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

Abstract

The application provides a kind of unmanned aerial vehicle distribution center site selection method and system considering interruption risk, it is related to unmanned aerial vehicle logistics network technical field.In the process of site selection, the interruption risk of distribution center and the demand uncertainty of demand point and other external factors are considered, a network total cost model containing construction cost, inventory cost and transportation cost is constructed, the minimum of the model is taken as objective function, the total cost model is linearized, Lagrange multiplier is introduced, specified constraint condition is relaxed, the minimum of the model is solved, lower bound solution is obtained, on the basis of lower bound solution and specified constraint condition, fixed optimization strategy is used, the minimum of upper bound model is solved, upper bound solution is obtained;According to multiplier iteration model, update Lagrange multiplier, put the updated Lagrange multiplier into the relaxation model, solve and judge in cycle, until the solution process meets the preset termination condition, the site selection scheme of unmanned aerial vehicle distribution center is obtained, to meet the demand point distribution, so that distribution center site selection is more reasonable.

Description

Technical Field

[0001] This invention relates to the field of drone logistics network technology, and more specifically, to a method and system for selecting drone delivery center locations that takes into account the risk of disruption. Background Technology

[0002] Logistics networks encompass diverse organizations and facilities, making them highly vulnerable to disruptions caused by natural disasters, trade conflicts, technological malfunctions, public health emergencies, and other natural and man-made factors. For instance, emerging diseases create high environmental uncertainty, necessitating unpredictable isolation in different regions and potentially causing significant disruptions to the supply chain. For temperature-sensitive, short-shelf-life pharmaceuticals, transportation time is limited, and in such unforeseen circumstances, drug quality and transportation cannot be guaranteed. While cold chain storage and transportation of pharmaceuticals can extend transit time, cold chain logistics has strict requirements for timeliness and temperature control. Drones, equipped with temperature control devices and protective mechanisms, demonstrate significant potential as an emerging delivery tool in terms of flexibility and cost-effectiveness in cold chain distribution, but while highlighting their advantages, they still face the influence of uncertainties.

[0003] Network infrastructure site selection is a strategic decision, irreversible once completed. Site selection is based on logistics requirements, considering the type of goods transported and the target customers, to choose suitable candidate locations. Previous research on drone delivery has focused primarily on the characteristics of the drones themselves and geographical scenarios, lacking research on complex external environmental factors. Summary of the Invention

[0004] The problem that this invention aims to solve is that existing site selection methods lack research on complex external environmental factors.

[0005] To address the aforementioned problems, in a first aspect, the present invention provides a method for selecting drone delivery center locations that considers the risk of disruption, comprising:

[0006] Initialization parameters; these parameters include Lagrange multipliers;

[0007] The goal is to minimize the value of the relaxation model, thereby obtaining the lower bound solution of the objective function. The relaxation model is obtained by linearizing the total cost model of the UAV, 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 the risk of interruption and the uncertainty of demand.

[0008] Based on the lower bound solution and specified constraints, a fixed optimization strategy is adopted, with the goal of minimizing the value of the upper bound model, to obtain the upper bound solution of the objective function; the upper bound model is the model obtained by fixing the parameters in the total cost model.

[0009] Determine whether the solution process meets the preset termination condition;

[0010] If not satisfied, then update the Lagrange multipliers according to the multiplier iteration model;

[0011] The updated Lagrange multipliers are substituted into the relaxation model, and the solution is iterated until the solution process meets the preset termination condition, thus obtaining the location of the drone delivery center.

[0012] Secondly, the present invention also provides a drone delivery center location selection system that takes into account the risk of disruption, comprising:

[0013] A parameter initialization module is used to initialize parameters; the parameters include Lagrange multipliers.

[0014] The lower bound solution analysis module is used to obtain the lower bound solution of the objective function by minimizing the value of the relaxation model. The relaxation model is obtained by linearizing the total cost model of the UAV, introducing Lagrange multipliers, and relaxing the specified constraints. The objective function is a function of the lowest glide total cost model, which is a model constructed after considering the risk of interruption and the uncertainty of demand.

[0015] 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 goal of minimizing the value of the upper bound model; the upper bound model is the model obtained by fixing the parameters in the total cost model.

[0016] The loop judgment module is used to determine whether the solution process meets the preset termination condition;

[0017] The multiplier update module is used to update the Lagrange multipliers according to the multiplier iteration model if the conditions are not met.

[0018] The loop analysis module is used to substitute the updated Lagrange multipliers into the relaxation model and perform loop calculations until the solution process meets the preset termination condition, thus obtaining the location of the drone delivery center.

