Forward and reverse logistics network planning method comprehensively considering supply and demand satisfaction

Abstract

The invention discloses a forward and reverse logistics network planning method comprehensively considering supply and demand satisfaction, and relates to the field of logistics network planning. According to the method, forward and reverse logistics network planning is carried out by integrally considering forward and reverse networks, an existing particle swarm optimization algorithm is improved, a minimum-cost maximum-flow algorithm is introduced in a scheme evaluation stage, and the network is converted into an adaptive algorithm structure, so that the forward and reverse network problems can be solved integrally; simulated annealing and cross double operators are introduced in the scheme updating stage, and the global optimization capacity of the algorithm is improved. Compared with the existing particle swarm optimization algorithm, the improved particle swarm optimization algorithm not only can integrally solve forward and reverse network problems, but also can solve a better network planning solution with higher stability in a shorter time. According to the method, under the set investment budget, the cargo delivery rate can be remarkably increased, the overall satisfaction degree of supply and demand parties is improved, and effective help can be provided for optimizing resource allocation and improving long-term market competitiveness for logistics enterprises.

Description

Technical Field

[0001] The present invention relates to the technical field of logistics network planning, and particularly relates to a method for planning a forward and reverse logistics network comprehensively considering supply and demand satisfaction. Background Art

[0002] With the booming development of e-commerce, the scale of commodity circulation has shown exponential growth. Under the online consumption mode, consumers can only conduct quality inspections when receiving goods, resulting in a high return rate. This phenomenon poses a dual challenge to logistics transportation enterprises: ensuring the reliability of both forward distribution and reverse returns.

[0003] The operation mode of the traditional logistics industry mainly relies on third-party logistics (3PL). Under this mode, usually the same 3PL company undertakes all logistics tasks. However, the limitations of the single 3PL mode in terms of response speed and cost control are gradually emerging, making it difficult to meet the high-efficiency requirements of modern logistics. In recent years, the rise of collaborative logistics has provided a new solution for cost reduction and efficiency improvement in the supply chain. By integrating the transportation resources of multiple logistics carriers, collaborative logistics can flexibly allocate transportation tasks, enabling different sections of transportation to be completed by different logistics transportation enterprises. Under this new logistics mode, the logistics platform not only needs to make decisions on facility location and route selection, but also needs to comprehensively consider factors such as the transportation capacity and transportation cost of each logistics transportation enterprise. Therefore, how to reasonably plan the forward and reverse networks under the collaborative logistics mode, thereby improving the satisfaction of both supply and demand sides, reducing costs and increasing efficiency for enterprises, and enhancing market competitiveness, is a current hot research topic. However, the existing research on this research topic has significant deficiencies at multiple levels:

[0004] Firstly, at the network structure level, the existing research plans the forward and reverse network (forwardandbackwordnetwork) in a phased and independent manner. For example, first design the forward network for transporting goods, and then after the goods are returned at the client side, design the entire reverse network according to the actual situation. This two-stage separation method of considering forward and reverse logistics not only weakens the resource allocation efficiency, but also increases the overall operating cost of the network. In addition, only focusing on route selection and ignoring the optimal allocation of different logistics carriers on the same route leads to an increase in the overall network cost and a decrease in distribution efficiency, which are also problems existing in the existing research.

[0005] Secondly, at the service object level, the current consideration object for satisfaction mainly focuses on the customer group, while ignoring the evaluation feedback of suppliers on service quality. This one-sided evaluation mode leads to obvious defects in the evaluation system of supply chain service quality.

[0006] Finally, the logistics network planning problem needs to find a feasible solution within a reasonable time range. When solving small and medium-sized networks, using commercial solution software can obtain the optimal solution within the ideal time range. However, for large-scale network planning problems, the complexity increases exponentially, and traditional solution methods are ineffective. Therefore, many studies have started to explore new methods, and intelligent optimization algorithms have become a major research hotspot. However, the existing intelligent optimization algorithms generally have the defects of low computational efficiency and slow convergence speed when dealing with large-scale problems. Summary of the Invention

[0007] In view of the above deficiencies of the prior art, the purpose of the present invention is to provide a forward and reverse logistics network planning method that comprehensively considers the satisfaction of supply and demand, aiming to solve the problem of collaborative logistics planning for forward and reverse networks with the goal of maximizing the satisfaction of bilateral service objects. The method of the present invention can significantly improve the goods delivery rate and enhance the overall satisfaction of both supply and demand sides under the constraint of a given investment budget, and can provide effective help for logistics enterprises to optimize resource allocation and improve long-term market competitiveness.

