Unmanned aerial vehicle distribution center site selection method and system considering interruption risk

Abstract

The invention provides an unmanned aerial vehicle distribution center site selection method and system considering an interruption risk, and relates to the technical field of unmanned aerial vehicle logistics networks. In a site selection process, external factors such as interruption risk of a distribution center and demand uncertainty of a demand point are considered, a network total cost model including construction cost, inventory cost and transportation cost is constructed, minimization of the model is taken as a target function, linearization processing is performed on the total cost model, a Lagrange multiplier is introduced, specified constraint conditions are relaxed, and a site selection result is obtained. A relaxation model is obtained, the minimum value of the model is solved, a lower bound solution is obtained, on the basis of the lower bound solution and specified constraint conditions, an immobilized optimization strategy is adopted, the minimum value of an upper bound model is solved, and an upper bound solution is obtained; and according to the multiplier iteration model, updating the Lagrange multiplier, substituting the updated Lagrange multiplier into the relaxation model, and circularly carrying out solving judgment until the solving process meets a preset termination condition, so as to obtain a site selection scheme of the unmanned aerial vehicle distribution center, so that demand point distribution is met, and site selection of the distribution center is more reasonable.

Description

Technical Field

[0001] The present invention relates to the field of drone logistics network technology, and in particular to a drone delivery center site selection method and system that takes interruption risks into consideration. Background Art

[0002] Logistics networks encompass a wide range of organizations and facilities, making them highly susceptible to disruptions caused by both natural and human factors, such as natural disasters, trade conflicts, technological failures, and public health incidents. For example, emerging diseases create a highly uncertain environment, necessitating periodic quarantines of different regions and causing significant disruptions to supply chain networks. For some temperature-sensitive medications with short shelf lives, transportation time is limited. In these emergencies, drug quality and delivery cannot be guaranteed. While cold chain storage and transportation can extend shipping times, cold chain logistics imposes strict requirements on timeliness and temperature control. Drones, equipped with temperature control devices and protective mechanisms, offer significant potential as an emerging delivery tool in terms of flexibility and cost effectiveness in cold chain delivery. However, while offering significant advantages, they still face uncertainties.

[0003] Network facility site selection is a strategic decision, irreversible once established. Site selection is based on logistics requirements, taking into account the type of goods being transported and the target audience, and selecting suitable candidate locations. Previous research on drone delivery has focused primarily on the characteristics of the drones themselves and the geographical context, but has lacked consideration of complex external environmental factors. Summary of the Invention

[0004] The problem to be solved by the present invention is that the existing site selection methods lack research on external complex environmental factors.

[0005] To solve the above problems, in a first aspect, the present invention provides a method for selecting a drone delivery center site taking into account the risk of interruption, comprising: Initialization parameters; the parameters include Lagrange multipliers; The goal is to minimize the value of the relaxed model and obtain a lower bound solution for the objective function. The relaxed model is obtained by linearizing the total cost model of the drone, introducing Lagrange multipliers, and relaxing the specified constraints. The objective function is a function that minimizes the total cost model, which is constructed after considering interruption risk and demand uncertainty. Based on the lower bound solution and the specified constraints, a fixed optimization strategy is adopted to obtain the upper bound solution of the objective function by taking the minimum value of the upper bound model as the solution goal; the upper bound model is the model obtained by fixing the parameters in the total cost model; Determine whether the solution process meets the preset termination conditions; If it is not satisfied, the Lagrange multiplier is updated according to the multiplier iteration model; The updated Lagrange multiplier is substituted into the relaxed model, and the solution judgment is repeated until the solution process meets the preset termination condition, and the location of the drone delivery center is obtained.

[0006] In a second aspect, the present invention further provides a drone delivery center site selection system that considers disruption risk, comprising: A parameter initialization module, used for initializing parameters; the parameters include Lagrange multipliers; A lower bound solution analysis module is used to obtain a lower bound solution to the objective function by minimizing the value of a relaxed model. The relaxed model is obtained by linearizing the total cost model of the drone, introducing Lagrange multipliers, and relaxing the specified constraints. The objective function is a function of the lowest-slip total cost model, which is constructed after considering interruption risk and demand uncertainty. An upper bound solution analysis module is used to obtain an upper bound solution of the objective function by adopting a fixed optimization strategy based on the lower bound solution and specified constraints, with the minimum value of the upper bound model as the solution goal; the upper bound model is a model obtained by fixing the parameters in the total cost model; A loop judgment module is used to judge whether the solution process meets the preset termination condition; A multiplier update module is used to update the Lagrange multiplier according to the multiplier iteration model if it is not satisfied; The cyclic analysis module is used to substitute the updated Lagrange multiplier into the relaxed model and perform solution judgment cyclically until the solution process meets the preset termination conditions to obtain the location of the drone delivery center.