[0019] This invention provides a method and system for selecting drone delivery center locations that considers the risk of disruption. Compared with existing technologies, it has the following advantages:

[0020] In the process of selecting locations for drone delivery centers, complex external environmental factors such as the risk of delivery center disruptions and the uncertainty of demand at demand points are considered. A total cost model is constructed to closely match the actual situation, making the location of the delivery center more reasonable. The objective function is obtained by minimizing the value of this model. However, due to the excessive constraints of the objective function, the analysis is complex. Therefore, the total cost model is linearized by introducing Lagrange multipliers and relaxing the specified constraints to obtain a relaxed model. The lower bound solution of the objective function is obtained by minimizing the value of the relaxed model. 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 the upper bound solution of the objective function. According to the multiplier iterative model, the Lagrange multipliers are updated and substituted into the relaxed model. The solution is iterated and judged to gradually bring the upper and lower bounds closer, thereby shortening the error value 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 location selection and construction process of drone logistics networks, providing enterprises with a more reliable and economical location planning solution. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 A flowchart illustrating a method for selecting a drone delivery center location that considers the risk of disruption, provided as an embodiment of the present invention;

[0023] Figure 2 This is a schematic diagram of the structure of a three-tier logistics network provided in an embodiment of the present invention;

[0024] Figure 3 This is a schematic diagram of a drone delivery center location selection system that takes into account the risk of disruption, provided as an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application are described clearly and completely. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0026] Quantitative analysis methods are commonly used for 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, determining the optimal location of a facility by calculating the weighted coordinates of demand points, with the core objective of minimizing total transportation costs. The gravity model quantifies the interaction between the facility and demand points as an "attraction factor," and is often used for competitive site selection of commercial outlets. However, existing methods only consider construction and transportation costs, making them unsuitable for drone site selection facing uncertainties. Therefore, improvements to the site selection methods are needed. Thus, the study of drone delivery center site selection should consider two complex external environmental factors: demand uncertainty and the risk of distribution center disruption.

[0027] By establishing a mathematical model with objective function and linear constraints, the optimal facility location is found under resource constraints, and the core problem of "cost minimization" or "coverage maximization" is solved. Unlike simply considering construction and transportation costs, this invention introduces the impact of inventory factors on total cost, making it more applicable to real-world models, improving the shortcomings of static modeling, and considering the impact of demand fluctuations and node interruptions on the model.

[0028] Before introducing the technical solution of this application, the technology or method used in the technical solution of this application will be briefly described.

[0029] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0030] like Figure 1 As shown in the figure, this application provides a method for selecting a drone delivery center location that considers the risk of disruption, including:

[0031] S1: Initialization parameters; the parameters include Lagrange multipliers, initial upper bound, and initial lower bound.

[0032] S2: The goal is to minimize the value of the relaxation model to obtain the lower bound solution of the objective function; the relaxation model is obtained by linearizing the total cost model of the UAV, introducing Lagrange multipliers, and relaxing the specified constraints; the objective function is the function that minimizes the total cost model, that is, the function that solves the minimum value of the total cost model, and the total cost model is the model constructed after considering the risk of interruption and the uncertainty of demand.

[0033] S3: Based on the lower bound solution and specified constraints, a fixed optimization strategy is adopted, with the goal of minimizing the value of the upper bound model, to obtain the upper bound solution of the objective function; the upper bound model is the model obtained by fixing the parameters in the total cost model.

[0034] S4: Determine whether the solution process meets the preset termination conditions.

[0035] S5: If not satisfied, update the Lagrange multipliers according to the multiplier iteration model.

[0036] S6: Substitute the updated Lagrange multipliers into the relaxation model and iteratively solve and judge until the solution process meets the preset termination condition to obtain the location scheme of the drone delivery center to meet the demand point allocation.

[0037] In this embodiment, during the selection of the drone delivery center location, complex external environmental factors such as the risk of delivery center interruption and the uncertainty of demand at demand points are considered. A total cost model is constructed to closely match the actual situation, making the location of the delivery center more reasonable. The objective function is obtained by minimizing the value of this model. However, due to the excessive constraints of the objective function and the complexity of the analysis, the total cost model is linearized by introducing Lagrange multipliers and relaxing the specified constraints to obtain a relaxed model. The lower bound solution of the objective function is obtained by minimizing the value of this model. 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 the upper bound solution of the objective function. According to the multiplier iteration model, the Lagrange multipliers are updated and substituted into the relaxed model. The solution is iterated and judged to gradually make the upper and lower bounds approach each other, thereby shortening the duality gap (i.e., the upper and lower bound error values) 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. Applying this method to the actual site selection and construction process of drone logistics networks provides enterprises with more reliable and economical site selection planning and demand allocation schemes.

[0038] When using the above method to solve for the optimal location scheme of drone delivery centers, the construction of the total cost model will be explained first.

[0039] Drone delivery provides new momentum for pharmaceutical logistics, such as pharmaceutical cold chain logistics, especially in the delivery of time-sensitive and urgent supplies like vaccines and blood products, ensuring both stability and reducing time costs. The site selection problem for drone delivery centers for pharmaceutical products, considering the risk of disruption, can be specifically described as follows: pharmaceutical products are transported by the manufacturer to a distribution center, and then delivered by drones. Limited by the maximum range of the drones, the distribution center can only serve demand points within its effective coverage radius. Unlike most two-tier transportation studies on disruption, this application extends the problem by constructing a three-tier logistics network structure: supplier-distribution center-demand point. Figure 2As shown in the diagram, two construction options are provided for candidate distribution center sites: one is normal construction (affected by interruption risk, thus an unreliable distribution center); the other is enhanced protection construction (unaffected by interruption risk, thus a reliable distribution center), which eliminates the impact of interruption risk through protective measures but requires higher construction costs. The interruption probability of an unreliable distribution center is only related to the location of the candidate site, and the candidate sites are independent of each other. Candidate sites can be hospitals, large pharmacies, or large medical institutions, while demand points can be small medical institutions, clinics, or medical stations. When an interruption occurs, the service capacity of the distribution center becomes completely ineffective, and the demand points must select a reliable downstream distribution center to provide services. The demand of the demand points is uncertain and is described using triangular fuzzy numbers.

