Maintenance resource global configuration optimization method for cross-domain multi-level safeguard network

Abstract

Provided in the present invention is a maintenance resource global configuration optimization method for a cross-domain multi-level safeguard network. The method comprises: on the basis of the topological structure of a safeguard network and the relationship, distance and traffic time between sites, proposing a maintenance resource inventory optimization mathematical problem; defining input and output parameters of the optimization mathematical problem; on the basis of the input parameters, constructing model equations for a maintenance resource transfer system, and providing mathematical expressions for the output parameters; when there is one resource in the system, calculating a site at which the resource should be configured; and repeating such calculation, confirming an optimal site of a k-th resource after the configuration of a (k-1)th resource has been completed, until the total number of resources reaches an input value of the system, ending the configuration, then providing a graph indicating that the total delayed delivery quantity decreases as the total inventory quantity increases, and confirming the optimal total inventory quantity. In the present invention, the number of maintenance resources between sites can be allocated on the basis of a safeguard network, so as to ensure that the overall time and cost of resource scheduling of the entire safeguard network are optimal when a fault occurs randomly.

Description

A global optimization method for maintenance resource allocation in cross-domain multi-level support networks Technical Field

[0001] This invention relates to the field of avionics equipment technology, and more specifically, to a method for global configuration optimization of maintenance resources for cross-domain multi-level support networks. Background Technology

[0002] Aviation integrated electronic equipment spans multiple theater commands, operation and maintenance centers, and branch centers in terms of spatial distribution. It has the characteristics of multiple platforms, multiple systems, and multiple levels across theater commands. Currently, there is a lack of unified maintenance resource management tools. There is no theoretical or tool support for how many resources should be allocated to each site. Resource allocation mainly relies on communication between support personnel by phone. Often, resources are allocated only when needed. The entire resource allocation process lacks automated tools and data support, resulting in long troubleshooting cycles, which may affect equipment mission execution and seriously damage customer reputation.

[0003] Summary of the Invention

[0004] This invention aims to provide a global configuration optimization method for maintenance resources in cross-domain multi-level support networks, in order to solve the problem of how to achieve optimal resource allocation among different sites.

[0005] This invention provides a method for global configuration optimization of maintenance resources for cross-domain multi-level support networks, comprising the following steps:

[0006] S1, based on the topology of the network and the relationships, distances and travel times between stations, proposes a mathematical problem for optimizing maintenance resource inventory;

[0007] S2 defines the input and output parameters of the mathematical problem of optimizing maintenance resource inventory;

[0008] S3. Based on the input parameters of the mathematical problem of optimizing maintenance resource inventory, construct the model equation of the maintenance resource transfer system and give the mathematical expression of the output parameters;

[0009] S4, using the model equations of the maintenance resource transfer system and the mathematical expressions of the output parameters, calculates which station the resource should be configured at when there is only one resource.

[0010] S5. Repeat step S4 to confirm the optimal site for the k-th resource after the (k-1)-th resource is configured, until the total number of resources reaches the system input value, and the configuration ends.

[0011] S6, after configuration, provides a graph showing how the total delayed delivery quantity decreases as the total inventory increases, thus confirming the optimal total inventory.

[0012] Further, step S1 includes:

[0013] Before proposing the mathematical problem of optimizing maintenance resource inventory, we first need to clarify the resource scheduling model among avionics product resource outlets, maintenance centers, and suppliers: When an avionics product resource outlet experiences a fault, it generates a resource demand and needs to send the faulty part to the maintenance center for testing. If the outlet has sufficient resources, it can be self-sufficient; if resources are insufficient, it requests resources from the maintenance center. The maintenance center receives the faulty part from the outlet and performs fault testing: if the test result is no fault, the resource is directly returned to the outlet; if the test result is a fault, the faulty part is repaired at the maintenance center and returned to the outlet; after receiving the resource request from the outlet, the maintenance center... If the operations and maintenance center has sufficient resources, it will provide one resource to the service point; if the operations and maintenance center has insufficient resources, it will request resources from the supplier and send the faulty component to the supplier regardless of the result after fault testing. When the service point has insufficient resources but the operations and maintenance center has sufficient resources, the operations and maintenance center will receive the faulty component from the service point and perform fault testing: if the test result is no fault, the resource will be returned to the operations and maintenance center; if the test result is a fault, the faulty component will be repaired at the operations and maintenance center and returned to the operations and maintenance center. After receiving the resource request from the operations and maintenance center, if the supplier has sufficient resources, it will provide one resource to the operations and maintenance center; if the supplier has insufficient resources, the resource request cannot be met temporarily.

