Double-layer logistics network distribution optimization method for multi-frequency multi-time limit products

Abstract

The present application relates to the technical field of distribution, in particular to a double-layer logistics network distribution optimization method for multi-frequency and multi-time-effect products. The steps are as follows: S1, analyzing the distribution characteristics of multi-frequency and multi-time-effect products; identifying the types of multi-time-effect products continuously arriving at the distribution center, and using a mixed distribution strategy to schedule multi-frequency distribution of multi-time-effect products; S2, constructing a multi-frequency and multi-time-effect product double-layer logistics distribution mathematical model; S3, using an improved Lagrange relaxation method to solve the multi-frequency and multi-time-effect product double-layer logistics network distribution problem. The double-layer logistics network distribution optimization method for multi-frequency and multi-time-effect products provided by the present application fully considers the multi-product characteristics and distribution frequency characteristics of urban logistics distribution, realizes an efficient multi-product and multi-frequency distribution resource allocation method, reduces distribution cost and improves distribution punctuality, and designs an efficient distribution model and a solving algorithm suitable for multi-frequency and multi-time-effect product distribution.

Description

Technical Field

[0001] This invention relates to the field of distribution technology, and in particular to a method for optimizing the distribution of high-frequency, high-time-sensitivity products through a two-tier logistics network. Background Technology

[0002] To meet the diverse time-sensitive needs of customers in express delivery, customers can choose a delivery time based on their requirements during the delivery process. However, in order to balance delivery costs, delivery companies cannot sort and deliver express packages with different time-sensitive delivery times that arrive at the city's distribution center in real time. Instead, they need to set the weekday delivery frequency based on business needs and the company's delivery resources, and deliver express packages with different time-sensitive delivery times to customers in batches.

[0003] Due to a lack of refined resource management and a lack of targeted services to meet customers' diverse time-sensitive needs, delivery companies exhibit insufficient differentiation among different time-sensitive products in urban delivery, resulting in a situation where "express packages are expensive but not fast, while slow packages have low average profits." Research and analysis revealed the main reason: in the urban last-mile delivery stage, different time-sensitive products are mixed together, and delivery services lack specificity. During delivery, express packages pull slow packages forward, and slow packages pull express packages backward, leading to insufficient targeted service and unmet customer needs for multiple time-sensitive delivery options. Therefore, coordinating the delivery of high-frequency, multi-time-sensitive products is one of the key issues in the company's operations.

[0004] Therefore, identifying and classifying express delivery types based on the diverse time-sensitive product categories, and designing integrated delivery strategies for these products, can more rationally allocate logistics resources and improve service quality and on-time delivery rates. The design of delivery frequency schemes needs to be based on the characteristics of various time-sensitive products, meeting both the overall delivery task requirements and the timeliness requirements of different products. Summary of the Invention

[0005] Therefore, it is necessary to provide a two-layer logistics network distribution optimization method for high-frequency and high-time-sensitivity products to address the aforementioned technical problems.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A two-tier logistics network delivery optimization method for high-frequency, high-time-sensitivity products includes the following steps:

[0008] S1. Analyze the characteristics of high-frequency, multi-time-delay product delivery;

[0009] By identifying the various time-sensitive product types that continuously arrive at the distribution center, and employing a hybrid delivery strategy, the express delivery of these products is scheduled for multiple frequencies.

[0010] S2. Construct a mathematical model for the delivery of high-frequency, high-time-sensitivity products using a two-tier logistics system.

[0011] S3. Relax the strong constraints of the two-layer logistics network distribution problem for high-frequency, high-time-sensitivity products to obtain an easily solvable subproblem of two-layer network distribution for high-time-sensitivity products. Solve the subproblem to obtain the lower bound solution and upper bound solution of the original problem. Finally, find the optimal solution of the high-frequency, high-time-sensitivity product problem.

[0012] As a preferred embodiment of the dual-layer logistics network distribution optimization method for multi-frequency and multi-time-efficiency products provided by the present invention, in step S1, multi-frequency refers to the number of express deliveries per natural day.

[0013] The set of express delivery frequencies is represented as H = {h1, h2, ..., h} n};

[0014] Where |H| represents the number of delivery frequencies; each element h in set H n This represents the start time of delivery frequency n. The setting of the multi-frequency delivery set H directly affects the number of decisions and the multi-delivery strategy.