[0008] The technical solution of the present invention is as follows:

[0009] A forward and reverse logistics network planning method that comprehensively considers the satisfaction of supply and demand, the method includes the following steps:

[0010] Step 1: Collect data related to logistics planning;

[0011] Step 2: Determine the decision variables and the satisfaction expressions of both supply and demand sides. Combining the data related to logistics planning and the satisfaction expressions of both supply and demand sides, consider the integration of forward and reverse networks. Taking suppliers, transfer centers, and customers as nodes, and the connection lines between suppliers and transfer centers, and between transfer centers and customers as paths, establish a forward and reverse integrated network planning model;

[0012] Step 3: Use the improved particle swarm algorithm to solve the forward and reverse integrated network planning model to obtain a logistics network planning scheme.

[0013] The forward and reverse logistics network planning method as described above, the logistics planning related data includes: 1) Market potential supplier information, including the location and supply capacity of suppliers; 2) Transshipment center information, including the location, type, cargo handling capacity, fixed construction cost, and unit cargo handling cost of the transshipment center; 3) Customer information, including the location, demand, return, and service level requirements of customers; 4) Transportation route information, including the routes between suppliers and transshipment centers, transshipment centers and customers, as well as the cargo transportation capacity, construction cost, and unit cargo handling cost on the routes; 5) Logistics transporter information, including the type, transportation capacity, operating cost, and unit cargo transportation cost of transporters; 6) Logistics enterprise investment cost information, including the cost budget for network construction and operation; The types of the transshipment centers include 3 types: forward transshipment center, reverse transshipment center, and mixed transshipment center.

[0014] The forward and reverse logistics network planning method as described above, sorts and classifies the supplier information to construct a supplier set; sorts and classifies the transshipment center information to construct a forward transshipment center set, a reverse transshipment center set, and a mixed transshipment center set respectively; integrates all available logistics transporter information to construct a logistics transporter set; sorts and classifies the customer information to construct a customer set, and uses the scenario planning method in the customer set to sort and classify the customer demand and return information according to different scenarios.

[0015] The forward and reverse logistics network planning method as described above, the satisfaction expressions of both the supply and demand sides include:

[0016] The customer satisfaction expression is:

[0017]

[0018] The supplier satisfaction expression is:

[0019]

[0020] Where

[0021]

[0022] m j represents the service level of the forward network to different customers; C represents the customer set, V represents the transshipment center set, V ij represents the forward logistics transporter set between nodes in the forward network, R represents the set of customer demands corresponding to different scenarios; R * represents the sum of all scenarios; N jr represents the actual cargo demand of customers under different scenarios; Z ijkr represents the actual cargo transportation volume of the k-th transporter between nodes in the forward network under different scenarios;

[0023]

[0024] n represents the service level of the reverse network to the suppliers, S represents the set of suppliers, and L pq represents the set of reverse logistics carriers between nodes in the reverse network, θ represents the proportion of customer returns, and Z qpkr represents the actual cargo transportation volume of the k-th carrier between nodes in the reverse network under different scenarios; m l represents the reference point of customer service level; n l represents the reference point of supplier service level; λ, α, and β are parameters of prospect theory.

[0025] For the positive and reverse logistics network planning method as described above, the establishment of the positive and reverse integrated network planning model includes:

[0026] (a) Taking the network planning scheme that can maximize the lowest level of satisfaction of both supply and demand sides as the goal of the positive and reverse integrated network planning problem considering the integration of positive and reverse networks, constructing an objective function, and the expression is:

[0027]

[0028] (b) According to when a certain transfer center is selected, at least one of the incoming path and the outgoing path adjacent to the transfer center node is selected; when a certain transfer center node is not selected, all paths connected to it cannot be selected; constructing the positive and reverse integrated network structure constraint, and the expression is:

[0029]

[0030]

[0031] Among them, W is the set of all nodes, V p is the set of forward transfer centers, V m is the set of hybrid transfer centers, V n is the set of reverse transfer centers, K ij is the set of all carriers between nodes in the positive and reverse networks, x ijk , y j are both decision variables, x ijk represents whether the k-th carrier between nodes is selected, and y j represents whether the transfer center is to be selected;

[0032] (c) According to the sum of various costs incurred by the overall network should be less than or equal to the size of the total investment budget, constructing the network investment cost constraint, and the expression is as follows:

[0033]