[0007] The present invention provides a method and system for selecting a drone delivery center site that takes interruption risk into account. Compared with existing technologies, it has the following advantages: In the process of selecting a drone delivery center, a total cost model is constructed to fit the actual situation and make the location of the delivery center more reasonable, considering complex external environmental factors such as the risk of distribution center disruption and demand uncertainty at the demand point. The objective function is obtained by minimizing the model. However, due to the excessive constraints of the objective function, the analysis is complex. Therefore, the total cost model is linearized, and Lagrange multipliers are introduced to relax the specified constraints to obtain a relaxed model. The minimum of this model is used as the solution target to obtain the lower bound solution of the objective function. Based on the lower bound solution and the specified constraints, a fixed optimization strategy is adopted to minimize the value of the upper bound model as the solution target to obtain the upper bound solution of the objective function. According to the multiplier iteration model, the Lagrange multiplier is updated and substituted into the relaxed model. The solution is repeated repeatedly, gradually approaching the upper and lower bounds, thereby reducing the error between the upper and lower bounds, until the solution process meets the preset termination condition, and the location of the drone delivery center is obtained. This method is applied to the actual site selection and construction process of drone logistics networks, providing enterprises with more reliable and economical site planning solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0009] Figure 1 A flowchart of a method for selecting a drone delivery center site that considers disruption risk, provided by an embodiment of the present invention; Figure 2 A schematic diagram of the structure of a three-level logistics network provided by an embodiment of the present invention; Figure 3 A schematic diagram of the structure of a drone delivery center site selection system that takes interruption risks into consideration, provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0010] To make the objectives, technical solutions, and advantages of the embodiments of this application more clear, the technical solutions in the embodiments of this application are clearly and completely described. Obviously, the described embodiments are part of the embodiments of this application, not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0011] Quantitative analysis methods are commonly used in site selection, such as the center of gravity method and the gravity model. The center of gravity method is a static site selection model based on plane geometry. It determines the optimal location of the facility by calculating the weighted coordinates of the demand points. The core goal is to minimize the total transportation cost. The gravity model quantifies the interactive relationship between the facility and the demand points as "attractiveness" and is often used for competitive site selection of commercial outlets. However, existing methods only consider construction costs and transportation costs. This method is not applicable to drone site selection, which is affected by uncertain factors, and the site selection method needs to be improved. Therefore, it is necessary to consider two complex external environmental factors: demand uncertainty and the risk of distribution center interruption to study the site selection problem of drone distribution centers.

[0012] By establishing a mathematical model of objective functions and linear constraints, the optimal facility location is sought while satisfying resource constraints, and the core problem of "cost minimization" or "coverage maximization" is solved. Different from considering only construction costs and transportation costs, this invention introduces the impact of inventory factors on total costs, is more suitable for realistic models, improves the shortcomings of static modeling, and considers the impact of demand fluctuations and node interruptions on the model.

[0013] Before introducing the technical solution of the present application, a brief description of the technology or method used in the technical solution of the present application is first given.

[0014] In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0015] like Figure 1 As shown, an embodiment of the present application provides a method for selecting a drone delivery center site that takes interruption risks into consideration, including: S1: Initialization parameters; the parameters include Lagrange multipliers, initial upper bounds, and initial lower bounds.

[0016] S2: The goal is to minimize the value of the relaxed model and obtain the lower bound solution of the objective function. The relaxed model is a model obtained by linearizing the total cost model of the drone, introducing Lagrange multipliers, and relaxing the specified constraints. The objective function is a function that minimizes the total cost model, that is, a function that solves the minimum value of the total cost model. The total cost model is a model constructed after considering interruption risk and demand uncertainty.

[0017] S3: Based on the lower bound solution and the specified constraints, a fixed optimization strategy is adopted, with the minimum value of the upper bound model as the solution goal, to obtain the upper bound solution of the objective function; the upper bound model is the model obtained after fixing the parameters in the total cost model.

[0018] S4: Determine whether the solution process meets the preset termination conditions.

[0019] S5: If not satisfied, update the Lagrange multiplier according to the multiplier iteration model.

[0020] S6: Substitute the updated Lagrange multiplier into the relaxed model and repeat the solution judgment until the solution process meets the preset termination condition, and obtain the location plan of the drone delivery center to meet the demand point allocation.

[0021] In this embodiment, during the site selection process for a drone delivery center, complex external environmental factors such as the risk of distribution center disruption and demand uncertainty at demand points are considered. A total cost model is constructed to align with actual conditions, making the site selection of the delivery center more reasonable. The objective function is obtained by minimizing the model. However, due to the excessive constraints of the objective function and the complexity of analysis, the total cost model is linearized, Lagrange multipliers are introduced, and the specified constraints are relaxed to obtain a relaxed model. The minimum of this model is used as the solution objective to obtain a lower bound solution for the objective function. Based on the lower bound solution and the specified constraints, a fixed optimization strategy is adopted, with the minimum value of the upper bound model as the solution objective to obtain an upper bound solution for the objective function. The Lagrange multiplier is updated according to the multiplier iteration model, and the updated Lagrange multiplier is substituted into the relaxed model. The solution judgment is repeated repeatedly, gradually approximating the upper and lower bounds, thereby shortening the duality gap between the upper and lower bounds (i.e., the error between the upper and lower bounds), until the solution process meets the preset termination condition, and the site selection of the drone delivery center is obtained. This method is applied to the actual site selection and construction process of drone logistics networks to provide enterprises with more reliable and economical site planning and demand allocation solutions.

[0022] When using the above method to solve the optimal drone delivery center location plan, the construction of the total cost model is first explained.