[0015] As a preferred embodiment of the dual-layer logistics network distribution optimization method for multi-frequency and multi-time-efficiency products provided by the present invention, in step S1, multi-time-efficiency refers to different time-efficiency delivery service products designed by the delivery company to meet the multi-time-efficiency needs of customers.

[0016] The set of products with multiple time-sensitive effects is represented as P = {1, 2, ..., p} n};

[0017] Where |P| represents the number of multi-time-sensitive product types;

[0018] In a preferred embodiment of the dual-layer logistics network distribution optimization method for high-frequency, high-time-sensitivity products provided by the present invention, the expression for the objective function of the mathematical model in step S2 is as follows:

[0019]

[0020] in, For the fixed cost of vehicle k, x ijkh The value of vehicle k is 1 when it travels along the delivery frequency h arc (i,j); otherwise it is 0. Let d be the unit distance cost of vehicle k. ij This represents the distance between two points in the network.

[0021] As a preferred embodiment of the two-layer logistics network distribution optimization method for high-frequency, high-time-sensitivity products provided by the present invention, the vehicle routing optimization in the mathematical model satisfies the following constraints:

[0022]

[0023]

[0024] Among them, z hp This is represented as 1 if product p can be delivered by frequency h; otherwise, it is 0, δ ih This means that customer point i is 1 when it is served in delivery frequency h; otherwise it is 0.

[0025] This indicates that at least one frequency h in the multiple frequencies can deliver service product p type express;

[0026] Ensure that each customer point i can be assigned only one delivery frequency.

[0027] As a preferred embodiment of the two-layer logistics network distribution optimization method for multi-frequency, multi-time-sensitive products provided by the present invention, the calculation steps for obtaining the lower bound solution and upper bound solution of the original problem by solving the slack subproblem in step S3 are as follows:

[0028] Step 1: Initialize algorithm parameters;

[0029] Step 2: Read logistics network node information Vehicle Information Customer needs

[0030] Step 3: Set parameters for multiple time-sensitive product types and delivery frequency;

[0031] Step 4: Identify the product type to which the customer's needs belong;

[0032] Step 5: Relax the Lagrange single-frequency constraint to obtain the subproblem;

[0033] Step 6: Identify and categorize the types of products needed by customers (δ), and establish an order set (O). h and O u ;

[0034] Step 7: Solve the subproblems using a heuristic algorithm based on delivery frequency to obtain the upper bound solution. and lower bound solution

[0035] Step 8: Determine if the lower bound solution is equal to the upper bound solution; if End, proceed to step 11; if Proceed to step 9;

[0036] Step 9: Determine if the preset algorithm execution time has ended; if the time has ended, proceed to step 11; if the time has not ended, proceed to step 10.

[0037] Step 10: Determine the subgradient optimization step size and optimization direction based on the Lagrange multipliers, continue optimization and feed back the results to Step 6;

[0038] Step 11: Output the current upper bound solution as the optimal feasible solution to the original problem.

[0039] As a preferred embodiment of the dual-layer logistics network distribution optimization method for multi-frequency, multi-time-sensitive products provided by the present invention, in step 7, the upper bound solution... and lower bound solution The calculation steps are as follows:

[0040] Based on known customer needs O h Heuristic algorithms are applied to solve subproblems to obtain lower bound solutions.

[0041] O u The customer demand is allocated, and a heuristic algorithm is applied to solve the subproblems to obtain O(log n). u Allocate all orders to obtain the upper bound solution.

[0042] We obtain the lower bound solution to the original problem. and the solution above

[0043] As a preferred embodiment of the dual-layer logistics network distribution optimization method for multi-frequency, multi-time-sensitive products provided by the present invention, the lower bound solution... and the solution above Perform subgradient optimization until the upper and lower bound solutions satisfy the termination condition, at which point the optimization result converges. Or ||d t When || = 0, all orders are delivered and the solution is accepted as the optimal solution to the original problem.

[0044] It is clear without a doubt that the technical solution described above in this application can solve the technical problem that this application aims to address.