[0034] In the formula, the first item represents the fixed construction cost of the transfer center; the second item represents the fixed operating cost of the transporter between nodes; the third item represents the handling cost of the transfer center for goods during the operation of the forward network; the fourth item represents the handling cost of the transfer center for goods during the operation of the reverse network; the fifth item represents the transportation cost of goods during the network operation, and the sum of the cost is less than or equal to the upper limit of the investment budget; F represents the upper limit of the maximum investment cost of the logistics enterprise, B j represents the fixed construction cost of the transfer center, C j represents the unit handling cost of the transfer center for goods, b ijk represents the fixed operating cost of the k-th transporter between nodes, c ijk represents the unit transportation cost of the k-th transporter between nodes for goods;

[0035] (d) Considering that the forward network cargo transportation volume should be less than or equal to the upper limit of the goods supply quantity of the supplier, a supplier supply quantity constraint is constructed, and the expression is:

[0036]

[0037] Among them, SA i represents the upper limit of the goods supply quantity of the supplier;

[0038] (e) Considering that in different demand scenarios, the customer goods demand quantity is less than or equal to the forward network cargo transportation volume, a forward network transportation volume constraint is constructed, and the expression is:

[0039]

[0040] (f) Considering that the customer return quantity should be greater than or equal to the reverse network return cargo volume, a reverse network transportation volume constraint is constructed, and the expression is:

[0041]

[0042] (g) Considering that in any demand scenario, the upper limit of the transporter's cargo transportation capacity should be greater than or equal to the actual transportation volume on the transportation path, a logistics transporter transportation capacity constraint is constructed, and the expression is:

[0043]

[0044] Among them, h ijk represents the transportation capacity of the k-th transporter between nodes;

[0045] (h) Considering that in any demand scenario, the actual cargo handling volume of the transfer center should be less than its maximum cargo handling capacity, a transfer center handling capacity constraint is constructed, and the expression is:

[0046]

[0047] Among which Q j represents the upper limit of the cargo handling capacity of the transfer center;

[0048] (i) Considering that for any transfer center, the quantity of incoming goods should be equal to the quantity of outgoing goods, a network flow balance constraint is constructed, and the expression is:

[0049]

[0050] (j) Taking the selection of transfer centers, the selection of logistics carriers, and the actual cargo transportation volume of logistics carriers as decision variables, a decision variable constraint for the problem is constructed. The actual cargo transportation volume of logistics carriers should be a non - negative integer, and the selection of transfer centers and logistics carriers should be {0, 1} variables. The expression is:

[0051]

[0052] For the positive - reverse logistics network planning method as described above, step 3 further includes the following steps:

[0053] Step 3.1: Based on the relevant data of logistics planning, number the network nodes in the order of suppliers, transfer centers, and customers, and connect the logistics transportation routes between the nodes in the positive and reverse logistics networks in the order of node numbers, so as to determine the basic structure of the positive - reverse network;

[0054] Step 3.2: Based on the relevant data of logistics planning, determine the number of available logistics carriers for each transportation route in the network structure, and then determine the value range of the number of available carriers;

[0055] Assume that when there are m available carriers between node pairs, the value range of the number of available carriers for each transportation route is [0, 2 m - 1];

[0056] Step 3.3: Set the maximum number of iterations and initial parameters of the improved particle swarm algorithm;

[0057] Step 3.4: Initialize a particle population with the number of Num. The information of each particle is randomly initialized according to the value range of the number of available carriers;

[0058] The information of each particle specifically includes: a position vector with a length of L a velocity vector with a length of L Among which the position vector represents the network planning scheme corresponding to the current particle, x iL ∈[0, 2 m - 1]; The velocity vector represents the improvement direction of the network planning scheme corresponding to the current particle, v iL ∈[1 - 2 m,2 m -1]; L represents the number of node pairs for which the decision-making carrier needs to select a situation;

[0059] Step 3.5: Determine whether the number of algorithm iterations has reached the maximum number of iterations T. If it has, execute Step 3.11; otherwise, execute the next step;

[0060] Step 3.6: Each particle represents a network planning scheme. Check and repair the infeasible schemes among them;

[0061] The infeasible schemes are divided into two types: the selection of carriers exceeds the value range and the network is not connected;

[0062] For the first type of infeasible scheme, the boundary value method is used for repair: when the current value exceeds the upper limit of the value range, the upper limit value of the range is used to replace the current value; when the current value is lower than the lower limit of the value range, the lower limit value of the range is used to replace the current value;

[0063] For the second type of infeasible scheme, there are three cases: ① The supplier is not connected to the network, that is, the supplier cannot ship goods normally in the forward network or cannot receive returns normally in the reverse network; ② The customer is not connected to the network, that is, the customer cannot receive goods normally in the forward network or cannot return goods normally in the reverse network; ③ The input or output end of the transfer center is not connected to the network, that is, the transfer center cannot transfer goods normally;