[0014] The mathematical problem of maintenance resource inventory optimization aims to solve the problem of allocating the amount of resources between each station based on the topology of the support network and the relationships, distances, and travel times between stations, given a fixed amount of resources, and under the premise that failures occur randomly, in order to ensure the optimal overall time cost of resource scheduling for the entire support network.

[0015] Furthermore, in step S2:

[0016] The input parameters for the mathematical problem of optimizing maintenance resource inventory include: total resource inventory s, and resource demand d per unit time at the service point. i Fault detection is based on the probability p of failure. f Repair time for faulty parts (T) m The time T for resources to be transported from the operations and maintenance center to the network site. si The time T for resources to be transported from the supplier to the operations and maintenance center fi The transportation time T for faulty parts from the service point to the maintenance center fi The time T for transporting faulty parts from the maintenance center to the supplier. ft .

[0017] The output parameters of the mathematical problem of optimizing maintenance resource inventory include: the number of service points, s. i Number of resources in the operation and maintenance center (s) t , number of supplier resources u The probability P that a network point can provide resources iThe operation and maintenance center can provide resource probability P t The probability P that the supplier can provide resources u Total delayed delivery quantity S BO .

[0018] Further, step S3 includes:

[0019] Based on the input parameters of the mathematical problem of optimizing maintenance resource inventory, a model equation for a resource transfer system is constructed. First, the mathematical expressions for the resource demand of the maintenance center and suppliers per unit time are given. Then, the average maintenance time for faulty parts detected at the maintenance center is given. Next, the mathematical expressions for the resources that the network outlets, maintenance centers, and suppliers should receive are given. Finally, a model equation for the maintenance resource transfer system of the network outlets, maintenance centers, and suppliers is constructed, and a mathematical expression for the total delayed delivery amount is given.

[0020] Furthermore, the mathematical expression for the resource demand generated by the operations and maintenance center and suppliers per unit time is:

[0021] The number of network resources is s i (i = 1, 2, ..., n); the resource demand generated by the branch per unit time is d. i After a resource demand arises, the probability that the branch can provide the resource is P. i The probability that a branch cannot provide resources is 1-P. i ;

[0022] The number of resources in the operation and maintenance center is s t The number of resource requirements generated by the operation and maintenance center per unit time, d t for:

[0023] After a resource request is generated from a branch, the probability that the operations and maintenance center can provide the resource is P. t The probability that no resources can be provided is 1-P. t ;

[0024] The number of supplier resources is s u ; The quantity of resources required by the supplier per unit of time, d u For: d u =(1-P t )d t (2)

[0025] Furthermore, the average repair time T for faulty parts M The mathematical expression is: T M =P f T m(3)

[0026] Among them, the probability of a faulty component being faulty after fault detection at the operation and maintenance center is P. f Repair time for faulty parts (T) m And it's restored to like-new condition.

[0027] Furthermore, the mathematical expressions for calculating the resources due to the network outlets, the resources due to the operation and maintenance center, and the resources due to the suppliers are as follows:

[0028] Treating all branches, operations centers, and suppliers as sites, under the inventory counting strategy of (s-1, s), each site satisfies the inventory balance equation: s = s OH +s DI -s BO (4)

[0029] In the formula: s represents the initial inventory of the site; s OH For the site's available inventory; s DI The amount of resources a site deserves; s BO Total delayed deliveries at the site;

[0030] When a resource request occurs, the site's s DI Add one, if the site has available inventory, then the site's s OH Decrease by one; if the site has no available inventory, then the site's s BO The value is incremented by one; when the system is in steady state, the available inventory s at each site is incremented by one. OH With total delayed delivery amount s BO They cannot coexist;

[0031] The amount of resources that the outlets deserve The quantity of resources transported to the network points The number of delayed resource deliveries generated by the operations and maintenance center for network points Composition; the amount of resources due to the outlets Calculated by the following formula:

[0032] Deserved resource quantity of the operation and maintenance center It consists of four items: the number of faulty parts being repaired by the operations and maintenance center. Number of resources transported to the operations and maintenance center and number of faulty parts The number of resources delayed by the supplier to the operations and maintenance center Deserved resource quantity of the operation and maintenance center Calculated by the following formula:

[0033] Supplier's due resources Number of faulty parts being repaired by the supplier and the number of faulty parts shipped to the supplier Composition; the amount of resources the supplier is entitled to Calculated by the following formula:

[0034] Furthermore, the resource transfer system model for outlets, operation and maintenance centers, and suppliers is constructed as follows:

[0035] Based on the assumptions and Palm's theorem, the delayed delivery amount of resources in steady state can be written as:

[0036] The probability that a site can fulfill a resource request after receiving it is:

[0037] Expanding the above formula, we obtain the resource transfer system model equation with n sites, operation and maintenance centers, and suppliers:

[0038] The total delayed delivery quantity of resources for the system is:

[0039] Further, step S4 includes:

[0040] First, calculate the condition when one resource is configured at point number 1, i.e., s1 = 1, s i (i = 2, 3, ..., n) = s t =s u =0, the total delayed delivery amount of the system;

[0041] The total delayed delivery amount of the system is calculated as follows:

[0042] Among them, record Both sets of parameters are unknown and nested, requiring iterative solutions. The method is as follows: First, set... The initial values ​​are substituted into equations (36)(37)(38) to solve for the results. Then Treat it as an unknown parameter, Substitute the values ​​of (30)(31)(32)(33)(34)(35) into the solution to obtain the new... New If the difference between the two values ​​is less than the error tolerance, then output the result. and Otherwise, let the new Using the initial value, repeat the above steps; solve for... and Then, substitute the values ​​into equations (28) and (29) to obtain the total delayed delivery amount of the system.

[0043] Further, step S5 includes:

[0044] Using the same calculation method as in step S4, calculate which site the second resource should be configured at; the method is to calculate the total delayed delivery amount of the second resource after the first resource is configured, and determine which site the second resource should be configured at by comparing the total delayed delivery amount of the system.

[0045] This process continues until all resources are configured on the most suitable site, i.e., the total number of resources reaches the system input value, at which point the configuration ends.

[0046] Furthermore, in step S6, a graph showing the decrease in total delayed delivery quantity as the total inventory increases is given, along with the resource quantity of each site under each total inventory quantity; if the final total delayed delivery quantity is less than the expected value of inventory optimization, it indicates that the total inventory is too high, and funds can be saved by reducing the inventory quantity.

[0047] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0048] This invention optimizes the resource allocation of avionics equipment network sites. Based on the network topology and the relationships, distances, and travel times between sites, it allocates the amount of resources between each site. Under the premise of random failures, it ensures optimal resource allocation for the entire support network, reduces resource loss during maintenance, lowers resource scheduling time during maintenance, rationally controls the total amount of resource inventory, promotes a reasonable balance between operation and maintenance efficiency and costs, ensures successful mission execution, and further improves user satisfaction with equipment operation and maintenance. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 is a flowchart of the global configuration optimization method for maintenance resources for cross-domain multi-level support networks in an embodiment of the present invention.

[0051] Figure 2 is a topology diagram between stations in an embodiment of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0053] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0054] Example

[0055] As shown in Figures 1 and 2, this embodiment proposes a global configuration optimization method for maintenance resources in cross-domain multi-level support networks, including the following steps:

[0056] S1, based on the topology of the network and the relationships, distances and travel times between stations, proposes a mathematical problem for optimizing maintenance resource inventory;

[0057] Before proposing the mathematical problem of optimizing maintenance resource inventory, we first need to clarify the resource scheduling model among avionics product resource outlets, maintenance centers, and suppliers: When an avionics product resource outlet experiences a fault, it generates a resource demand and needs to send the faulty part to the maintenance center for testing. If the outlet has sufficient resources, it can be self-sufficient; if resources are insufficient, it requests resources from the maintenance center. The maintenance center receives the faulty part from the outlet and performs fault testing: if the test result is no fault, the resource is directly returned to the outlet; if the test result is a fault, the faulty part is repaired at the maintenance center and returned to the outlet; after receiving the resource request from the outlet, the maintenance center... If the operations and maintenance center has sufficient resources, it will provide one resource to the service point; if the operations and maintenance center has insufficient resources, it will request resources from the supplier and send the faulty component to the supplier regardless of the result after fault detection. When the service point has insufficient resources but the operations and maintenance center has sufficient resources, the operations and maintenance center will receive the faulty component from the service point and perform fault detection: if the detection result is no fault, the resource will be returned to the operations and maintenance center; if the detection result is a fault, the faulty component will be repaired at the operations and maintenance center and returned to the operations and maintenance center. After receiving the resource request from the operations and maintenance center, if the supplier has sufficient resources, it will provide one resource to the operations and maintenance center; if the supplier has insufficient resources, the resource request cannot be met temporarily.