[0040] Specifically, triangular fuzzy number theory is an important concept in fuzzy mathematics, primarily used to handle uncertain and fuzzy information in the real world. It provides a concise and intuitive mathematical tool for representing and calculating such fuzzy information. It is commonly used in supply chain management, fuzzy prediction and control, and engineering research. The principles of triangular fuzzy numbers are as follows:

[0041] Let some uncertain information be... , ,in and These are the lower and upper bounds of the fuzzy number, respectively. It is the most probable number. Its membership function is:

[0042] ,

[0043] The fuzzy number is clarified by transforming 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 made according to the problem.

[0044] This application makes the following assumptions:

[0045] Assumption 1: A primary distribution center (either a reliable or unreliable facility) is configured for each demand point. 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, so a backup distribution center is configured, and the backup distribution center is a reliable distribution center. This assignment method ensures that the demand of the demand point is met.

[0046] Assumption 2: A distribution center is served by a single supplier with unlimited production capacity.

[0047] Assumption 3: Each candidate location can only choose one type of distribution center to build, and there is no capacity limit for the built distribution centers.

[0048] Assumption 4: Considering the drone's flight endurance, mileage limits are imposed during planning. Because pharmaceutical product delivery is characterized by small batches and light weight, payload constraints can be ignored, meaning a single flight is sufficient to complete the delivery task.

[0049] Construct a model with the objective of minimizing total cost, which includes the cost of the facility distribution center, product storage and inventory costs, and logistics and transportation service costs.

[0050] Consider building a reliable or unreliable distribution center at candidate location j, and the cost of building a distribution center at candidate location j. :

[0051] (1)

[0052] Where J represents the set of candidate locations for drone delivery centers; This represents the fixed cost of setting up a reliable distribution center at candidate location j, where j∈J. This represents the fixed cost of setting up an unreliable distribution center at candidate location j. ; The value is 1 if a reliable distribution center is built at candidate location j, and 0 otherwise. The value is 1 if an unreliable distribution center is built at candidate location j, and 0 otherwise.

[0053] Products are transferred and stored at the distribution center at candidate location j, with product storage and inventory costs incurred. :

[0054] (2)

[0055] Where I represents the set of supply sources, and the index is i, i∈I; Indicates candidate location Unit inventory rate of goods at the distribution center Indicates the source of supply To candidate sites The volume of goods transported by the distribution center.

[0056] If candidate location j is an unreliable distribution center, an interruption is considered a complete failure of that distribution center. Based on Assumption 1, demand assignment is performed, and transportation service costs are related to distance and quantity. The unit cost differs when the same distribution center serves as a primary / backup distribution center, thus affecting the transportation service costs of the logistics network. :

[0057] (3)

[0058] in, This represents the unit service cost from 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 The value is 1 when providing service to the distribution center at candidate location j, and 0 otherwise; K represents the set of demand points with index k, k∈K; This indicates that the distribution center at candidate location j is the service demand point for the main distribution center. The unit cost; This indicates the distance from the distribution center at candidate location j to the demand point. The transportation distance; Indicate demand points The demand for goods; The value is 1 if the reliable distribution center at candidate location j is the main distribution center, and 0 otherwise. This represents the probability of an unreliable distribution center failing at candidate location v, 0 ≤ ≤1, v∈J; Let represent the probability of interruption of the reliable distribution center at candidate location j. =0; This indicates the unreliable distribution center at candidate location v as the service demand point for the primary distribution center. The unit cost; This indicates the unreliable distribution center at candidate location v to the demand point. The transportation distance; The value of 1 indicates that demand point k is primarily distributed by an unreliable distribution center at candidate location v and secondarily by a reliable distribution center at candidate location j; otherwise, the value of 0 indicates that demand point k is a reliable distribution center at candidate location j. Let $j$ represent the unit cost of the distribution center at candidate location $j$ serving the demand point $k$ as a backup distribution center. If the 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, the reliable distribution center at candidate location j will only serve the demand point if the unreliable distribution center at candidate location v is interrupted, and v ≠ j.

[0059] Therefore, the total cost model of the drone was constructed after considering the risk of disruption and the uncertainty of demand.

[0060] (4)

[0061] The objective function is then min C, where min C represents taking the minimum value of C in the total cost model.

[0062] The preset constraints of the objective function include:

[0063] (5), (6),

[0064] (7), (8),

[0065] (9), (10)

[0066] (11),

[0067] (12)

[0068] (13)

[0069] (14)

[0070] (15)

[0071] (16)

[0072] Where R represents the maximum range of the drone, and M represents a preset positive real number. The value is 1 if an unreliable distribution center is built at candidate location v, and 0 otherwise.

[0073] Regarding the above constraints, constraint (5) restricts a candidate site to constructing at most one type of facility, namely, one reliable facility or one unreliable facility; there are two scenarios for demand allocation at a demand point, constraint (6) states that the demand at 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 allocated to only one level of facility, then the facility is reliable; constraints (8) and (9) indicate that if a demand point is allocated to two levels of facility, then the primary facility is unreliable and the backup facility is reliable; constraints ( 10) indicates that at least one reliable facility should be opened to meet the demand; constraints (11), (12) and (13) are to meet the flight endurance constraint of the UAV. This constraint needs to be met when service occurs between the distribution center and the demand point, that is, the distance between them must be less than or equal to the maximum flight range of the UAV; constraint (14) ensures that the supply source only provides service to 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 range of values ​​for each decision variable.