[0023] Drone transportation provides new impetus for pharmaceutical logistics, such as pharmaceutical cold chain logistics, especially in the field of delivery of time-sensitive emergency materials such as vaccines and blood products, which can not only ensure stability but also reduce time costs. The site selection problem of drone delivery centers for pharmaceutical products considering the risk of interruption can be specifically described as: pharmaceutical products are supplied by manufacturers, who transport the pharmaceutical products to distribution centers, and then drones complete the terminal delivery. Limited by the maximum range of drones, distribution centers can only serve demand points within their effective coverage radius. Different from the two-level transportation in most interruption studies, under this problem, this application expands and constructs a three-level logistics network structure of supplier-distribution center-demand point, such as Figure 2As shown in the figure, two construction options are available for candidate distribution center sites: normal construction (subject to disruption risk, representing an unreliable distribution center); and enhanced protection construction (unaffected by disruption risk, representing a reliable distribution center). This approach mitigates the impact of disruption risk through protective measures, but incurs higher construction costs. The disruption probability of an unreliable distribution center is solely dependent on the location of the candidate site, which is independent of each other. A candidate site can be a hospital, large pharmacy, or large medical institution, while a demand point can be a small medical institution, clinic, or health station. When a disruption occurs, the distribution center's service capabilities are completely lost, and the demand point must reselect a reliable downstream distribution center for service. The demand point's demand is uncertain and is described using triangular fuzzy numbers.

[0024] Specifically, triangular fuzzy number theory is a key concept in fuzzy mathematics, primarily used to process uncertain and ambiguous information in the real world. It provides a concise and intuitive mathematical tool to represent and operate on such fuzzy information. It is commonly used in fields such as supply chain management, fuzzy prediction and control, and engineering research. The principles of triangular fuzzy numbers are as follows: Suppose some uncertain information is , ,in and are the lower and upper bounds of fuzzy numbers, is the most likely number. Its membership function is , Clarify the fuzzy number and convert it into an interval based on the confidence level α , , , uncertain information , confidence level ,when When , it means that all uncertainties within the range of fuzzy numbers are fully considered. When , it means that only the most likely value of the fuzzy number is considered. In practical applications, the choice should be based on the problem.

[0025] This application makes the following assumptions: Assumption 1: Each demand point is assigned a primary distribution center (either a reliable facility or an unreliable facility). When the primary distribution center is a reliable distribution center, there is no backup distribution center. When the primary distribution center is an unreliable distribution center, there is a risk of interruption, and a backup distribution center is assigned, and the backup distribution center is also a reliable distribution center. This assignment method ensures that the needs of the demand point are met.

[0026] Assumption 2: A distribution center is served by a single supply source with unlimited production capacity.

[0027] Assumption 3: Each candidate site can only choose one type of distribution center for construction, and there is no capacity limit for the distribution center built.

[0028] Assumption 4: Consider the drone's flight endurance and impose mileage constraints during flight planning. Because pharmaceutical product delivery is typically small-batch and lightweight, payload constraints can be ignored, meaning a single flight can complete the delivery mission.

[0029] A model is constructed with the goal of minimizing the total cost, which includes the cost of the facility distribution center, product storage inventory costs, and logistics transportation service costs.

[0030] Consider building a reliable distribution center or an unreliable distribution center at candidate location j. The cost of building a distribution center at the candidate location is : (1) Among them, J represents the set of candidate locations for drone delivery centers; represents the fixed cost of opening a reliable distribution center at candidate location j, j∈J, represents the fixed cost of opening an unreliable distribution center at candidate location j, ; It is 1 when a reliable distribution center is built at candidate location j, otherwise it is 0; It is 1 when an unreliable distribution center is built at candidate location j, and 0 otherwise.

[0031] Transfer and store products at the distribution center at candidate location j, and the product storage inventory costs : (2) Where I represents the supply source set, indexed by i, i∈I; Indicates candidate location The unit commodity inventory rate of the distribution center at Indicates the source of supply To the candidate site The volume of merchandise shipped from distribution centers in the United States.

[0032] When candidate location j is an unreliable distribution center, an interruption occurs, which means that the distribution center is completely ineffective. According to assumption 1, the demand is assigned. The transportation service cost is related to the distance and quantity. The unit cost of the same distribution center is different when it is used as the main / backup distribution center. The transportation service cost of the logistics network is : (3) in, represents the unit service cost of the supply source i to the distribution center at candidate location j; Indicates the source of supply The transportation distance to the distribution center at candidate location j; Indicates the source of supply It is 1 when providing service to the distribution center at candidate location j, otherwise it is 0; K represents the set of demand points, indexed as k, k∈K; Indicates that the distribution center at candidate location j is the main distribution center service demand point Unit cost; Represents the distribution center at candidate location j to the demand point transportation distance; Indicates demand points the demand for goods; It is 1 when the reliable distribution center at candidate location j is the main distribution center for demand point k, otherwise it is 0; represents the interruption probability of an unreliable distribution center at candidate location v, 0≤ ≤1, v∈J; represents the probability of interruption of a reliable distribution center at candidate location j, =0; Indicates that the unreliable distribution center at candidate location v is the main distribution center service demand point Unit cost; Represents the unreliable distribution center at candidate location v to the demand point transportation distance; It is 1 when the unreliable distribution center at candidate location v is the primary distribution center and the reliable distribution center at candidate location j is the backup distribution center; otherwise, it is 0. represents the unit cost of the distribution center at candidate location j as a backup distribution center to serve demand point k, ; If demand point k is served by the unreliable distribution center at candidate location v as the main distribution center and the reliable distribution center at candidate location j as the backup distribution center, when the unreliable distribution center at candidate location v is interrupted, it will be served by the reliable distribution center at candidate location j, v≠j.

[0033] Therefore, the total cost model of the UAV is constructed after considering the interruption risk and demand uncertainty. (4) Then the objective function is min C, which means taking the minimum value of the total cost model C.