[0058] The mathematical problem of maintenance resource inventory optimization aims to solve the problem of allocating the amount of resources between each station based on the topology of the support network and the relationships, distances, and travel times between stations, given a fixed amount of resources, and under the premise that failures occur randomly, in order to ensure the optimal overall time cost of resource scheduling for the entire support network.

[0059] S2 defines the input and output parameters of the mathematical problem of optimizing maintenance resource inventory;

[0060] The input parameters for the mathematical problem of optimizing maintenance resource inventory include: total resource inventory s, and resource demand d per unit time at the service point. i Fault detection is based on the probability p of failure. f Repair time for faulty parts (T) m The time T for resources to be transported from the operations and maintenance center to the network site. si The time T for resources to be transported from the supplier to the operations and maintenance center fi The transportation time T for faulty parts from the service point to the maintenance center fi The time T for transporting faulty parts from the maintenance center to the supplier. ft .

[0061] The output parameters of the mathematical problem of optimizing maintenance resource inventory include: the number of service points, s. i Number of resources in the operation and maintenance center (s) t , number of supplier resources u The probability P that a network point can provide resources i The operation and maintenance center can provide resource probability P t The probability P that the supplier can provide resources u Total delayed delivery quantity S BO .

[0062] S3. Based on the input parameters of the mathematical problem of optimizing maintenance resource inventory, construct the model equation of the maintenance resource transfer system and give the mathematical expression of the output parameters;

[0063] Based on the input parameters of the mathematical problem of optimizing maintenance resource inventory, a model equation for a resource transfer system is constructed. First, the mathematical expressions for the resource demand of the maintenance center and suppliers per unit time are given. Then, the average maintenance time for faulty parts detected at the maintenance center is given. Next, the mathematical expressions for the resources that the network outlets, maintenance centers, and suppliers should receive are given. Finally, a model equation for the maintenance resource transfer system of the network outlets, maintenance centers, and suppliers is constructed, and a mathematical expression for the total delayed delivery amount is given.

[0064] Furthermore, the mathematical expression for the resource demand generated by the operations and maintenance center and suppliers per unit time is:

[0065] The number of network resources is s i(i = 1, 2, ..., n). The resource demand generated by the network points per unit time is d. i After a resource demand arises, the probability that the branch can provide the resource is P. i The probability that a branch cannot provide resources is 1-P. i .

[0066] The number of resources in the operation and maintenance center is s t The amount of resources required by the operations and maintenance center per unit time, d. t for:

[0067] After a resource request is generated from a branch, the probability that the operations and maintenance center can provide the resource is P. t The probability that no resources can be provided is 1-P. t .

[0068] The number of supplier resources is s u The quantity of resources required by the supplier per unit of time, d. u For: d u =(1-P t )d t (2)

[0069] Furthermore, the mathematical expression for the average repair time of faulty components is:

[0070] After the faulty component undergoes fault detection at the operations and maintenance center, the probability of it being faulty is P. f Repair time for faulty parts (T) m And the repairs are as good as new, therefore the average repair time T for faulty parts is very short. M For: T M =P f T m (3)

[0071] Furthermore, the mathematical expressions for calculating the resources due to network outlets, the resources due to operation and maintenance centers, and the resources due to suppliers are as follows:

[0072] Treating all branches, operations centers, and suppliers as sites, under the inventory counting strategy of (s-1, s), each site satisfies the inventory balance equation: s = s OH +s DI -s BO (4)

[0073] In the formula: s represents the initial inventory of the site; s OH For the site's available inventory; s DI The amount of resources a site deserves; sBO This represents the total delayed delivery volume for the site.

[0074] When a resource request occurs, the site's s DI Add one, if the site has available inventory, then the site's s OH Decrease by one; if the site has no available inventory, then the site's s BO Increment the value by one. When the system is in steady state, the available inventory s at each site... OH With total delayed delivery amount s BO They cannot coexist.