[0064] The repair strategies for the infeasible schemes in the above three cases are as follows:

[0065] Check whether there is a situation where the supplier is not connected to the network. If there is, check the transfer center connected to the supplier in the basic network structure and randomly select one or some transfer centers to connect;

[0066] Check whether there is a situation where the customer is not connected to the network. If there is, check the transfer center connected to the customer in the basic network structure and randomly select one or some transfer centers to connect;

[0067] Finally, check whether there is a situation where the input or output end of the transfer center is not connected to the network. If the transfer center has no input end, check the suppliers connected to the transfer center in the basic network structure and randomly select one or some suppliers to connect; if the transfer center has no output end, check the customers connected to the transfer center in the basic network structure and randomly select one or some customers to connect;

[0068] Step 3.7: Convert the basic network structure, introduce the minimum cost maximum flow algorithm, and calculate the objective value of the network planning scheme;

[0069] Step 3.8: According to the objective value of the network planning scheme corresponding to each particle, record the optimal objective value that has appeared during the particle iteration process as the historical optimal value of the particle, and the corresponding particle is the historical optimal solution; and find the optimal objective value among all particles as the current global optimal value of the population, and the corresponding particle is the global optimal solution;

[0070] Step 3.9: Update the particle swarm, that is, update the network planning scheme, and check and repair the infeasible scheme after the update;

[0071] Step 3.10: The iteration number t = t + 1, and execute Step 3.5;

[0072] Step 3.11: Output the global optimal solution of the population, and the global optimal solution is the optimal network planning scheme.

[0073] For the forward and reverse logistics network planning method as described above, Step 3.7 further includes the following steps:

[0074] Step 3.7.1: In the basic network structure, equivalent the reverse return process to the forward delivery process of transporting return goods to obtain a forward and reverse integrated network;

[0075] Step 3.7.2: Perform structural topology on the forward and reverse integrated network: Add a source point v S , a sink point v t , virtual nodes and virtual arcs, and further convert the equivalent network into a single-source point - single-sink point network structure so that it can be solved by the minimum cost maximum flow algorithm;

[0076] Step 3.7.3: Use the minimum cost maximum flow algorithm to solve the forward and reverse integrated network topology structure obtained in Step 3.7.2 to obtain the actual cargo transportation volume under the network planning scheme;

[0077] Step 3.7.4: Calculate the network service level through the actual cargo transportation volume, and then obtain the objective value of the network planning scheme.

[0078] For the forward and reverse logistics network planning method as described above, Step 3.9 further includes the following steps:

[0079] Step 3.9.1: Update the particle swarm according to the standard particle swarm algorithm update formula;

[0080] Step 3.9.2: Check and repair the infeasible network planning scheme after the update, and the process is the same as Step 3.6; Solve the objective value of the new network planning scheme, and the process is the same as Step 3.7;

[0081] Step 3.9.3: Introduce a simulated annealing operator, and use the Metropolis criterion of the simulated annealing operator to accept the scheme with a deteriorated objective value after the update with a certain probability;

[0082] Step 3.9.4: Introduce the crossover operator to further update the new population updated in Step 3.9.3 through crossover.

[0083] The positive and reverse logistics network planning method as described above, Step 3.9.3 further includes the following steps:

[0084] Step 3.9.3.1: Compare the change in the objective value of the network planning scheme before and after the update. If the objective value of the new scheme is higher than that of the old scheme, replace it with the new scheme. If the objective value of the new scheme is lower than that of the old scheme, accept the replacement with a certain probability according to the Metropolis criterion for the scheme with a deteriorated objective value after the update. The calculation formula for the acceptance probability P is as follows:

[0085]

[0086] where T(t) is the temperature of each iteration of the simulated annealing operator, and the calculation formula for T(t) is as follows:

[0087]

[0088] where μ is the cooling coefficient, and f(t) is the global optimal value of the population particles at the t-th iteration;

[0089] Step 3.9.3.2: Generate a random number r belonging to U[0,1]. When P≥r, accept the replacement with the scheme having a deteriorated objective value after the update; when P<r, do not accept.

[0090] The positive and reverse logistics network planning method as described above, Step 3.9.4 further includes the following steps:

[0091] Step 3.9.4.1: According to the objective value of the new scheme updated in Step 3.9.3, sort the particles in ascending order of the objective value;

[0092] Step 3.9.4.2: Use the roulette wheel selection method to select the particles to be subjected to the crossover operation from the population. After Num selections, the particle population composed of the selected particles is denoted as group1;

[0093] Step 3.9.4.3: Perform the crossover operation by dividing every two particles in group1 into a group. After performing the crossover operation on all the particles in group1, the new particle population obtained is denoted as group2;

[0094] Step 3.9.4.4: For the population group2, check and repair the infeasible scheme after the update, and the process is the same as that in Step 3.6; solve the objective value of the new network planning scheme, and the process is the same as that in Step 3.7.