[0034] The preset constraints of the objective function include: (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), Among them, R represents the maximum range of the drone, M represents a preset positive real number, It is 1 when an unreliable distribution center is built at candidate location v, and 0 otherwise.

[0035] For the above constraints, constraint (5) limits a candidate site to build at most one type of facility, i.e., one reliable facility or one unreliable facility; there are two cases for the demand allocation of demand points, constraint (6) indicates that the demand of a demand point can be allocated to a reliable primary facility, or an unreliable primary facility and a reliable backup facility; constraint (7) indicates that if a facility is only allocated to one level of facilities, the facility is reliable; constraints (8) and (9) indicate that if a demand point is allocated to two levels of facilities, the primary facility is unreliable and the backup facility is reliable; constraints ( 10) means that at least one reliable facility must be opened to meet the demand; Constraints (11), (12) and (13) are to meet the flight endurance constraints of the drone. When a service occurs between the distribution center and the demand point, the constraint must be met, that is, the distance must be less than or equal to the maximum range of the drone; Constraint (14) ensures that the supply source only serves the candidate locations with distribution centers; Constraint (15) ensures that the demand of each distribution center is met, that is, the amount of goods delivered by the supply source to the distribution center is not less than the demand of customers who need the distribution center to supply goods; Constraint (16) defines the value range of each decision variable.

[0036] The following is a detailed description of each step to provide a more detailed understanding of the process of determining the site selection for a drone delivery center.

[0037] S1: Initialization parameters; the parameters include Lagrange multipliers, initial upper bounds, and initial lower bounds.

[0038] Initialize the Lagrange multiplier, for example, let the number of iterations n = 1, the initial upper bound = , initial lower bound = , the maximum number of iterations (i.e. the preset number of iterations) , error tolerance , preset step size adjustment factor .

[0039] S2: The goal is to minimize the value of the relaxed model and obtain the lower bound solution of the objective function. The relaxed model is a model obtained by linearizing the total cost model of the drone, introducing Lagrange multipliers, and relaxing the specified constraints. The objective function is a function for solving the minimum value of the total cost model, which is a model constructed after considering interruption risk and demand uncertainty.

[0040] By introducing Lagrange multipliers, the "hard" constraints (i.e., specified constraints) that make the problem difficult to solve are relaxed, resulting in a relaxed problem that is relatively easy to solve. The relaxed solution provides a lower bound, based on which a feasible solution to the original problem is constructed, resulting in an upper bound. By continuously narrowing the duality gap through multiplier updates, the two bounds are continuously tightened until convergence to the optimal solution. The algorithm flow is as follows: Figure 1 shown.

[0041] The objective function is nonlinear, so the constraints Perform linearization processing, let ; Add constraints: (17) (18) (19) The relaxed specified constraints include the constraints (6) and (15) in the above preset constraints, and the Lagrange multiplier is introduced. and Lagrange multipliers , respectively corresponding to the relaxation of the specified constraints, and the relaxation model is obtained: (20) The relaxation problem is to find the minimum value of the above relaxation model.

[0042] By merging the relaxed models, we can get: (twenty one) make , , , then the relaxed model is simplified to: (twenty two) st(5),(7)-(14),(16)-(19) The solution to the Lagrange relaxation problem is a lower bound of the solution to the original problem. By introducing the Lagrange multiplier, the minimum value of the objective function is maximized, providing a lower bound solution to the original problem.

[0043] Constraint (10) is a redundant constraint to tighten the Lagrangian constraint. It can be obtained by using constraints (6)-(9). When analyzing the Lagrangian relaxation problem, this constraint is ignored. The last term in the simplified relaxation model (Formula 22) is a constant term and is not considered in the optimization problem. The relaxation problem can be solved according to It is decomposed into a series of sub-problems. For each candidate location, a decision needs to be made. There are three possibilities: not to build a facility, to build an unreliable facility, or to build a reliable facility. , according to the opening conditions of the facilities, the relaxation problem is decomposed into sub-problems that are easy to solve: (twenty three) When discussing the different situations, first analyze the relaxation model. Two items. When candidate site j does not establish a distribution center , the two items are 0; when the candidate Establish a distribution center, there is always a supply source ,make , ,Right now For the remaining terms in the relaxed model, the following are true: Case 1: When no distribution center is built at candidate location j, that is, , according to the constraints , at this time the values ​​of the remaining terms of the relaxation model ,illustrate When no facilities are built, there is no impact on the objective function and the relaxation model value is zero. Therefore, only the case of building facilities needs to be considered.

[0044] Case 2: When an unreliable distribution center is built at candidate location j, that is, , according to the constraints , at this time the values ​​of the remaining terms of the relaxation model .

[0045] Case 3: When a reliable distribution center is built at candidate location j, that is , then the values ​​of the remaining terms in the relaxed model are: and The values ​​are as follows: .

[0046] Solve for the minimum of the relaxed model.

[0047] when , corresponding to the first case; when When , it corresponds to the second case; when , which corresponds to the third case.

[0048] Reconsider constraint (10), let represents the set of candidate locations where reliable distribution centers are established; Indicates the set of candidate locations where unreliable distribution centers are established; represents the set of candidate sites that do not have any facilities. According to the constraint (10), it is required to have at least one reliable facility. , at this point, the lower bound has been reached; otherwise, it is necessary to select a candidate location from JU and JN to open a reliable distribution center and determine the location of the reliable distribution center: make , ;make , ;if , , ;otherwise , .