[0074] The following detailed description of each step provides a more comprehensive understanding of the process for determining the location of a drone delivery center.

[0075] S1: Initialization parameters; the parameters include Lagrange multipliers, initial upper bound, and initial lower bound.

[0076] Initialize the Lagrange multipliers, for example, let the number of iterations n=1, and the initial upper bound = Initial lower bound = Maximum number of iterations (i.e., preset number of iterations) Error tolerance Preset step size adjustment factor .

[0077] S2: The goal is to minimize the value of the relaxation model to obtain the lower bound solution of the objective function; the relaxation model is obtained by linearizing the total cost model of the UAV, introducing Lagrange multipliers, and relaxing the specified constraints; the objective function is the function to find the minimum value of the total cost model, and the total cost model is a model constructed after considering the risk of interruption and the uncertainty of demand.

[0078] By introducing Lagrange multipliers, the "hard" constraints (i.e., specified constraints) that make the problem difficult to solve are relaxed, resulting in a relatively easy-to-solve relaxed problem. The relaxed solution provides a lower bound, and based on this, a feasible solution to the original problem is constructed, yielding an upper bound. The duality gap is continuously reduced through multiplier updates, and the two bounds are continuously tightened until convergence to the optimal solution. The algorithm flow is as follows: Figure 1 As shown.

[0079] The objective function is non-linear, and the specified constraints will be... Perform linearization, let Add constraints:

[0080] (17)

[0081] (18)

[0082] (19)

[0083] The relaxed specified constraints include constraints (6) and (15) from the above-mentioned preset constraints, and introduce Lagrange multipliers. and Lagrange multipliers The relaxation model is obtained by relaxing the specified constraints respectively:

[0084] (20)

[0085] The relaxation problem is to find the minimum value of the relaxation model described above.

[0086] After merging the relaxation models, we get:

[0087] (twenty one)

[0088] make , ,

[0089] Then the relaxation model simplifies to:

[0090] (twenty two)

[0091] st(5),(7)-(14),(16)-(19)

[0092] The solution to the Lagrange relaxation problem is a lower bound of the solution to the original problem. By introducing Lagrange multipliers, the objective function is minimized to the maximum extent, thus providing a lower bound solution to the original problem.

[0093] Constraint (10) is a redundant constraint used to tighten the Lagrange constraints. It can be obtained from constraints (6)-(9). This constraint is ignored when analyzing the Lagrange relaxation problem. The last term in the simplified relaxation model (Equation 22) is a constant term, which is not considered in the optimization problem. The relaxation problem can be solved by... The problem is broken down into a series of sub-problems, and a decision needs to be made for each candidate location. There are three possibilities: do not build a facility, build an unreliable facility, or build a reliable facility. Based on the availability of facilities, the relaxation problem is decomposed into subproblems that are easier to solve:

[0094] (twenty three)

[0095] When discussing different cases, first analyze the relaxation model. Two items. When candidate location j does not establish a distribution center. Both of these are 0; when candidate location The establishment of a distribution center always requires a certain source of supply. ,make , ,Right now

[0096]

[0097] For the remaining terms in the relaxation model, the following cases apply:

[0098] Scenario 1: When no distribution center is built at candidate location j, i.e. According to the constraints At this point, the values ​​of the remaining terms in the relaxation model ,illustrate When no facility is built, it has no impact on the objective function, and the relaxation model value is zero. Therefore, we only need to consider the case where the facility is built.

[0099] Scenario 2: When an unreliable distribution center is built at candidate location j, i.e. According to the constraints At this point, the values ​​of the remaining terms in the relaxation model .

[0100] Scenario 3: When a reliable distribution center is built at candidate location j, i.e. At this point, the values ​​of the remaining terms in the relaxation model are:

[0101]

[0102] and The values ​​are as follows:

[0103]

[0104] .

[0105] Find the minimum value of the relaxation model.

[0106] when At that time, it corresponds to the first case;

[0107] when At that time, it corresponds to the second situation;

[0108] when This corresponds to the third scenario.

[0109] Reconsider constraint (10), let This indicates that a set of candidate locations for reliable distribution centers has been established; This indicates that a set of candidate locations for unreliable distribution centers has been established; This represents the set of candidate sites for which no facilities have been established. According to constraint (10), at least one reliable facility must be established. At this point, the lower bound has been reached; otherwise, a reliable distribution center needs to be established in one of the candidate locations, JU or JN, and the location of the reliable distribution center needs to be determined:

[0110] make , ;make , ;if , , ;otherwise , .

[0111] By solving the Lagrange slack part problem, the lower bound can be obtained:

[0112] .

[0113] S3: Based on the lower bound solution and specified constraints, a fixed optimization strategy is adopted, with the goal of minimizing the value of the upper bound model, to obtain the upper bound solution of the objective function; the upper bound model is the model obtained by fixing the parameters in the total cost model.