[0045] Meanwhile, through the above technical solutions, the present invention has at least the following beneficial effects:

[0046] This invention provides a two-layer logistics network distribution optimization method for multi-frequency and multi-time-sensitive products. By fully considering the multi-product characteristics and distribution frequency characteristics of urban logistics distribution, it optimizes the urban distribution network layout, designs an efficient distribution model and solution algorithm, realizes an efficient resource allocation method for multi-time-sensitive and multi-frequency distribution, reduces distribution costs and improves on-time delivery rate.

[0047] The strong constraints of high-frequency delivery are relaxed by using the Lagrange relaxation method, thereby decomposing the complex original problem of high-frequency delivery into easily solvable subproblems. The subproblems are then solved by a hybrid heuristic algorithm, and the optimal solution to the original problem is found by subgradient optimization. Attached Figure Description

[0048] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a schematic diagram illustrating the express delivery frequency of the present invention;

[0050] Figure 2 This is a schematic diagram of the multi-frequency, multi-time-efficiency product collaborative delivery of the present invention;

[0051] Figure 3 The flowchart of the Lagrange relaxation hybrid algorithm of the present invention is as follows. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0053] It should be noted that, unless otherwise specified, the embodiments and features and technical solutions in the present invention can be combined with each other.

[0054] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0055] Reference Figures 1-3 A two-tier logistics network delivery optimization method for high-frequency, high-time-sensitivity products, comprising the following steps:

[0056] S1, Characteristics of a high-frequency, high-delivery product delivery system:

[0057] The two-tiered urban delivery network model for high-frequency, high-delivery products is based on a "distribution center-transfer station-customer point" network, taking into account the characteristics of high-delivery products and the patterns of high-frequency delivery, such as... Figure 1 This involves identifying multi-time-sensitive product types that continuously arrive at the distribution center and employing a hybrid delivery strategy to schedule and deliver these products. Figure 2As shown. "Frequency" refers to the number of deliveries per natural day set by the courier company; that is, the number of times a package is dispatched from the distribution center, delivered to the customer's location via a transit station.

[0058] The set of express delivery frequencies is represented as H = {h1, h2, ..., h} n}, |H| represents the number of delivery frequencies. Each element h in set H n This indicates the start time of delivery frequency n. For example, if h1 is set to 06:30, it means that the first delivery frequency starts at 06:30.

[0059] Once a delivery frequency begins, no new orders can be added to that frequency; all orders can only be delivered by a specific frequency after their arrival time; multi-time-delivery products are delivery service products with different delivery times designed by the delivery company to meet customers' diverse time-delivery needs. The set of multi-time-delivery products is represented as P = {1, 2, ..., p}. n Let |P| represent the number of multi-time-sensitive product types. The setting of the multi-frequency delivery set H directly affects the number of decision-making processes and the multi-time-sensitive delivery strategy.

[0060] The two-layer delivery network consists of a delivery center (Depot), a transit station (Satellite), and a customer point (Customer). The arrival time of packages at the delivery center is staggered. After sorting at the delivery center, packages are delivered to the transit station, and then from the transit station to the customer. This invention uses a directed graph to represent the nodes and delivery paths of the two-layer network model for high-frequency, high-time-sensitivity products, such as G = (N, A). The set of logistics nodes and the set of path arcs are represented as follows: N = N d ∪N s ∪N c Let N represent the set of all logistics nodes. d ={1,2,…,n d} represents the set of all distribution centers, N s ={n d +1,n d +2,…,n d +n s} represents the set of all transfer stations and N. c ={n d +n s +1,n d +n s +2,...,n d +n s +n c} represents the set of all customer points. N1 = N d ∪N s N2 represents the set of all logistics nodes in the first-layer distribution network; N2 = N S ∪N CThis represents the set of all logistics nodes in the second-layer distribution network. In this invention, i and j are used as subscript indices, and... i∈N represents the coordinates of node i, (i,j) represents the path arc between node i and node j, and A=A1∪A2 represents the set of all path arcs in the two-layer delivery network, where A1={(i,j) / i∈N1,j∈N1,i≠j} represents the set of all path arcs in the first-layer delivery network, and A2={(i,j) / i∈N2,j∈N2,i≠j} represents the set of all path arcs in the second-layer delivery network.