[0049] By solving the Lagrangian relaxation subproblem, we can obtain the lower bound: .

[0050] S3: Based on the lower bound solution and the specified constraints, a fixed optimization strategy is adopted, with the minimum value of the upper bound model as the solution goal, to obtain the upper bound solution of the objective function; the upper bound model is the model obtained after fixing the parameters in the total cost model.

[0051] When solving a Lagrangian relaxation problem, if the resulting solution is a feasible solution to the original problem, an upper bound is obtained in addition to the lower bound. However, due to the relaxation of some constraints, this is generally infeasible. Therefore, a fixed optimization method is used to find a feasible solution to the original problem, which is used to provide an upper bound. The fixed optimization method is a large neighborhood search heuristic algorithm that fixes the values ​​of some variables based on the Lagrangian relaxation solution and optimizes the remaining parameters to obtain the optimal solution.

[0052] S31: According to the preset lemma, the lower bound solution is modified to obtain a feasible solution that satisfies the relaxed specified constraints.

[0053] In the supplier and demand point allocation stage, the preset lemmas include: Lemma 1: If there is a reliable distribution center at a candidate location at the demand point k as its backup distribution center, then , JG represents the set of candidate locations for establishing reliable distribution centers, and argmin is used to select the facility with the minimum transportation service cost; Lemma 2: Assume , if there is a candidate location at demand point k If the unreliable distribution center is used as the main distribution center, , JU represents the set of candidate locations for establishing unreliable distribution centers, Indicates candidate location The distribution center at the location serves as a backup distribution center to serve the demand point The unit cost, Indicates candidate location Distribution center to demand point transportation distance; Lemma 3: Assume , , ,like , then you should select the candidate The reliable distribution center at the location is selected as the main distribution center, otherwise the candidate location is selected. The unreliable distribution center at the candidate location is used as its main distribution center. A reliable distribution center at a certain location is used as its backup distribution center; among them, Indicates candidate location The unreliable distribution center at the location serves as the main distribution center service demand point The unit cost, Indicates candidate location Unreliable distribution centers to demand points transportation distance, Indicates candidate location The probability of an outage at an unreliable distribution center, Indicates candidate location The unit cost of the reliable distribution center at location as a backup distribution center to serve demand point k is, Indicates candidate location Reliable distribution centers to demand points transportation distance, Indicates candidate location Reliable distribution centers at the main distribution center serve as demand points The unit cost, Indicates candidate location Reliable distribution centers to demand points transportation distance.

[0054] Lemma 4: If the distribution center is supplied by the source Provide services, then .

[0055] Through the above preset lemma, the candidate sites are screened, the scope is narrowed, and the lower bound solution is corrected. If the lower bound solution is not within the narrowed scope, then consider reselecting a feasible solution from the narrowed scope.

[0056] S32: Fix the parameters and location decisions obtained in the feasible solution, and then reselect the remaining parameters to satisfy the objective function and obtain the upper bound solution.

[0057] Considering that fixed optimization methods take a long time to solve large-scale problems and are prone to falling into local optima, we propose a Lagrangian relaxation solution, retaining the decision to open facilities and reselecting allocations that do not meet the constraints. Based on the four lemmas above, we allocate demand points and select suppliers within the open facilities. The objective function corresponding to this feasible solution is as follows, yielding an upper bound model for the original problem: in, Indicates the source of supply To the candidate site The volume of goods transported by the distribution center, Indicates the source of supply The unit service cost to the distribution center at candidate location j is, Indicates the source of supply The transportation distance to the distribution center at candidate location j.

[0058] In order to further improve the quality of feasible solutions, a fixed optimization strategy is adopted: on this basis, 70%-80% of the decision variables are fixed, and the solver is used to solve the remaining simple subproblems. Repeated verification is carried out to determine the appropriate initial fixed values, and the solution with the smallest objective value is selected as the improved upper bound.

[0059] S4: Determine whether the solution process meets the preset termination conditions. This step includes: S41: Determine whether the upper and lower bound error values ​​are less than the error tolerance or whether the number of Lagrange multiplier update iterations is greater than the preset number of iterations or whether the Lagrange step size adjustment factor is less than the preset step size adjustment factor. The upper and lower bound error values ​​are the difference between the minimum upper bound obtained in the iteration process and the maximum lower bound obtained in the iteration process, and then divided by the maximum lower bound obtained in the iteration process. The lower bound is the minimum value of the relaxed model, and the upper bound is the minimum value of the upper bound model. The upper and lower bound error values ​​= , UB represents the smallest upper bound obtained during the iteration process, and LB represents the largest lower bound obtained during the iteration process.

[0060] S42: When the upper and lower bound error values ​​are less than the error tolerance or the number of Lagrange multiplier update iterations is greater than the preset number of iterations or the Lagrange step size adjustment factor is less than the preset step size adjustment factor, it is determined that the preset termination condition is met.

[0061] S43: Otherwise, it is determined that the preset termination condition is not satisfied.

[0062] S5: If the preset termination condition is not met, the Lagrange multiplier is updated according to the multiplier iteration model.

[0063] The multiplier iteration model is Where A is the Claude damping constant, which can effectively prevent the iteration from looping. Set A to 0.3; Lagrange multiplier and The directions at the nth iteration are respectively denoted as and ; The directions at the 0th iteration are respectively recorded as and , the Lagrange multipliers after the n-1th update are and ; The Lagrange multipliers after the nth update are and .