[0114] When solving the Lagrange relaxation problem, if the obtained solution is a feasible solution to the original problem, it provides both a lower bound and an upper bound. However, since some constraints are relaxed, it is generally not feasible. Therefore, a fixed optimization method is used to find a feasible solution to the original problem, which provides an upper bound solution. The fixed optimization method is a large neighborhood search heuristic algorithm that, based on the Lagrange relaxation solution, fixes the values ​​of some variables and optimizes the remaining parameter variables to obtain the optimal solution.

[0115] S31: Modify the lower bound solution according to the preset lemma to obtain a feasible solution that satisfies the specified relaxed constraints.

[0116] In the supplier and demand point allocation phase, the pre-defined lemmas include:

[0117] Lemma 1: If there is a reliable distribution center at a candidate location at demand point k as its backup distribution center, then JG represents the set of candidate locations for establishing a reliable distribution center, and argmin is used to select the facility with the lowest transportation service cost.

[0118] Lemma 2: Assumption If there is a candidate location at the demand point k If an unreliable distribution center is used as its main distribution center, then... JU represents the set of candidate locations for establishing unreliable distribution centers. Indicates candidate location The distribution center serves as a backup distribution center for service demand. unit cost Indicates candidate location From the distribution center to the point of demand The transportation distance;

[0119] Lemma 3: Assumptions ,

[0120] , ,like Then, a candidate location should be selected. If a reliable distribution center is located in the area, it should be used as its primary distribution center; otherwise, a candidate distribution center should be selected. Unreliable distribution centers in the area are used as its main distribution center, candidate locations A reliable distribution center in the location serves as its backup distribution center; among which, Indicates candidate location Unreliable distribution centers serve as service demand points for the main distribution center. unit cost Indicates candidate location From unreliable distribution centers to demand points The transportation distance Indicates candidate location The probability of disruption at unreliable distribution centers. Indicates candidate location The unit cost of serving demand point k as a reliable distribution center as a backup distribution center. Indicates candidate location Reliable distribution centers to demand points The transportation distance Indicates candidate location A reliable distribution center serves as the main distribution center for service demand. unit cost Indicates candidate location Reliable distribution centers to demand points The transportation distance.

[0121] Lemma 4: If the distribution center is supplied by a source If services are provided, .

[0122] By using the aforementioned pre-defined lemma, candidate locations are screened, the scope is narrowed, and the lower bound solution is revised. If the lower bound solution is not within the narrowed scope, a feasible solution is re-selected from the narrowed scope.

[0123] S32: Fix the parameters and location decisions obtained from the feasible solution, and then reselect the remaining parameters to satisfy the objective function to obtain the upper bound solution.

[0124] Considering that the fixed optimization method is time-consuming and prone to getting trapped in local optima when solving large-scale problems, this paper, based on the Lagrange relaxation solution, retains the decision to open facilities and re-selects allocations for those that do not meet the constraints. According to the four lemmas mentioned above, demand point allocation and supplier selection are performed on the already opened facilities. The objective function corresponding to this feasible solution is as follows, yielding an upper bound model for the original problem:

[0125]

[0126] in, Indicates the source of supply To candidate sites The volume of goods transported by the distribution center at the location Indicates the source of supply The unit service cost to the distribution center at candidate location j. Indicates the source of supply The transportation distance to the distribution center at candidate location j.

[0127] 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, the solver is used to solve the remaining simple subproblems, and the verification is repeated to determine a suitable initial fixed value, and the solution with the smallest objective value is selected as the upper bound for improvement.

[0128] S4: Determine whether the solution process meets the preset termination conditions. This step includes:

[0129] 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 during the iteration process and the maximum lower bound obtained during the iteration process, divided by the maximum lower bound obtained during the iteration process. The lower bound is the minimum value of the relaxation model, and the upper bound is the minimum value of the upper bound model. The upper and lower bound error values ​​= UB represents the minimum upper bound obtained during the iteration process, and LB represents the maximum lower bound obtained during the iteration process.

[0130] S42: If 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, then the preset termination condition is satisfied.

[0131] S43: Otherwise, it is determined that the preset termination condition is not met.

[0132] S5: If the preset termination condition is not met, update the Lagrange multipliers according to the multiplier iteration model.

[0133] The multiplier iteration model is as follows:

[0134]

[0135]

[0136]

[0137] In the formula, A is the Claude damping constant, which can effectively prevent the iteration from entering a dead loop. A is set to 0.3; Lagrange multipliers. and The directions in the nth iteration are denoted as follows: and The directions at the 0th iteration are denoted as follows: and The Lagrange multipliers after the (n-1)th update are respectively and The Lagrange multipliers after the nth update are respectively and .

[0138] Lagrange step size adjustment factor ;

[0139] Where UB represents the minimum upper bound obtained during the iteration process, and LB represents the maximum lower bound obtained during the iteration process. This represents the lower bound obtained in the nth iteration. It satisfies 0 < Scalars ≤ 2.

[0140] S6: Substitute the updated Lagrange multipliers into the relaxation model and iteratively solve the problem until the solution process meets the preset termination condition, thus obtaining the location of the drone delivery center to meet the demand point allocation (i.e., the demand points served by each delivery center). This step includes:

[0141] If the lower bound stalls during the specified number of iterations, then... Halve the step size and then re-determine the Lagrange step size adjustment factor. Usually through settings It was determined that.

[0142] Alternatively, if the lower bound stalls during the specified number of iterations, the average subgradient is used instead of the current iteration direction to update the Lagrange multipliers. The stalling phenomenon is defined as the change in the lower bound being less than or equal to... The average subgradient is the average value of the iteration directions in the T historical iterations adjacent to the current iteration.