[0075] The amount of resources that the outlets deserve The quantity of resources transported to the network points The number of delayed resource deliveries generated by the operations and maintenance center for network points Composition. The amount of resources that each branch should receive. Calculated by the following formula:

[0076] Deserved resource quantity of the operation and maintenance center It consists of four items: the number of faulty parts being repaired by the operations and maintenance center. Number of resources transported to the operations and maintenance center and number of faulty parts The number of resources delayed by the supplier to the operations and maintenance center Deserved resource quantity of the operation and maintenance center Calculated by the following formula:

[0077] Supplier's due resources Number of faulty parts being repaired by the supplier and the number of faulty parts shipped to the supplier Composition. The amount of resources the supplier is entitled to. Calculated by the following formula:

[0078] The resource transfer system model for network outlets, operation and maintenance centers, and suppliers is constructed as follows:

[0079] Based on the assumptions and Palm's theorem, the delayed delivery amount of resources in steady state can be written as:

[0080] The probability that a site can fulfill a resource request after receiving it is:

[0081] Expanding the above formula, we obtain the resource transfer system model equation with n sites, operation and maintenance centers, and suppliers:

[0082] The total delayed delivery quantity of resources for the system is:

[0083] S4, using the model equations of the maintenance resource transfer system and the mathematical expressions of the output parameters, calculates which station the resource should be configured at when there is only one resource.

[0084] First, calculate the case where one resource is configured at point number 1 (i.e., s1 = 1, s...). i (i = 2, 3, ..., n) = s t =s u =0), the total delayed delivery amount of the system.

[0085] The total delayed delivery amount of the system is calculated as follows:

[0086] Among them, record Both sets of parameters are unknown and nested within each other, requiring iterative solutions. The method is as follows:

[0087] First, set The initial values ​​are substituted into equations (36)(37)(38) to solve for the results. Then Treat it as an unknown parameter, Substitute the values ​​of (30)(31)(32)(33)(34)(35) into the solution to obtain the new... New If the difference between the two values ​​is less than the error tolerance, then output the result. and Otherwise, let the new Use the initial value as an example and repeat the above steps.

[0088] Solve and Then, substitute the values ​​into equations (28) and (29) to obtain the total delayed delivery amount of the system.

[0089] S5. Repeat step S4 to confirm the optimal site for the k-th resource after the (k-1)-th resource is configured, until the total number of resources reaches the system input value, and the configuration ends.

[0090] Using the same calculation method as in step S4, calculate which site the second resource should be configured at; the method is to calculate the total delayed delivery amount of the second resource after the first resource is configured, and determine which site the second resource should be configured at by comparing the total delayed delivery amount of the system.

[0091] This process continues until all resources are configured on the most suitable site, i.e., the total number of resources reaches the system input value, at which point the configuration ends.

[0092] S6, after configuration, provides a graph showing how the total delayed delivery quantity decreases as the total inventory increases, thus confirming the optimal total inventory.

[0093] The graph shows how the total delayed delivery quantity decreases as the total inventory increases, and it also provides the resource quantity for each site under each inventory quantity. If the final total delayed delivery quantity is less than the expected value for inventory optimization, it indicates that the total inventory is too high, and the inventory quantity can be appropriately reduced to save money.

[0094] The aforementioned method for global configuration optimization of maintenance resources for cross-domain, multi-level support networks can be applied to multiple fields. This invention optimizes the resource allocation of avionics equipment network points. Based on the network topology and the relationships, distances, and travel times between stations, it allocates resources to each station. Under the premise of random fault occurrence, it ensures optimal resource allocation across the entire support network, reduces resource shortages during maintenance, lowers resource scheduling time during maintenance, rationally controls total resource inventory, promotes a reasonable balance between operational efficiency and costs, ensures successful task execution, and further enhances user satisfaction with equipment maintenance.

[0095] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for global configuration optimization of maintenance resources for cross-domain multi-level support networks, characterized in that, Includes the following steps: S1, based on the topology of the network and the relationships, distances and travel times between stations, proposes a mathematical problem for optimizing maintenance resource inventory; S2 defines the input and output parameters of the mathematical problem of optimizing maintenance resource inventory; S3. Based on the input parameters of the mathematical problem of optimizing maintenance resource inventory, construct the model equation of the maintenance resource transfer system and give the mathematical expression of the output parameters; S4, using the model equations of the maintenance resource transfer system and the mathematical expressions of the output parameters, calculates which station the resource should be configured at when there is only one resource. S5. Repeat step S4 to confirm the optimal site for the k-th resource after the (k-1)-th resource is configured, until the total number of resources reaches the system input value, and the configuration ends. S6, after configuration, provides a graph showing how the total delayed delivery quantity decreases as the total inventory increases, thus confirming the optimal total inventory.