[0095] Compared with the prior art, the present invention has the following beneficial effects:

[0096] (1) It breaks through the limitations of the traditional logistics network, considers both the forward delivery and reverse return processes, and realizes the integrated planning of the forward and reverse networks;

[0097] (2) It realizes the collaborative optimization of different carriers on the transportation route, effectively integrates multiple logistics resources, and significantly improves the overall operation efficiency of the network;

[0098] (3) It quantifies the network service level through the goods delivery rate, depicts the satisfaction degrees of both the supply and demand sides based on the prospect theory, and improves the bilateral service object satisfaction evaluation system;

[0099] (4) Aiming at the technical problem that the complexity of network planning solution increases exponentially with the scale, the present invention improves the standard particle swarm optimization algorithm. The minimum cost maximum flow algorithm is introduced in the scheme evaluation stage of the algorithm, and the network is innovatively converted into a structure adapted to the algorithm, enabling it to solve the forward and reverse network problems integrally; in the scheme update stage of the algorithm, the simulated annealing and crossover double operators are innovatively introduced, improving the global optimization ability of the algorithm and the solution accuracy. Finally, compared with the standard particle swarm algorithm, the improved particle swarm optimization algorithm can not only solve the forward and reverse network problems integrally, but also obtain a better network planning solution with higher stability in a shorter time. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 It is a flow schematic diagram of the forward and reverse logistics network planning method that comprehensively considers the satisfaction degrees of supply and demand in this embodiment;

[0101] Figure 2 It is a flow schematic diagram of solving the forward and reverse integrated logistics network planning model in this embodiment;

[0102] Figure 3 It is a basic structure schematic diagram of the forward and reverse network in this embodiment;

[0103] Figure 4 It is a schematic diagram of the corresponding relationship between the transportation route and the carriers on the route in this embodiment;

[0104] Figure 5 It is a flow schematic diagram of the improved particle swarm algorithm in this embodiment;

[0105] Figure 6 It is a topological structure diagram of the forward and reverse integrated network in this embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0106] To facilitate the understanding of the present application, the present application will be described more comprehensively below with reference to the relevant drawings.

[0107] The schematic flow chart of the forward and reverse logistics network planning method that comprehensively considers the supply and demand satisfaction provided by this embodiment is as follows Figure 1 as shown, and the specific implementation steps are as follows:

[0108] Step 1: Extract logistics planning-related data from relevant business information;

[0109] The logistics planning-related data extracted from relevant business information in this embodiment includes: 1) Market potential supplier information, including the location and supply capacity of suppliers; 2) Transshipment center information, including the location, type (a total of 3 types: forward transshipment center, reverse transshipment center, and mixed transshipment center), cargo handling capacity, fixed construction cost, and unit cargo handling cost of the transshipment center; 3) Customer information, including the location, demand, return, and service level requirements of customers; 4) Transportation route information, including the routes between suppliers and transshipment centers, transshipment centers and customers, and the cargo transportation capacity, construction cost, and unit cargo handling cost on the routes; 5) Logistics transporter information, including the type, transportation capacity, operating cost, and unit cargo transportation cost of transporters; 6) Logistics enterprise investment cost information, including the cost budget for network construction and operation.

[0110] For the convenience of subsequent steps, this embodiment sorts and classifies some of the above logistics planning data, specifically including: sorting and classifying according to supplier information to construct a supplier set; sorting and classifying according to transshipment center information to construct a forward transshipment center set, a reverse transshipment center set, and a mixed transshipment center set respectively; integrating all available logistics transporter information to construct a logistics transporter set; sorting and classifying according to customer information to construct a customer set, and using scenario planning methods to sort and classify customer demand and return information according to different scenarios in the customer set.

[0111] Step 2: Determine decision variables and depict the satisfaction of both supply and demand sides. Combining the logistics planning-related data with the satisfaction expressions of both supply and demand sides, considering the integration of forward and reverse networks, taking suppliers, transshipment centers, and customers as nodes and the connection lines between suppliers and transshipment centers, transshipment centers and customers as paths, establish a forward and reverse integrated network planning model.

[0112] This embodiment takes the selection of transshipment centers, the selection of logistics transporters, and the actual cargo transportation volume of logistics transporters as decision variables.