[0061] S2. Construction of a Mathematical Model for Two-Layer Logistics Distribution of High-Frequency, High-Time-Demand Products

[0062] Urban express delivery costs mainly include fixed vehicle costs, vehicle transportation costs, and express processing costs. Based on the 2E-VRP basic model, and combined with the characteristics of multi-time-sensitive products and the pattern of multi-frequency delivery, this invention designs a mathematical model for the two-layer delivery problem of multi-frequency, multi-time-sensitive products (MF-MP-2E-VRP), with the objective of optimizing delivery costs. The model is expressed as follows:

[0063]

[0064] in, For the fixed cost of vehicle k, x ijkh The value of vehicle k is 1 when it travels along the delivery frequency h arc (i,j); otherwise it is 0. Let d be the unit distance cost of vehicle k. ij This represents the distance between two points in the network.

[0065] The two-layer network vehicle routing optimization model for high-frequency, high-time-efficiency products satisfies the following constraints:

[0066]

[0067]

[0068] Formula (1) indicates that at least one frequency h among multiple frequencies can deliver service product p type express; Formula (2) guarantees that each customer point i can only be assigned to one delivery frequency, where z hp This is represented as 1 if product p can be delivered by frequency h; otherwise, it is 0, δ ih This means that customer point i is 1 when it is served in delivery frequency h; otherwise it is 0.

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] Formula (3) indicates that each customer i is visited only once during the delivery process, and the number of vehicles entering and leaving the demand point is balanced; Formula (4) indicates that the customer demand is accurately delivered; Formulas (5) and (6) indicate that each vehicle at each transfer station and distribution center is called at most once per frequency; Formula (7) indicates that the number of vehicles entering and leaving each transfer station is balanced for any delivery frequency.

[0075] Where, x ijkh Q is 1 when vehicle k travels along the delivery frequency h arc (i,j); otherwise it is 0. ijk Let be the vehicle load when vehicle k leaves node i and heads towards node j.

[0076]

[0077]

[0078]

[0079]

[0080]

[0081] Formulas (8) and (9) indicate that the delivery volume and pickup volume of each transit station in each delivery frequency do not exceed the transit station's processing capacity; Formulas (10) and (11) indicate that the transit station's processing volume is the same as the total demand of the customers it serves; Formula (12) ensures that each transit station in each frequency is accessed only once by vehicles from the same distribution center.

[0082] Among them, y ij For customer point i, transfer station j∈N s 1 when in service; 0 otherwise; δ ih The value for customer order i is 1 when the delivery frequency h is used; otherwise, it is 0. Let i be the delivery volume for demand i; Q represents the collection volume of demand i; ijk Let be the vehicle load when vehicle k leaves node i and heads towards node j.

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] Formulas (13) and (14) represent the decision-making process for matching multi-time-sensitive products with delivery frequency; Formula (15) represents the decision-making variables for order and delivery frequency; Formulas (16) and (17) represent the range of values ​​for the decision-making variables for vehicle delivery route planning.

[0089] Among them, w ish For customers, the transfer station provides services at a frequency of h, z. hp The value of δ is 1 if product p can be delivered by frequency h; otherwise, it is 0. ih For customer order i, the value is 1 when the delivery frequency h is used; otherwise, it is 0. ijkh For vehicle k, the value is 1 when it travels along the delivery frequency k arc (i,j); otherwise, it is 0. ij For customer point i, transfer station j∈N s The value is 1 when the service is active; otherwise, it is 0.

[0090] S3. Design of a solution method based on Lagrange relaxation

[0091] The main methods for solving the Vehicle Routing Problem (VRP) and its variants are exact algorithms and heuristic algorithms.

[0092] Exact algorithms can find the optimal solution to a model. These include branching methods, branching pricing methods, column generation methods, and Benders decomposition, but they are not suitable for solving large-scale problems.

[0093] Heuristic algorithms mainly include genetic algorithms, tabu search algorithms, ant colony algorithms, and neighborhood search algorithms. Their advantage is that they can solve large-scale problems in a finite amount of time and obtain near-optimal solutions.