[0143] Specifically, during the iteration process, the upper and lower bounds of each iteration are recorded, with the lower bound being... Stagnation occurs during multiple iterations (e.g., 15 iterations), i.e. Change ≤ To change the subgradient direction, use the average subgradient and calculate the average direction of the most recent T iterations, such as... The rest of the formulas remain unchanged, and the changes in the lower bound solution are observed after several iterations.

[0144] When the preset termination condition is reached through multiple iterations, the upper and lower bounds become close to each other. From the close upper and lower bounds, a limited number of candidate sites can be determined. From the limited number of candidate sites, the candidate sites that satisfy the objective function are selected to determine the final drone delivery center location scheme and demand allocation scheme.

[0145] In summary, compared with existing technologies, it has the following beneficial effects:

[0146] 1. The constructed three-level logistics network model incorporates inventory costs into the objective function to explore the site selection optimization problem of drone delivery centers. The modeling and solution show that the scheme including two types of facilities is feasible and beneficial. At the same time, the adoption of a primary and backup delivery center service mode not only solves the problem of insufficient reliability of single-level service, but also avoids the complexity brought about by multi-level service.

[0147] 2. The impact of demand uncertainty and distribution center disruption on the logistics network is characterized in detail, providing enterprises with a clear approach 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 is constructed, which is an extension of the model that takes into account factors such as drone energy consumption and airspace restrictions. The extended site selection model is more realistic, and the site selection scheme determined by the model is more reasonable, significantly enhancing the reliability and robustness of the cold chain drone delivery network under the dual impact of supply-side disruption and demand-side fluctuations.

[0148] 3. Improvements were made to the Lagrange relaxation algorithm for solving complex problems, with a focus on refining the subgradient algorithm and the feasible solution generation mechanism. These improvements shorten the solution time and improve the solution quality for large-scale instances.

[0149] like Figure 3 As shown in the figure, an embodiment of this application provides a drone delivery center location selection system that considers the risk of disruption, comprising:

[0150] The parameter initialization module 100 is used to initialize parameters, including Lagrange multipliers.

[0151] The lower bound solution analysis module 200 is used to obtain the lower bound solution of the objective function by minimizing the value of the relaxation model. The relaxation model is a model obtained by linearizing the total cost model of the UAV, 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 the risk of interruption and the uncertainty of demand.

[0152] The upper bound solution analysis module 300 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 goal of minimizing the value of the upper bound model; the upper bound model is the model obtained by fixing the parameters in the total cost model.

[0153] The loop judgment module 400 is used to determine whether the solution process meets the preset termination condition.

[0154] The multiplier update module 500 is used to update the Lagrange multipliers according to the multiplier iteration model if the condition is not met.

[0155] The loop analysis module 600 is used to substitute the updated Lagrange multipliers into the relaxation model and perform loop calculations until the solution process meets the preset termination conditions, thereby obtaining the location of the drone delivery center to meet the demand point allocation.

[0156] In this embodiment, the beneficial effects of the drone delivery center location system that takes into account the risk of interruption are similar to those of the drone delivery center location method that takes into account the risk of interruption, and will not be repeated here.

[0157] An electronic device provided in this application includes a memory and a processor; the memory is used to store a computer program; the processor is used to implement the drone delivery center site selection method considering interruption risk as described above when executing the computer program.

[0158] This application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the drone delivery center site selection method that considers the risk of interruption, as described above.

[0159] In this embodiment, the beneficial effects of the electronic device and the computer-readable storage medium are similar to those of the above-described drone delivery center location method that takes into account the risk of interruption, and will not be repeated here.

[0160] The present invention describes electronic devices that can serve as servers or clients of this application, which are examples of hardware devices that can be applied to various aspects of this 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 processors, cellular phones, smartphones, 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 application described and / or claimed herein.

[0161] Electronic devices include a computing unit that can perform various appropriate actions and processes based on a computer program stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). The RAM can also store various programs and data required for device operation. The computing unit, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0162] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc. In this application, the units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments of this application according to actual needs. Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units can be implemented in hardware or as software functional units.