2. The method for global configuration optimization of maintenance resources for cross-domain multi-level support networks according to claim 1, characterized in that, Step S1 includes: Before proposing the mathematical problem of optimizing maintenance resource inventory, we first clarify the resource scheduling model among avionics product resource outlets, maintenance centers, and suppliers: When an avionics product resource outlet experiences a fault, generating a resource demand, the faulty component needs to be sent to the maintenance center for testing. If the outlet has sufficient resources, it can be self-sufficient; if resources are insufficient, it requests resources from the maintenance center. The maintenance center receives the faulty component from the outlet and performs fault testing: if the test result is no fault, the resource is directly returned to the outlet; if the test result is a fault, the faulty component is repaired at the maintenance center and returned to the outlet. After receiving the resource request from the outlet, if the maintenance center has sufficient resources, it provides one resource to the outlet; if the maintenance center has insufficient resources, it requests resources from the supplier, and simultaneously performs fault testing on the faulty component and sends it to the supplier regardless of the result. If the outlet's resources are insufficient and the maintenance center's resources are sufficient... When the time is right, the operations and maintenance center receives faulty parts from the network points and performs fault detection: if the detection result is no fault, the resource is returned to the operations and maintenance center; if the detection result is faulty, the faulty part is repaired at the operations and maintenance center and then returned to the operations and maintenance center; after the supplier receives the resource request from the operations and maintenance center, if the supplier has sufficient resources, it will provide one resource to the operations and maintenance center; if the supplier has insufficient resources, the resource request cannot be met temporarily. The mathematical problem of maintenance resource inventory optimization aims to solve the problem of allocating the amount of resources between each station based on the topology of the support network and the relationships, distances, and travel times between stations, given a fixed amount of resources, and under the premise that failures occur randomly, in order to ensure the optimal overall time cost of resource scheduling for the entire support network.

3. The method for global configuration optimization of maintenance resources for cross-domain multi-level support networks according to claim 1, characterized in that, In step S2: The input parameters for the mathematical problem of optimizing maintenance resource inventory include: total resource inventory s, and resource demand d per unit time at the service point. i Fault detection is based on the probability p of failure. f Repair time for faulty parts (T) m The time T for resources to be transported from the operations and maintenance center to the network site. si The time T for resources to be transported from the supplier to the operations and maintenance center fi The transportation time T for faulty parts from the service point to the maintenance center fi The time T for transporting faulty parts from the maintenance center to the supplier. ft . The output parameters of the mathematical problem of optimizing maintenance resource inventory include: the number of service points, s. i Number of resources in the operation and maintenance center (s) t , number of supplier resources u The probability P that a network point can provide resources i The operation and maintenance center can provide resource probability P t The probability P that the supplier can provide resources u Total delayed delivery quantity S BO .

4. The method for global configuration optimization of maintenance resources for cross-domain multi-level support networks according to claim 3, characterized in that, Step S3 includes: Based on the input parameters of the mathematical problem of optimizing maintenance resource inventory, a resource transfer system model equation is constructed. First, mathematical expressions for the resource demand per unit time of the maintenance center and suppliers are given. Then, the average repair time for faulty parts detected at the maintenance center is given. Next, mathematical expressions for the resources that service points, maintenance centers, and suppliers should receive are given. Finally, a model of the service points and maintenance... The model equations for the maintenance resource transfer system of the center and suppliers are presented, along with a mathematical expression for the total delayed delivery volume.

5. The method for global configuration optimization of maintenance resources for cross-domain multi-level support networks according to claim 4, characterized in that, The mathematical expressions for the resource requirements generated by the operations and maintenance center and suppliers per unit of time are: The number of network resources is s i (i = 1, 2, ..., n); the resource demand generated by the branch per unit time is d. i After a resource demand arises, the probability that the branch can provide the resource is P. i The probability that a branch cannot provide resources is 1-P. i ; The number of resources in the operation and maintenance center is s t The number of resource requirements generated by the operation and maintenance center per unit time, d t for: After a resource request is generated from a branch, the probability that the operations and maintenance center can provide the resource is P. t The probability that no resources can be provided is 1-P. t ; The number of supplier resources is s u ; The quantity of resources required by the supplier per unit of time, d u for: d u =(1-P t )d t (2)。 6. The method for global configuration optimization of maintenance resources for cross-domain multi-level support networks according to claim 5, characterized in that, Average repair time T for faulty parts M The mathematical expression is: T M =P f T m (3) Among them, the probability of a faulty component being faulty after fault detection at the operation and maintenance center is P. f Repair time for faulty parts (T) m And it's restored to like-new condition.