[0094] The two-layer network path optimization model for multi-frequency, multi-time-delivery products in this invention is an NP-hard problem, unsuitable for applying exact algorithms, and a single heuristic algorithm is insufficient to construct a feasible solution encoding for the multi-frequency delivery model. Therefore, this invention combines Lagrange relaxation and heuristic algorithms to design a Lagrangean relaxation hybrid heuristic algorithm (LRHHA).

[0095] The Lagrange relaxation method was first proposed by Marshall L. Fisher in 1981 and has now been applied to solve optimization problems. The advantage of this method is that it applies relaxation operators to relax the strong constraints in the model, reduces the dimensionality of the complex problem model, constructs easily solvable subproblems, obtains the upper and lower bound solutions of the original problem by solving the subproblems, and finally obtains the feasible solution of the original problem by correcting the upper and lower bound solutions.

[0096] This invention employs a Lagrange relaxation heuristic algorithm to relax the strong constraints of the multi-frequency, multi-time-sensitivity product two-layer logistics network distribution problem, yielding an easily solvable subproblem of multi-time-sensitivity product two-layer network distribution. Solving this subproblem provides the lower and upper bound solutions to the original problem. Then, a subgradient optimization method is applied to refine the solution, resulting in a feasible solution to the original problem. In summary, this invention addresses the multi-frequency, multi-time-sensitivity product two-layer logistics network distribution problem by partitioning the product into multiple time-sensitivity products, matching these products with multiple frequencies, solving the Lagrange relaxation subproblem, and optimizing the upper and lower bound solutions using subgradient optimization, ultimately obtaining the optimal solution to the original problem.

[0097] The solution method combines Lagrange relaxation and heuristic algorithms to construct a hybrid solution algorithm for a two-layer network vehicle routing model for multi-frequency, multi-time-effect products. This algorithm applies Lagrange relaxation to decompose the complex problem into easily solvable subproblems, uses heuristic algorithms to solve these subproblems, and obtains upper and lower bound solutions to the original problem. Then, it optimizes the original problem using a subgradient optimization method. Finally, it obtains an approximate optimal feasible solution to the original problem. Figure 3 The steps are as follows:

[0098] Step 1: Initialize algorithm parameters, including population size, number of iterations, optimization operators, optimization time, etc. in heuristic algorithm solution;

[0099] Step 2: Read logistics network node information Vehicle Information Customer needs

[0100] Step 3: Set parameters for multiple time-sensitive product types and delivery frequency;

[0101] Step 4: Identify the product type to which the customer's needs belong;

[0102] Step 5: Relax the Lagrange single-frequency constraint to obtain the subproblem;

[0103] Step 6: Identify and categorize the types of products needed by customers (δ), and establish an order set (O). h and O u ;

[0104] Step 7: Solve subproblems by calling a heuristic algorithm based on delivery frequency;

[0105] Step 7.1: Based on known customer needs O h Heuristic algorithms are applied to solve subproblems to obtain lower bound solutions.

[0106] Step 7.2: Place O u The customer demand is allocated, and a heuristic algorithm is applied to solve the subproblems to obtain O(log n). u Allocate all orders to obtain the upper bound solution.

[0107] Step 7.3: Obtain the lower bound solution to the original problem. and the solution above

[0108] Step 8: Determine if the lower bound solution is equal to the upper bound solution; if End, proceed to step 11; if Proceed to step 9;

[0109] Step 9: Determine if the preset algorithm execution time has ended; if the time has ended, proceed to step 11; if the time has not ended, proceed to step 10.

[0110] Step 10: Determine the subgradient optimization step size and optimization direction based on the Lagrange multipliers, continue optimization and feed back the results to Step 6;

[0111] Step 11: Output the current upper bound solution as the optimal feasible solution to the original problem.

[0112] Matching relationships between time-sensitive products and high-frequency products.

[0113] In a two-layer vehicle routing model for multi-frequency, multi-time-sensitive products, the present invention sets this constraint as follows: This means that each delivery frequency can deliver all service products. If Then customer point i's demand is service product p, which can be delivered at frequency h. If Then customer order i's request can only be delivered at frequency h; if Then, the customer's order i can be delivered at multiple alternative frequencies h.