[0163] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0164] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for selecting locations for drone delivery centers considering disruption risk, characterized in that, include: Initialize parameters; The parameters include Lagrange multipliers; The goal is to minimize the value of the relaxation model, thus obtaining the lower bound solution of the objective function. The relaxation model is obtained by linearizing the total cost model of the UAV, 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 the risk of interruption and the uncertainty of demand. Based on the lower bound solution and specified constraints, a fixed optimization strategy is adopted, with the goal of minimizing the value of the upper bound model, to obtain the upper bound solution of the objective function; 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 condition; If not satisfied, then update the Lagrange multipliers according to the multiplier iteration model; The updated Lagrange multipliers are substituted into the relaxation model, and the solution is iterated until the solution process meets the preset termination condition, thus obtaining the location of the drone delivery center. Assume a primary distribution center is configured for each demand point. 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 : ， Where J represents the set of candidate locations for drone delivery centers; This represents the fixed cost of setting up a reliable distribution center at candidate location j, where j∈J. This represents the fixed cost of setting up an unreliable distribution center at candidate location j. ; The value is 1 if a reliable distribution center is built at candidate location j, and 0 otherwise. The value is 1 if an unreliable distribution center is built at candidate location j, and 0 otherwise. Product storage and inventory costs after constructing a distribution center at the candidate site : ， Where I represents the set of supply sources, and the index is i, i∈I; This represents the unit inventory rate for the distribution center at candidate location j. This represents the quantity of goods transported from supply source i to the distribution center at candidate location j; Transportation service costs of logistics networks : ， in, This represents the unit service cost from 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 The value is 1 when providing service to the distribution center at candidate location j, and 0 otherwise; K represents the set of demand points with index k, k∈K; This indicates that the distribution center at candidate location j is the service demand point for the main distribution center. The unit cost; This indicates the distance from the distribution center at candidate location j to the demand point. The transportation distance; Indicate demand points The demand for goods; The value is 1 if the reliable distribution center at candidate location j is the main distribution center, and 0 otherwise. This represents the probability of an unreliable distribution center failing at candidate location v, 0 ≤ ≤1, v∈J; This indicates the unreliable distribution center at candidate location v as the service demand point for the primary distribution center. The unit cost; This indicates the unreliable distribution center at candidate location v to the demand point. The transportation distance; The value of 1 indicates that demand point k is primarily distributed by an unreliable distribution center at candidate location v and secondarily by a reliable distribution center at candidate location j; otherwise, the value of 0 indicates that demand point k is a reliable distribution center at candidate location j. Let $j$ represent the unit cost of the distribution center at candidate location $j$ serving the demand point $k$ as a backup distribution center. If demand point k is served by an unreliable distribution center at candidate location v as the primary distribution center and a reliable distribution center at candidate location j as the backup distribution center, the reliable distribution center at candidate location j will only serve the demand point if the unreliable distribution center at candidate location v is interrupted, where v ≠ j. The total cost model for the aforementioned drone, constructed after considering disruption risk and demand uncertainty, is as follows: ， The objective function is: ; The pre-defined constraints of the objective function include: ， ， ， ， ， ， ， ， ， ， ， ， Where R represents the maximum range of the drone, and M represents a preset positive real number. The value is 1 if an unreliable distribution center is built at candidate location v, and 0 otherwise.

2. The drone delivery center site selection method considering disruption risk as described in claim 1, characterized in that, 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 determination of whether the solution process meets the preset termination condition includes: Determine whether the upper and lower bound error values ​​are less than the error tolerance. The upper and lower bound error values ​​are the difference between the minimum upper bound obtained during the iteration process and the maximum lower bound obtained during the iteration process, and then divided by the maximum lower bound obtained during the iteration process. If the upper and lower bound error values ​​are less than the error tolerance, the preset termination condition is determined to be met. Otherwise, the preset termination condition is not met.

3. The drone delivery center site selection method considering disruption risk as described in claim 1, characterized in that, The determination of whether the solution process meets 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; If 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, then the preset termination condition is satisfied. Otherwise, the preset termination condition is not met.

4. The drone delivery center site selection method considering disruption risk as described in claim 1, characterized in that, The specified relaxed constraints include: ， ， In the specified constraints Perform linearization, let Add constraints: , , ; Introducing Lagrange multipliers and Lagrange multipliers The relaxation model is obtained by relaxing the specified constraints respectively: ， in, , , ， Ignore the preset constraints first For relaxation models Two items, with the following possibilities: ； For the remaining terms in the relaxation model, the following cases apply: When no distribution center is built at candidate location j, the value of the remaining terms in the relaxation model is zero; When an unreliable distribution center is built at candidate location j, the value of the remainder in the relaxation model is... ; When a reliable distribution center is built at candidate location j, the value of the remainder terms in the relaxation model is... ， and The values ​​are as follows: ； make This indicates that a set of candidate locations for reliable distribution centers has been established; This indicates that a set of candidate locations for unreliable distribution centers has been established; This refers to the set of candidate sites for which no facilities have been established, requiring a reconsideration of pre-defined constraints. It requires the establishment of at least one reliable distribution center; like If the value is 0, it means that the lower bound has been reached; Otherwise, a reliable distribution center must be established by selecting one of the candidate locations, JU and JN, and the location of the reliable distribution center must be determined: make , ;make , ;if , , ;otherwise , The lower bound is obtained by solving for the minimum value of the relaxation model: 。 5. The drone delivery center site selection method considering disruption risk as described in claim 1, characterized in that, Based on the lower bound solution and specified constraints, a fixed optimization strategy is adopted, with the goal of minimizing the value of the upper bound model. The upper bound solutions of the objective function include: The lower bound solution is modified according to the preset lemma to obtain a feasible solution that satisfies the specified relaxed constraints. The parameters and location decisions obtained from the feasible solutions are fixed, and then the remaining parameters are reselected to satisfy the objective function, thus obtaining the upper bound.