7. The method for global configuration optimization of maintenance resources for cross-domain multi-level support networks according to claim 6, characterized in that, The mathematical expressions for calculating the resources due to network outlets, the resources due to operation and maintenance centers, and the resources due to suppliers are as follows: Treating all outlets, operation and maintenance centers, and suppliers as sites, under the inventory counting strategy of (s-1,s), Each site satisfies the inventory balance equation: s=s OH +s DI -s BO (4) In the formula: s represents the initial inventory of the site; s OH For the site's available inventory; s DI The amount of resources a site deserves; s BO Total delayed deliveries at the site; When a resource request occurs, the site's s DI Add one, if the site has available inventory, then the site's s OH Subtract one; If the site has no available inventory, then the site's s BO The value is incremented by one; when the system is in steady state, the available inventory s at each site is incremented by one. OH With total delayed delivery volume s BO They cannot coexist; The amount of resources that the outlets deserve The quantity of resources transported to the network points The number of delayed resource deliveries generated by the operations and maintenance center for network points Composition; the amount of resources due to the outlets Calculated by the following formula: Deserved resource quantity of the operation and maintenance center It consists of four items: the number of faulty parts being repaired by the operations and maintenance center. Number of resources transported to the operations and maintenance center and number of faulty parts The number of resources delayed by the supplier to the operations and maintenance center Deserved resource quantity of the operation and maintenance center Calculated by the following formula: Supplier's due resources Number of faulty parts being repaired by the supplier and direction Number of faulty parts from the supplier Composition; the amount of resources the supplier is entitled to Calculated by the following formula:

8. The method for global configuration optimization of maintenance resources for cross-domain multi-level support networks according to claim 7, characterized in that, The resource transfer system model for network outlets, operation and maintenance centers, and suppliers is constructed as follows: Based on the assumptions and Palm's theorem, the delayed delivery amount of resources in steady state can be written as: The probability that a site can fulfill a resource request after receiving it is: Expanding the above formula, we obtain the resource transfer system model equation with n sites, operation and maintenance centers, and suppliers: The total delayed delivery amount of resources for the system is:

9. The method for global configuration optimization of maintenance resources for cross-domain multi-level support networks according to claim 8, characterized in that, Step S4 includes: First, calculate the condition when one resource is configured at point number 1, i.e., s1 = 1, s i (i = 2, 3, ..., n) = s t =s u =0, the total delayed delivery amount of the system; The total delayed delivery amount of the system is calculated as follows: Among them, record Both sets of parameters are unknown and nested, requiring iterative solutions. The method is as follows: First, set... The initial values ​​are substituted into equations (36)(37)(38) to solve for the results. Then Treat it as an unknown parameter, Substitute the values ​​of (30)(31)(32)(33)(34)(35) into the solution to obtain the new... New If the difference between the two values ​​is less than the error tolerance, then output the result. and Otherwise, let the new Using the initial value, repeat the above steps; solve for... and Then, substitute the values ​​into equations (28) and (29) to obtain the total delayed delivery amount of the system.

10. The method for global configuration optimization of maintenance resources for cross-domain multi-level support networks according to claim 1, characterized in that, Step S5 includes: Using the same calculation method as in step S4, calculate which site the second resource should be configured at; the method is to calculate the total delayed delivery amount of the second resource after the first resource is configured, and determine which site the second resource should be configured at by comparing the total delayed delivery amount of the system. This process continues until all resources are configured on the most suitable site, i.e., the total number of resources reaches the system input value, at which point the configuration ends.

11. The method for global configuration optimization of maintenance resources for cross-domain multi-level support networks according to claim 1, characterized in that, In step S6, a graph showing the decrease in total delayed delivery quantity as the total inventory increases is given, along with the resource quantity for each site under each total inventory quantity. If the final total delayed delivery quantity is less than the expected value for inventory optimization, it indicates that the total inventory is too high, and funds can be saved by reducing the inventory quantity.

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