[0064] Lagrangian step size adjustment factor ; Among them, UB represents the smallest upper bound obtained during the iteration process, and LB represents the largest lower bound obtained during the iteration process. represents the lower bound obtained at the nth iteration, Is to satisfy 0< A scalar ≤ 2.

[0065] S6: Substitute the updated Lagrange multiplier into the relaxed model and repeat the solution judgment until the solution process meets the preset termination condition, and obtain the location of the drone distribution center to meet the demand point allocation (i.e., the demand points served by each distribution center). This step includes: If the lower bound stagnates during the specified number of iterations, Halve it, and then redefine the Lagrange step size adjustment factor, Usually by setting To be determined.

[0066] Or, if the lower bound stagnates during the specified number of iterations, the average subgradient is used instead of the current iteration direction to re-update the Lagrange multiplier. The stagnation phenomenon is when the change of the lower bound is less than or equal to , the average subgradient is the average value of the iteration directions in T historical iterations adjacent to the current iteration.

[0067] Specifically, during the iteration process, the upper and lower bounds of each iteration are recorded. When the lower bound During multiple iterations (e.g. 15 iterations), a stagnation phenomenon occurs, i.e. Change ≤ , change the sub-gradient direction, use the average sub-gradient, and calculate the average direction of the most recent T iterations, such as , the rest of the formulas remain unchanged, and iterate several times to observe the changes in the lower bound solution.

[0068] After multiple iterations, the preset termination condition is reached. At this time, the upper bound and the lower bound approach each other. A limited number of candidate sites can be determined from the approximated upper and lower bounds. From the limited candidate sites, the candidate site that meets the objective function is selected to determine the final drone delivery center site selection plan and demand allocation plan.

[0069] In summary, compared with the existing technology, the present invention has the following beneficial effects: 1. A three-level logistics network model was constructed, incorporating inventory costs into the objective function. The location optimization problem of drone delivery centers was explored, modeled and solved, showing that a solution including two types of facilities is feasible and beneficial. At the same time, the primary and backup delivery center service model was adopted, which not only solved the problem of insufficient reliability of single-level service, but also avoided the complexity brought by multi-level service.

[0070] 2. The impact of both demand uncertainty and distribution center disruption risks on the logistics network was described in detail, providing a clear approach for enterprises to cope with the impact of uncertainty risks and helping to establish a reliable distribution network. A site selection model that takes uncertainty into account was constructed, which is an extension of factors such as drone energy consumption and airspace restrictions. The expanded site selection model is more realistic, and the site selection plan determined by this model is more reasonable, significantly enhancing the reliability and robustness of the cold chain drone distribution network under the dual influence of supply-side disruptions and demand-side fluctuations.

[0071] 3. Improvements have been made to the Lagrangian relaxation algorithm used to solve complex problems, with a focus on improving the subgradient algorithm and the feasible solution generation mechanism. This can shorten solution time and improve solution quality when solving large-scale examples.

[0072] like Figure 3 As shown, an embodiment of the present application provides a drone delivery center site selection system that considers interruption risks, including: The parameter initialization module 100 is used to initialize parameters; the parameters include Lagrange multipliers.

[0073] The lower bound solution analysis module 200 is used to obtain a lower bound solution to the objective function by minimizing the value of the relaxed model; the relaxed model is a model obtained by linearizing the total cost model of the drone, introducing Lagrange multipliers, and relaxing the specified constraints; the objective function is a function that minimizes the total cost model, and the total cost model is a model constructed after considering interruption risk and demand uncertainty.

[0074] The upper bound solution analysis module 300 is used to adopt a fixed optimization strategy based on the lower bound solution and specified constraints, with the minimum value of the upper bound model as the solution goal, to obtain the upper bound solution of the objective function; the upper bound model is a model obtained by fixing the parameters in the total cost model.

[0075] The loop determination module 400 is used to determine whether the solution process meets a preset termination condition.

[0076] The multiplier updating module 500 is used to update the Lagrange multiplier according to the multiplier iteration model if it is not satisfied.

[0077] The loop analysis module 600 is used to substitute the updated Lagrange multiplier into the relaxation model, and perform solution judgment in a loop until the solution process meets the preset termination condition, thereby obtaining the location of the drone distribution center to meet the demand point allocation.

[0078] In this embodiment, the beneficial effects of the drone delivery center site selection system considering the interruption risk are similar to the beneficial effects of the drone delivery center site selection method considering the interruption risk described above, and will not be repeated here.

[0079] An embodiment of the present application provides an electronic device comprising a memory and a processor; the memory is used to store a computer program; and the processor is used to implement the drone delivery center site selection method that considers the risk of interruption as described above when executing the computer program.

[0080] An embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for selecting a drone delivery center site that takes into account the risk of interruption as described above is implemented.

[0081] In this embodiment, the beneficial effects of the electronic device and the computer-readable storage medium are similar to the beneficial effects of the above-mentioned drone delivery center site selection method considering the interruption risk, and will not be repeated here.

[0082] An electronic device that can serve as a server or client of the present application will now be described, which is an example of a hardware device that can be applied to various aspects of the present application. Electronic devices are intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present application described and / or required herein.

[0083] Electronic devices include a computing unit that can perform various appropriate actions and processes based on computer programs stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). RAM can also store various programs and data required for device operation. The computing unit, ROM, and RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus.