[0114] This model relates to the demand and frequency allocation constraints, which are key strong constraints in the frequency delivery problem. This invention relaxes these constraints, yielding easily solvable subproblems. The order generation time for customer point i... Later than the start time of delivery frequency h Then δ ih =0; Generation time of order i Earlier than the start time of delivery frequency h If order i can be delivered by frequency h, then δ ih =1. Then assign order i to set O. h .

[0115] If customer order i requires delivery at delivery frequency h, that is... Obtain the initial set O of the demand for delivery at delivery frequency h. h If the customer's order does not specify a delivery frequency, then If the demand from customer point i can be allocated to multiple delivery frequencies, then the demand from customer point i is allocated to set O. u .

[0116] S4. Constructing the Lagrange relaxation model

[0117] By relaxing the strong constraint on delivery frequency in the MF-MP-2E-VRP model, the original problem is decomposed into multiple sub-problems, achieving dimensionality reduction. In the MF-MP-2E-VRP model, demand and delivery frequency constraints... It is a strong constraint. Therefore, this invention relaxes the frequency constraint and sets the Lagrange multiplier to λ. s Construct the Lagrange relaxation model, as shown in the following formula;

[0118]

[0119] The linear programming model can be decomposed into |H| subproblems, each subproblem corresponding to a delivery frequency h and the set O of all orders delivered at that frequency. h The sub-problem model is as follows:

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132] If the delivery frequency H is known, then the number of subproblems is |H|. If h represents the encoding of a certain delivery frequency, then when h = 1, subproblem one can be expressed as:

[0133]

[0134] Similarly, when h = 2, h = 3, ..., h = n, each corresponds to a subproblem identical to h = 1, as shown in the above equation. These subproblems are all solvable multi-time-dependent product two-level vehicle routing problems.

[0135] S5. Find the lower bound solution and the upper bound solution.

[0136] I. Finding the Lower Bound Solution

[0137] The process of solving subproblems using the Lagrange relaxation method is essentially finding a lower bound solution to a feasible solution. The first step is to define the relationships between multi-time-sensitive products and multi-frequency delivery (i.e., z). hp Then, the decision variable values ​​δ for all customer needs can be obtained. ih =1, h∈H or δ ih ∈{0,1}, h∈H. According to δ ih =1, h∈H, generate the initial set O of delivery orders with delivery frequency h. h .

[0138] When h=1, the subproblem becomes a two-layer network vehicle routing problem, which can be solved using a hybrid heuristic algorithm to obtain the set O of delivery orders completed at this delivery frequency. h Delivery solutions and delivery costs for all needs in C LR (λ1). Similarly, when h=2, h=3,…,h=n, the subproblem delivery cost C LR (λ n Therefore, the solution set of the subproblems in the Lagrange relaxation model is:

[0139]

[0140] During the solution process of each subproblem, the set of delivery orders for each subproblem is O. h Only includes δ from all order sets ih Order i with a value of 1; at this time, the uncompleted allocation constraint is And δ ih =1, Orders that are not completed u The allocation of orders. Therefore, the relationship between the solution set of all subproblems and the solution of the original problem can be obtained as follows:

[0141]

[0142] therefore, This is the lower bound solution to the original problem.

[0143] II. Finding the solution above the bound

[0144] In the preprocessing of the relationship between multi-time-dependent products and multi-frequency products in this invention, O u This represents the set of demand from all customer points i whose delivery frequency is not yet determined. Based on order time attribute The unallocated demand set O is sequentially... u The demand in the middle is allocated to O h And update the order set for each delivery frequency, denoted as O. h The specific operation is as follows: If the customer selects the time attribute of i... Later than the start time of delivery frequency h Then δ ih =0; if the time attribute of customer point i is 0; Earlier than the start time of delivery frequency h If order i can be delivered by frequency h, then δ ih =1, and assign the demand of customer point i to set O. h '. Based on a hybrid heuristic algorithm, for all frequencies h and the demand set O h Solving the corresponding two-layer network vehicle path subproblem yields the following results: After the above demand allocation operation and subproblem solving, for any order i, there exists This indicates that all orders have been delivered.

[0145] when The expression "when" indicates that the delivery requirement for the corresponding multi-time-sensitive product is met only if customer point i completes delivery at delivery frequency h; it also indicates that the current Lagrange slack problem only completes one delivery for customer point i, consistent with the requirements of the original problem.