6. The drone delivery center site selection method considering disruption risk as described in claim 5, characterized in that, The predefined lemma includes: Lemma 1: If there is a reliable distribution center at a candidate location at demand point k as its backup distribution center, then JG represents the set of candidate locations for establishing a reliable distribution center; Lemma 2: Assumption If there is a candidate location at the demand point k If an unreliable distribution center is used as its main distribution center, then... JU represents the set of candidate locations for establishing unreliable distribution centers. Indicates candidate location The distribution center serves as a backup distribution center for service demand. unit cost Indicates candidate location From the distribution center to the point of demand The transportation distance; Lemma 3: Assumptions , , ,like Then, a candidate location should be selected. If a reliable distribution center is located in the area, it should be used as its primary distribution center; otherwise, a candidate distribution center should be selected. Unreliable distribution centers in the area are used as its main distribution center, candidate locations A reliable distribution center in the location serves as its backup distribution center; among which, Indicates candidate location Unreliable distribution centers serve as service demand points for the main distribution center. unit cost Indicates candidate location From unreliable distribution centers to demand points The transportation distance Indicates candidate location The probability of disruption at unreliable distribution centers. Indicates candidate location The unit cost of serving demand point k as a reliable distribution center as a backup distribution center. Indicates candidate location Reliable distribution centers to demand points The transportation distance Indicates candidate location A reliable distribution center serves as the main distribution center for service demand. unit cost Indicates candidate location Reliable distribution centers to demand points The transportation distance; Lemma 4: If the distribution center is supplied by a source If services are provided, .

7. The drone delivery center site selection method considering disruption risk as described in claim 6, characterized in that, The upper bound model is ， in, Indicates the source of supply To candidate sites The volume of goods transported by the distribution center at the location Indicates the source of supply The unit service cost to the distribution center at candidate location j. Indicates the source of supply The transportation distance to the distribution center at candidate location j.

8. The drone delivery center site selection method considering disruption risk as described in claim 7, characterized in that, The multiplier iteration model is as follows: ， ， Where A represents the Claude damping constant; Lagrange multipliers and The directions in the nth iteration are denoted as follows: and The directions at the 0th iteration are denoted as follows: and The directions in the (n-1)th iteration are denoted as follows: and The Lagrange multipliers after the (n-1)th update are respectively and The Lagrange multipliers after the nth update are respectively and ; Lagrange step size adjustment factor ; Where UB represents the minimum upper bound obtained during the iteration process. This represents the lower bound obtained in the nth iteration. It satisfies 0 < Scalars ≤ 2.

9. A drone delivery center location selection system considering disruption risk, characterized in that, include: A parameter initialization module is used to initialize parameters; the parameters include Lagrange multipliers. The lower bound solution analysis module is used to obtain the lower bound solution of the objective function by minimizing the value of the relaxation model. The relaxation model is obtained by linearizing the total cost model of the UAV, 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 the risk of interruption and the uncertainty of demand. 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 goal of minimizing the value of the upper bound model. The upper bound model is the model obtained by fixing the parameters in the total cost model; The loop judgment module is used to determine whether the solution process meets the preset termination condition; The multiplier update module is used to update the Lagrange multipliers according to the multiplier iteration model if the conditions are not met. The loop analysis module is used to substitute the updated Lagrange multipliers into the relaxation model and perform the solution and judgment in a loop until the solution process meets the preset termination condition to obtain the location of the drone delivery center. Assume a primary distribution center is configured for each demand point. 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 : ， Where J represents the set of candidate locations for drone delivery centers; This represents the fixed cost of setting up a reliable distribution center at candidate location j, where j∈J. This represents the fixed cost of setting up an unreliable distribution center at candidate location j. ; The value is 1 if a reliable distribution center is built at candidate location j, and 0 otherwise. The value is 1 if an unreliable distribution center is built at candidate location j, and 0 otherwise. Product storage and inventory costs after constructing a distribution center at the candidate site : ， Where I represents the set of supply sources, and the index is i, i∈I; This represents the unit inventory rate for the distribution center at candidate location j. This represents the quantity of goods transported from supply source i to the distribution center at candidate location j; Transportation service costs of logistics networks : ， in, This represents the unit service cost from 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 The value is 1 when providing service to the distribution center at candidate location j, and 0 otherwise; K represents the set of demand points with index k, k∈K; This indicates that the distribution center at candidate location j is the service demand point for the main distribution center. The unit cost; This indicates the distance from the distribution center at candidate location j to the demand point. The transportation distance; Indicate demand points The demand for goods; The value is 1 if the reliable distribution center at candidate location j is the main distribution center, and 0 otherwise. This represents the probability of an unreliable distribution center failing at candidate location v, 0 ≤ ≤1, v∈J; This indicates the unreliable distribution center at candidate location v as the service demand point for the primary distribution center. The unit cost; This indicates the unreliable distribution center at candidate location v to the demand point. The transportation distance; The value of 1 indicates that demand point k is primarily distributed by an unreliable distribution center at candidate location v and secondarily by a reliable distribution center at candidate location j; otherwise, the value of 0 indicates that demand point k is a reliable distribution center at candidate location j. Let $j$ represent the unit cost of the distribution center at candidate location $j$ serving the demand point $k$ as a backup distribution center. If demand point k is served by an unreliable distribution center at candidate location v as the primary distribution center and a reliable distribution center at candidate location j as the backup distribution center, the reliable distribution center at candidate location j will only serve the demand point if the unreliable distribution center at candidate location v is interrupted, where v ≠ j. The total cost model for the aforementioned drone, constructed after considering disruption risk and demand uncertainty, is as follows: ， The objective function is: ; The pre-defined constraints of the objective function include: ， ， ， ， ， ， ， ， ， ， ， ， Where R represents the maximum range of the drone, and M represents a preset positive real number. The value is 1 if an unreliable distribution center is built at candidate location v, and 0 otherwise.

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