capabilities of the corresponding store. The method for initializing attribute parameters based on the collaborative scheduling potential vector is as follows: Calculate the order acceptance willingness and order transfer willingness of each scheduling agent based on the first and second potential components; construct a collaborative neighbor list for each scheduling agent based on the set of directed edges in the dynamic store state graph; calculate the comprehensive scheduling index for each scheduling agent based on the third potential component and the complete node features; integrate the order acceptance willingness, order transfer willingness, collaborative neighbor list, and comprehensive scheduling index corresponding to each scheduling agent to obtain the attribute parameters for each scheduling agent.

6. The method for dynamic scheduling and allocation of print order resources for multi-store collaboration as described in claim 5, characterized in that, Methods for each scheduling agent to independently calculate its local reward function include: For each order to be assigned, all scheduling agents are traversed, and the capability matching degree, capacity adaptation degree, and timeliness feasibility between each scheduling agent and each order to be assigned are calculated in turn. Based on the capability matching degree, capacity adaptation degree, and timeliness feasibility, the local processing adaptation score between each scheduling agent and each order to be assigned is calculated in turn. Based on the order urgency and order complexity in the order attribute data, the order value coefficient of each order to be assigned is calculated. Based on the order acceptance willingness degree and comprehensive scheduling index of each scheduling agent, the local processing willingness score of each scheduling agent is calculated. Based on the local processing adaptation score, the order value coefficient, and the local processing willingness score, the local revenue function value of each scheduling agent for each order to be assigned is calculated.

7. The method for dynamic scheduling and allocation of print order resources for multi-store collaboration as described in claim 6, characterized in that, Methods for each scheduling agent to independently calculate the cooperative benefit function include: Obtain the list of collaborating neighbors for the scheduling agent, and iterate through each collaborating neighbor in the list. For each collaborating neighbor, calculate the collaboration compatibility between the scheduling agent and the collaborating neighbor, the neighbor processing adaptation score for the collaborating neighbor in handling orders to be assigned, the collaboration efficiency coefficient between the scheduling agent and the collaborating neighbor, and the neighbor's willingness to accept orders score. Obtain the order transfer willingness of the scheduling agent and use the order transfer willingness as the transfer tendency coefficient. Based on the collaboration compatibility, neighbor processing adaptation score, collaboration efficiency coefficient, neighbor's willingness to accept orders score, and transfer tendency coefficient, calculate the single-neighbor collaboration benefit of the scheduling agent for each collaborating neighbor. Traverse all cooperative neighbors, summarize the single-neighbor cooperative benefits of the scheduling agent for all cooperative neighbors, and construct a cooperative benefit vector; obtain the single-neighbor cooperative benefit with the largest value in the cooperative benefit vector and take it as the optimal cooperative benefit; mark the cooperative neighbor corresponding to the optimal cooperative benefit as the optimal transfer target; calculate the product of the optimal cooperative benefit and the order value coefficient to obtain the cooperative benefit function value of the scheduling agent for the order to be assigned.

8. The method for dynamic scheduling and allocation of print order resources for multi-store collaboration according to claim 7, characterized in that, Methods for achieving Nash equilibrium solutions for order allocation through multi-round game iterations include: For each order to be assigned, an order allocation game model is constructed. The game participants in the order allocation game model are all scheduling agents. The policy space of each scheduling agent includes local processing policy and cooperative transfer policy. Based on the local payoff function value and cooperative payoff function value of each scheduling agent, the current policy selection of each scheduling agent is determined from the policy space. Define the game iteration process in the order allocation game model as follows: traverse all scheduling agents, calculate the strategy response payoff for each scheduling agent under the corresponding current strategy choice based on the current strategy selection of the optimal transfer target for each scheduling agent; take the strategies in the strategy space corresponding to each scheduling agent that are not the current strategy choice as the evaluation strategy choice; for each scheduling agent, calculate the strategy response payoff under the corresponding evaluation strategy choice and mark it as the evaluation response payoff; compare the strategy response payoff of each scheduling agent with the evaluation response payoff, and determine whether to update the current strategy choice of the scheduling agent to the evaluation strategy choice based on the comparison result; For each order allocation game model, the game iteration process is executed cyclically until the iteration termination condition is met; when the iteration termination condition is met, it is determined that the order allocation game has reached a Nash equilibrium solution; the iteration termination condition includes the convergence condition and the maximum iteration condition.

9. The method for dynamic scheduling and allocation of print order resources for multi-store collaboration as described in claim 8, characterized in that, Methods for generating a set of cooperative scheduling policies include: For each order to be assigned, record the current strategy choice of each scheduling agent in the corresponding order allocation game model under the Nash equilibrium solution, and take the scheduling agent with the largest local payoff function value as the recommended execution store for the corresponding order to be assigned; if the local payoff function value of all scheduling agents that choose the local processing strategy is zero, then mark the order source store of the order to be assigned as the recommended execution store. For each order to be assigned, a corresponding order scheduling strategy is generated. The order scheduling strategy includes the recommended execution store, execution strategy type, transfer path, and expected revenue. The execution strategy type includes local execution and collaborative transfer. The order scheduling strategies of all orders to be assigned are aggregated to construct a collaborative scheduling strategy set.

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