[0146] when "At that time" indicates that delivery can be made at multiple frequencies for customer order i; it also indicates the cost of sub-problems. In the process of solving, customer order i is delivered. Therefore, the total delivery cost is greater than the optimal solution to the original problem, which shows that:

[0147]

[0148] therefore, Let its upper bound be the solution.

[0149] III. Subgradient Optimization

[0150] Subgradient optimization promotes convergence of solutions by reducing the difference between the upper and lower bounds, until the solutions satisfy the termination condition and are accepted as approximate optimal solutions to the original problem. This invention's subgradient optimization is... The demand allocation of customer points is optimized using a sub-gradient approach. First, for all... Customer points based The values ​​are sorted to identify the set of alternative delivery frequencies for each order. The value represents the number of available delivery shifts for order i. Secondly, to improve the solution speed, the distance of the delivery schemes in the optimization process is estimated based on the shortest path approximation method proposed by Beardwood, as shown in the equation:

[0151]

[0152] Where n represents the number of customers, A s This represents the service area of ​​transfer station s.

[0153] When setting up Lagrange multipliers, prioritize the selection of alternative delivery frequencies. The fewest customer points i, identify the order y ij =1, i∈N c ,j∈N s The transit station s, and the δ ih For all delivery frequencies h = 1, the Lagrange multiplier expression is as follows:

[0154]

[0155]

[0156] in, Indicates the search direction. Indicates the search step size, β t The initial value is set to 1.5. If the result is not improved after three consecutive iterations of optimization, its value is halved. When it becomes less than a certain predetermined value ε, it is reset to the initial value.

[0157] The subgradient optimization process continues until the optimization result converges, i.e. Or ||d t If || = 0, then all orders have been delivered. If all orders have been assigned, the upper and lower bounds have not converged, and the algorithm has run for the preset time, then the upper bound solution is output as the approximate optimal feasible solution to the original problem.

[0158] Technical effect

[0159] A multi-time-sensitive product, multi-frequency delivery dataset was constructed using the 2E-VRP public dataset 2e-ijk, and named 2e-ij-(k1k2k3), where i represents the number of orders, j represents the number of transit stations, and k represents the sequence number of the same type of dataset. In the new dataset name, k1, k2, and k3 represent the original sequence numbers of the selected dataset, indicating that the demand data of the original dataset represents the demand for different delivery frequencies of the new dataset. Therefore, when the test dataset is relatively small, this invention uses a Genetic Algorithm (GA) and Simulated Annealing (SA) to solve for the delivery cost of each original dataset, and uses the total cost as a comparison benchmark. The Lagrangean Relaxation Hybrid Heuristic Algorithm (LRHHA) designed in this invention performs a one-time complete solution for the new dataset, outputting the delivery cost of the new dataset. Each algorithm solves for each dataset 10 times, and the optimal solution and the average solution are compared and analyzed. The results are shown in the table below. Where BR represents the Best Result (BR), AVGR represents the Average Result (AVGR), and Gap represents the fluctuation in the difference between BR and AVGR. All dataset tests were run on a PC configured with an Intel(R) Core(TM) i5-7500, 3.40GHz processor and 4GB of RAM.

[0160] Multi-frequency delivery dataset algorithm test

[0161]

[0162] As shown in the table above, the results demonstrate that the Lagrange relaxation hybrid algorithm of this invention can effectively solve the multi-frequency delivery problem. The optimal and average solutions of LRHHA are superior to those of GA and SA. Regarding stability, LRHHA maintains a gap of less than 2.5%, demonstrating better stability than GA and SA.