[0113] Step 2.1: Depict the satisfaction of both supply and demand sides and establish an expression for the satisfaction of both supply and demand sides. Specifically, it includes the following three steps:

[0114] Step 2.1.1: Establish an evaluation criterion for customer service level.

[0115] This embodiment characterizes the service level of the network to customers by the actual delivery rate of the goods demanded by customers (the proportion of the actual delivered quantity in the forward network logistics transportation process to the total customer demand), and the expression is:

[0116]

[0117] where m j represents the service level of the forward network to different customers, C represents the set of customers, V represents the set of transfer centers, and V ij represents the set of forward logistics transporters between nodes in the forward network, R represents the set of customer demands corresponding to different scenarios; R * represents the sum of all scenarios; N jr represents the actual goods demand of customers under different scenarios; Z ijkr represents the actual goods transportation volume of the k-th transporter between nodes in the forward network under different scenarios.

[0118] Step 2.1.2: Establish the evaluation criteria for the supplier service level.

[0119] This embodiment characterizes the service level of the network to suppliers by the actual delivery rate of the goods returned to the suppliers (the proportion of the actual returned quantity in the reverse network logistics transportation process to the total customer returns), and the expression is:

[0120]

[0121] where n represents the service level of the reverse network to suppliers, S represents the set of suppliers, L pq represents the set of reverse logistics transporters between nodes in the reverse network, θ represents the customer return ratio, and Z qpkr represents the actual goods transportation volume of the k-th transporter between nodes in the reverse network under different scenarios.

[0122] Step 2.1.3: Use the value function in prospect theory and the established evaluation criteria for the service levels of suppliers and customers to characterize the satisfaction degrees of both the supply and demand sides. The expression for customer satisfaction is:

[0123]

[0124] The expression for supplier satisfaction is:

[0125]

[0126] where m l represents the customer service level reference point (threshold), n l represents the supplier service level reference point (threshold), and λ, α, and β are prospect theory parameters.

[0127] Step 2.2: Combine the relevant data of logistics planning with the satisfaction expressions of both the supply and demand sides, consider the integration of the forward and reverse networks, take suppliers, transfer centers, and customers as nodes, and the connection lines between suppliers and transfer centers, and between transfer centers and customers as paths to establish a forward and reverse integrated network planning model;

[0128] Step 2.2.1: According to the characterized satisfaction of both the supply and demand sides, take the network planning scheme that can maximize the lowest level of the satisfaction of both sides as the goal of the forward and reverse integrated network planning problem considering the integration of the forward and reverse networks, and construct an objective function. The function expression is:

[0129]

[0130] Step 2.2.2: Determine the constraints of the forward and reverse integrated network structure according to the characteristics of the forward and reverse integrated network structure.

[0131] When a certain transfer center is selected, at least one of the incoming path and the outgoing path adjacent to this transfer center node is selected; when a certain transfer center node is not selected, all paths connected to it cannot be selected. The constraint expression of the forward and reverse integrated network structure is:

[0132]

[0133]

[0134] Among them, W is the set of all nodes, V p is the set of forward transfer centers, V m is the set of mixed transfer centers, V n is the set of reverse transfer centers, K ij is the set of all carriers between the nodes of the forward and reverse networks, x ijk and y j are both decision variables. x ijk represents whether the kth carrier between nodes is selected, and y j represents whether the transfer center is to be selected.

[0135] Step 2.2.3: Construct a network investment cost constraint according to the sum of the costs incurred in constructing the overall network should be less than or equal to the size of the total investment budget. The expression is as follows:

[0136]

[0137] In the formula, the first term represents the fixed construction cost of the transfer center; the second term represents the fixed operating cost of the transporter between nodes; the third term represents the handling cost of the transfer center for goods in the forward network operation process; the fourth term represents the handling cost of the transfer center for goods in the reverse network operation process; the fifth term represents the transportation cost of goods in the network operation process, and the sum of the cost is less than or equal to the upper limit of the investment budget.

[0138] Among them, F represents the upper limit of the maximum investment cost of the logistics enterprise, and B j represents the fixed construction cost of the transfer center, and C j represents the unit handling cost of the transfer center for goods, and b ijk represents the fixed operating cost of the k-th transporter between nodes, and c ijk represents the unit transportation cost of the k-th transporter between nodes for goods.

[0139] Step 2.2.4: Considering that the forward network cargo transportation volume should be less than or equal to the upper limit of the goods supply quantity of the supplier, a supplier supply quantity constraint is constructed. The constraint expression is:

[0140]

[0141] Among them, SA i represents the upper limit of the goods supply quantity of the supplier.