[0084] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware through a computer program. The program can be stored in a computer-readable storage medium, and when executed, the program can include the processes in the above-described method embodiments. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM). In this application, the units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network elements. Some or all of these units can be selected based on actual needs to achieve the objectives of the embodiments of this application. Furthermore, the functional units in each embodiment of this application can be integrated into a single processing unit, each unit can exist physically separately, or two or more units can be integrated into a single unit. These integrated units can be implemented in either hardware or software functional units.

[0085] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0086] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for selecting a drone delivery center location considering disruption risk, characterized in that: include: Initialization parameters; The parameters include Lagrange multipliers; Taking the minimum value of the relaxed model as the solution goal, the lower bound solution of the objective function is obtained; The relaxation model is a model obtained by linearizing the total cost model of the drone, introducing Lagrange multipliers, and relaxing the specified constraints. The objective function is a function that minimizes the total cost model, which is a model constructed after considering interruption risk and demand uncertainty. Based on the lower bound solution and the specified constraints, a fixed optimization strategy is adopted to minimize the value of the upper bound model and obtain the upper bound solution of the objective function. The upper bound model is a model obtained by fixing the parameters in the total cost model; Determine whether the solution process meets the preset termination conditions; If it is not satisfied, the Lagrange multiplier is updated according to the multiplier iteration model; The updated Lagrange multiplier is substituted into the relaxed model, and the solution judgment is repeated until the solution process meets the preset termination condition, and the location of the drone delivery center is obtained.

2. The method for selecting a drone delivery center site considering interruption risk according to claim 1, wherein: The lower bound is the minimum of the relaxed model, and the upper bound is the minimum of the upper bound model; The determination of whether the solution process satisfies the preset termination condition includes: Determine whether the upper and lower bound error values ​​are less than the error tolerance, where the upper and lower bound error values ​​are the difference between the minimum upper bound obtained during the iteration and the maximum lower bound obtained during the iteration, divided by the maximum lower bound obtained during the iteration; When the upper and lower bound errors are less than the error tolerance, it is determined that the preset termination condition is met; Otherwise, it is determined that the preset termination condition is not met.

3. The method for selecting a drone delivery center site considering interruption risk according to claim 1, wherein: The determination of whether the solution process satisfies the preset termination condition includes: Whether the number of Lagrange multiplier update iterations is greater than the preset number of iterations or whether the Lagrange step size adjustment factor is less than the preset step size adjustment factor; When the number of Lagrange multiplier update iterations is greater than the preset number of iterations or the Lagrange step size adjustment factor is less than the preset step size adjustment factor, it is determined that the preset termination condition is met; Otherwise, it is determined that the preset termination condition is not met.

4. The method for selecting a drone delivery center site considering interruption risk according to claim 1, wherein: Assume that a demand point is configured with a primary distribution center. When the primary distribution center is a reliable distribution center, there is no backup distribution center. When the primary distribution center is an unreliable distribution center, a backup distribution center is configured, and the backup distribution center is a reliable distribution center. Cost of building a distribution center at the candidate site : ， Among them, J represents the set of candidate locations for drone delivery centers; represents the fixed cost of opening a reliable distribution center at candidate location j, j∈J, represents the fixed cost of opening an unreliable distribution center at candidate location j, ; It is 1 when a reliable distribution center is built at candidate location j, otherwise it is 0; It is 1 when an unreliable distribution center is built at candidate site j, otherwise it is 0; Product storage and inventory costs after the distribution center is built in the candidate site : ， Where I represents the supply source set, indexed by i, i∈I; represents the unit commodity inventory rate of the distribution center at candidate location j, represents the quantity of goods transported from supply source i to the distribution center at candidate location j; Transportation service costs of the logistics network : ， in, represents the unit service cost of the supply source i to the distribution center at candidate location j; Indicates the source of supply The transportation distance to the distribution center at candidate location j; Indicates the source of supply It is 1 when providing service to the distribution center at candidate location j, otherwise it is 0; K represents the set of demand points, indexed as k, k∈K; Indicates that the distribution center at candidate location j is the main distribution center service demand point Unit cost; Represents the distribution center at candidate location j to the demand point transportation distance; Indicates demand points the demand for goods; It is 1 when the reliable distribution center at candidate location j is the main distribution center for demand point k, otherwise it is 0; represents the interruption probability of an unreliable distribution center at candidate location v, 0≤ ≤1, v∈J; Indicates that the unreliable distribution center at candidate location v is the main distribution center service demand point Unit cost; Represents the unreliable distribution center at candidate location v to the demand point transportation distance; It is 1 when the unreliable distribution center at candidate location v is the primary distribution center and the reliable distribution center at candidate location j is the backup distribution center; otherwise, it is 0. represents the unit cost of the distribution center at candidate location j as a backup distribution center to serve demand point k, If demand point k is served by the unreliable distribution center at candidate location v as the primary distribution center and the reliable distribution center at candidate location j as the backup distribution center, and only when the unreliable distribution center at candidate location v is disconnected will it be served by the reliable distribution center at candidate location j, v≠j; The total cost model of the drone is constructed after considering the disruption risk and demand uncertainty: ， The objective function is ; The preset constraints of the objective function include: ， ， ， ， ， ， ， ， ， ， ， ， Among them, R represents the maximum range of the drone, M represents a preset positive real number, It is 1 when an unreliable distribution center is built at candidate location v, and 0 otherwise.