[0163] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for optimizing the distribution of high-frequency, high-time-sensitivity products through a two-tier logistics network, characterized in that: The steps are as follows: S1. Analyze the characteristics of high-frequency, multi-time-delay product delivery; By identifying the various time-sensitive product types that continuously arrive at the distribution center, and employing a hybrid delivery strategy, the express delivery of these products is scheduled for multiple frequencies. S2. Construct a mathematical model for the delivery of high-frequency, high-time-sensitivity products using a two-tier logistics system. S3. Relax the strong constraints of the two-layer logistics network distribution problem for high-frequency, high-time-sensitivity products to obtain an easily solvable subproblem of two-layer network distribution for high-time-sensitivity products. Solve the subproblem to obtain the lower bound and upper bound solutions of the original problem. Finally, find the optimal solution to the high-frequency, high-time-sensitivity product problem. In step S1, the frequency refers to the number of express deliveries per natural day. The set of express delivery frequencies is represented as ; in, Indicates the number of delivery frequencies; set Each element in Indicates delivery frequency Start time; multiple delivery collections The settings directly affect the number of decision-making processes and multi-time-sensitive delivery strategies; In step S2, the expression for constructing the objective function of the mathematical model is as follows: in, For the fixed cost of vehicle k, x ijkh For vehicle k in the delivery frequency h travel arc The value is 1 if the condition is met; otherwise, it is 0. Let d be the unit distance cost of vehicle k. ij The distance between two points in the network; In step S3, the calculation steps for obtaining the lower bound solution and upper bound solution of the original problem by solving the slack subproblem are as follows: Step 1: Initialize algorithm parameters; Step 2: Read logistics network node information Vehicle information Customer needs ; Step 3: Set parameters for multiple time-sensitive product types and delivery frequency; Step 4: Identify the product type to which the customer's needs belong; Step 5: Relax the Lagrange single-frequency constraint to obtain the subproblem; If delivery frequency Given that, the number of subproblems is If The code representing a certain delivery frequency, then when Subproblem one can be expressed as: Similarly, when Each corresponds to a pair The same subproblems are shown in the equation; the corresponding subproblems are all solvable multi-time-dependent product two-layer vehicle routing problems. Step 6: Identify the types of products customers need. Then classify and create order collections. and ; Step 7: Solve the subproblems using a heuristic algorithm based on delivery frequency to obtain the upper bound solution. and lower bound solution ; Step 8: Determine if the lower bound solution is equal to the upper bound solution; if End, proceed to step 11; if Proceed to step 9; Step 9: Determine if the preset algorithm execution time has ended; if the time has ended, proceed to step 11; if the time has not ended, proceed to step 10. Step 10: Determine the subgradient optimization step size and optimization direction based on the Lagrange multipliers, continue optimization and feed back the results to Step 6; Step 11: Output the current upper bound solution as the optimal feasible solution to the original problem.

2. The method for optimizing the distribution of multi-frequency, multi-time-sensitive products through a two-tier logistics network according to claim 1, characterized in that, In step S1, the multi-time-sensitive products are delivery service products with different time-sensitive requirements designed by the delivery company to meet customers' diverse time-sensitive needs. A collection of products with multiple time-sensitive effects is represented as ; in, This indicates the number of product types with multiple time-sensitive delivery times.

3. The method for optimizing the distribution of multi-frequency, multi-time-sensitive products through a two-tier logistics network according to claim 1, characterized in that, The vehicle routing optimization in the mathematical model satisfies the following constraints: Among them, z hp This is represented as 1 if product p can be delivered by frequency h; otherwise, it is 0, δ ih This means that customer point i is 1 when it is served in delivery frequency h; otherwise it is 0. Indicates that at least one frequency is present in a plurality of frequencies. Delivery service products Types of express delivery; Ensure that each customer point i can be assigned only one delivery frequency.

4. The method for optimizing the distribution of multi-frequency, multi-time-sensitive products through a two-tier logistics network according to claim 1, characterized in that, In step 7, the upper bound solution and lower bound solution The calculation steps are as follows: Based on known customer needs Heuristic algorithms are applied to solve subproblems to obtain lower bound solutions. ; Will The customer demand is allocated, and a heuristic algorithm is applied to solve the subproblems to obtain the desired results. Allocate all orders to obtain the upper bound solution. ; We obtain the lower bound solution to the original problem. and the solution above .

5. The method for optimizing the distribution of multi-frequency, multi-time-sensitive products through a two-tier logistics network according to claim 4, characterized in that, Solution to the lower bound and the solution above Perform subgradient optimization until the upper and lower bound solutions satisfy the termination condition, at which point the optimization result converges. or At this point, all orders have been delivered and the solution is accepted as the optimal solution to the original problem.

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