[0142] Step 2.2.5: Considering that in different demand scenarios, the customer goods demand quantity is less than or equal to the forward network cargo transportation volume, a forward network transportation volume constraint is constructed. The constraint expression is:

[0143]

[0144] Step 2.2.6: Considering that the customer return quantity should be greater than or equal to the reverse network return cargo arrival volume, a reverse network transportation volume constraint is constructed. The constraint expression is:

[0145]

[0146] Step 2.2.7: Considering that in any demand scenario, the upper limit of the cargo transportation capacity of the transporter should be greater than or equal to the actual transportation volume on the transportation path, a logistics transporter transportation capacity constraint is constructed, and the constraint expression is:

[0147]

[0148] Among them, h ijk represents the transportation capacity of the k-th transporter between nodes.

[0149] Step 2.2.8: Considering that the actual cargo handling volume of the transfer center under any demand scenario should be less than its maximum cargo handling capacity, a constraint on the handling capacity of the transfer center is constructed, and this constraint holds for both forward, reverse, and hybrid transfer centers. The constraint expression is:

[0150]

[0151] where Q j represents the upper limit of the cargo handling capacity of the transfer center.

[0152] Step 2.2.9: Considering that for any transfer center, the quantity of inflowing goods should be equal to the quantity of outflowing goods, a network flow balance constraint is constructed. The constraint expression is:

[0153]

[0154] Step 2.2.10: A constraint on the decision variables of the problem is constructed. The actual cargo transportation volume of the logistics transporter should be a non - negative integer, and the selection of the transfer center and the logistics transporter should be a {0, 1} variable. The constraint expression is:

[0155]

[0156] Step 3: Use the meta - heuristic algorithm to solve the forward - reverse integrated network planning model to obtain the logistics network planning scheme.

[0157] In this embodiment, the meta - heuristic algorithm used is an improved particle swarm optimization algorithm. The core idea of the particle swarm optimization algorithm is: randomly generate a particle population, and find the optimal solution by simulating the search behavior of a group of particles in a multi - dimensional space. Each particle represents a potential solution to the problem and has two attributes, velocity and position. Each solution corresponds to a network planning scheme. The velocity represents how fast the particle moves, and the position represents the direction of the particle's movement. Each particle searches for the optimal solution alone in the search space and records it as the current individual extreme value. At the same time, all particles in the particle swarm share information about the quality of the solutions, guiding the entire group to iteratively improve towards a better solution. The particle swarm continuously updates its position during the iteration process and finally converges to the global optimal solution to obtain the final network planning scheme.

[0158] This embodiment makes the following improvements to the standard particle swarm optimization algorithm: introducing the minimum - cost maximum - flow algorithm in the scheme evaluation stage and innovatively converting the network into a structure adapted to this algorithm so that it can solve the forward - reverse network problem integrally; in the scheme update stage, innovatively introducing simulated annealing and crossover double operators to improve the global optimization ability of the particle swarm optimization algorithm.

[0159] The specific process of applying the improved particle swarm optimization algorithm to solve the forward - reverse integrated logistics network planning model in this embodiment is as Figure 2 shown and includes the following steps:

[0160] Step 3.1: Based on the logistics planning related data, number the network nodes in the order of suppliers, transfer centers, and customers, and connect the logistics transportation routes between the nodes in the forward and reverse logistics networks in the order of node numbers, so as to determine the basic structure of the forward and reverse networks.

[0161] In this embodiment, the basic structure of the forward and reverse networks is as Figure 3 shown. The entire process of goods transportation in the forward and reverse networks can be understood as follows: When customers (square nodes numbered 6, 7, 8, and 9) have a demand for goods, the goods are sent from suppliers (circular nodes numbered 1 and 2), and are transported to customers via the forward logistics transportation line. For example, the line: node 1 representing the supplier - node 3 representing the forward transfer center - node 6 representing the customer; when returns occur at the customer end, the returned goods are sent from the customer and returned to the supplier via the reverse logistics transportation line. For example, the line: node 9 representing the customer - node 5 representing the reverse transfer center - node 2 representing the supplier.

[0162] Step 3.2: Based on the logistics planning related data, determine the number of available logistics carriers for each transportation route in the network structure, and then determine the value range of the number of available carriers for the carriers. The corresponding relationship between the transportation routes and the carriers is as Figure 4 shown. Assume that when there are m available carriers between node pairs, the value range of the number of available carriers for each transportation route is [0, 2 m -1].