5. The method for selecting a drone delivery center site considering interruption risk according to claim 4, wherein: The specified constraints that are relaxed include: ， ， Specify the constraints Perform linearization and let ; Add constraints: , , ; Introducing Lagrange multipliers and Lagrange multipliers , respectively corresponding to the relaxation of the specified constraints, and the relaxation model is obtained: ， in, , , ， Ignore the preset constraints for now , for the relaxed model Two items, the following situations: ； For the remaining terms in the relaxed model, the following are true: When no distribution center is built at candidate location j, the values ​​of the remaining items in the relaxation model are zero; When an unreliable distribution center is built at candidate location j, the values ​​of the remaining items in the relaxation model are ; When a reliable distribution center is built at candidate location j, the values ​​of the remaining items in the relaxation model are ， and The values ​​are as follows: ； make represents the set of candidate locations where reliable distribution centers are established; Indicates the set of candidate locations where unreliable distribution centers are established; Represents a set of candidate sites that do not have any facilities, reconsidering the preset constraints , requiring the opening of at least one reliable distribution center; like , it means that the lower bound has been reached; Otherwise, select a candidate location between JU and JN to open a reliable distribution center. Determine the location of the reliable distribution center: make , ;make , ;if , , ;otherwise , ; The lower bound is obtained by solving the minimum value of the relaxed model: 。 6. The method for selecting a drone delivery center site considering interruption risk according to claim 4, wherein: Based on the lower bound solution and the specified constraints, a fixed optimization strategy is adopted to minimize the value of the upper bound model as the solution goal, and the upper bound solution of the objective function is obtained, including: The lower bound solution is modified according to the preset lemma to obtain a feasible solution that satisfies the relaxed specified constraints; The parameters and location decisions obtained in the feasible solution are fixed, and the remaining parameters are reselected to satisfy the objective function and obtain the upper bound.

7. The method for selecting a drone delivery center site considering interruption risk according to claim 6, wherein: The preset lemma includes: Lemma 1: If there is a reliable distribution center at a candidate location at the demand point k as its backup distribution center, then , JG represents the set of candidate locations for establishing reliable distribution centers; Lemma 2: Assume , if there is a candidate location at demand point k If the unreliable distribution center is used as the main distribution center, , JU represents the set of candidate locations for establishing unreliable distribution centers, Indicates candidate location The distribution center at the location serves as a backup distribution center to serve the demand point The unit cost, Indicates candidate location Distribution center to demand point transportation distance; Lemma 3: Assume , , ,like , then you should select the candidate The reliable distribution center at the location is selected as the main distribution center, otherwise the candidate location is selected. The unreliable distribution center at the candidate location is used as its main distribution center. A reliable distribution center at a certain location is used as its backup distribution center; among them, Indicates candidate location The unreliable distribution center at the location serves as the main distribution center service demand point The unit cost, Indicates candidate location Unreliable distribution centers to demand points transportation distance, Indicates candidate location The probability of an outage at an unreliable distribution center, Indicates candidate location The unit cost of the reliable distribution center at location as a backup distribution center to serve demand point k is, Indicates candidate location Reliable distribution centers to demand points transportation distance, Indicates candidate location Reliable distribution centers at the main distribution center serve as demand points The unit cost, Indicates candidate location Reliable distribution centers to demand points transportation distance; Lemma 4: If the distribution center is supplied by the source Provide services, then .

8. The method for selecting a drone delivery center site considering interruption risk according to claim 7, wherein: The upper bound model is ， in, Indicates the source of supply To the candidate site The volume of goods transported by the distribution center, Indicates the source of supply The unit service cost to the distribution center at candidate location j is, Indicates the source of supply The transportation distance to the distribution center at candidate location j.

9. The method for selecting a drone delivery center site considering interruption risk according to claim 8, wherein: The multiplier iteration model is ， ， Where A is the Claude damping constant; Lagrange multiplier and The directions at the nth iteration are respectively denoted as and ; The directions at the 0th iteration are respectively recorded as and , the directions at the n-1th iteration are respectively recorded as and ; The Lagrange multipliers after the n-1th update are and ; The Lagrange multipliers after the nth update are and ; Lagrangian step size adjustment factor ; Among them, UB represents the minimum upper bound obtained during the iteration process, represents the lower bound obtained at the nth iteration, Is to satisfy 0< A scalar ≤ 2.

10. A drone delivery center site selection system considering interruption risk, characterized in that: include: A parameter initialization module, used for initializing parameters; the parameters include Lagrange multipliers; A lower bound solution analysis module is used to obtain a lower bound solution to the objective function by minimizing the value of a relaxed model; the relaxed model is obtained by linearizing the total cost model of the drone, introducing Lagrange multipliers, and relaxing the specified constraints; the objective function is a function that minimizes the total cost model, which is constructed after considering interruption risk and demand uncertainty; The upper bound solution analysis module is used to obtain the upper bound solution of the objective function by adopting a fixed optimization strategy based on the lower bound solution and specified constraints, with the minimum value of the upper bound model as the solution goal; The upper bound model is a model obtained by fixing the parameters in the total cost model; A loop judgment module is used to judge whether the solution process meets the preset termination condition; A multiplier update module is used to update the Lagrange multiplier according to the multiplier iteration model if it is not satisfied; The cyclic analysis module is used to substitute the updated Lagrange multiplier into the relaxed model and perform solution judgment cyclically until the solution process meets the preset termination conditions to obtain the location of the drone delivery center.

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