[0163] Step 3.3: Set the maximum number of iterations and initial parameters of the improved particle swarm optimization algorithm;

[0164] In this embodiment, the improved particle swarm optimization algorithm is used to solve the forward and reverse network planning model. The overall process of the improved particle swarm optimization algorithm is as Figure 5 shown. First, set the maximum number of iterations and initial parameters of the improved particle swarm optimization algorithm. Set the maximum number of iterations to T, and the initial parameters include the number of particle swarms Num, inertia weight w, individual learning factor c1, population learning factor c2, cooling coefficient μ, and crossover probability P c .

[0165] Among them, the inertia weight w represents the ability of the particle to retain its original solution, and generally takes values in [0.4, 0.9]; the individual learning factor c1 represents the degree of learning of the particle from its own historical optimal solution, and generally takes values in [0, 3.0]; the population learning factor c2 represents the degree of learning of the particle from the global optimal solution, and generally takes values in [0, 3.0]; the cooling coefficient μ affects the solution accuracy of the algorithm, and generally takes values in [0.9, 1.0]; the crossover probability P c affects the optimization effect of the algorithm, and generally takes values in [0.5, 1.0].

[0166] Step 3.4: Initialize a particle swarm with the number of particles being Num. The information of each particle is randomly initialized according to the value range available for selection by the carriers. The information of each particle specifically includes: a position vector of length L a velocity vector of length L where the position vector represents the network planning scheme corresponding to the current particle, and x iL ∈[0, 2 m -1]; the velocity vector represents the improvement direction of the network planning scheme corresponding to the current particle, and v iL ∈[1 - 2 m , 2 m -1]; L represents the number of node pairs for which the selection of carriers needs to be determined. The order of each bit in the two vectors, the position vector and the velocity vector, corresponds to the order of the node pairs for which the selection of carriers needs to be determined in the network.

[0167] Step 3.5: Determine whether the number of algorithm iterations has reached T. If it has, execute Step 3.11; otherwise, execute the next step;

[0168] Step 3.6: Each particle represents a network planning scheme. Check and repair the infeasible schemes among them.

[0169] Infeasible schemes may exist both after the population initialization and during the update process of the network planning scheme, and both need to be checked and repaired. In this embodiment, the types of infeasible schemes can be specifically divided into: ① The selection of carriers exceeds the value range; ② The network is not connected.

[0170] For the first type, it is necessary to ensure that the value of each bit of the particle position and velocity vector is within the value range shown in Step 3.4. Therefore, for this type, the boundary value method is used for repair. When the current value exceeds the upper limit of the value range, the upper limit value of the range is used to replace the current value; when it is lower than the lower limit of the value range, the lower limit value of the range is used to replace the current value.

[0171] For the second type, there are three cases: ① The supplier is not connected to the network, that is, the supplier cannot ship goods normally in the forward network or cannot receive returns normally in the reverse network; ② The customer is not connected to the network, that is, the customer cannot receive goods normally in the forward network or cannot return goods normally in the reverse network; ③ The in - end or out - end of the transfer center is not connected to the network, that is, the transfer center cannot transfer goods normally.

[0172] The repair strategies for the infeasible schemes in the above three cases are as follows:

[0173] 1. Check whether there is a situation where the supplier is not connected to the network. If so, check the transfer center connected to the supplier in the basic network structure and randomly select one or some transfer centers to connect.

[0174] 2. Check whether there is a situation where the customer is not connected to the network. If so, check the transfer center connected to the customer in the basic network structure and randomly select one or some transfer centers to connect.

[0175] 3. Finally, check whether there is a situation where the in - end or out - end of the transfer center is not connected to the network. If the transfer center has no in - end, check the suppliers connected to the transfer center in the basic network structure and randomly select one or some suppliers to connect; if there is no out - end, check the customers connected to the transfer center in the basic network structure and randomly select one or some customers to connect.

[0176] Step 3.7: Transform the basic network structure, introduce the minimum - cost maximum - flow algorithm, and calculate the objective value of the network planning scheme.

[0177] The standard minimum - cost maximum - flow algorithm is only applicable to solving single - source - single - sink networks and cannot integrate the forward delivery and reverse return processes. Therefore, it is necessary to transform the basic network structure. The transformed integrated forward - reverse network topology is as Figure 6 shown. The present invention aims to improve the lowest level of satisfaction of both the supply and demand sides. The satisfaction value is the objective value of the network planning scheme. The larger the objective value, the better the scheme. The specific steps of this embodiment are as follows:

[0178] Step 3.7.1: In the basic network structure, equivalent the reverse return process to the forward delivery process of transporting return goods to obtain an integrated forward - reverse network structure.

[0179] Considering that the basic network structure of the reverse transportation process is the same as that of the forward transportation process, only the direction of goods transportation and the composition of transfer centers participating in different transportation processes are different. Therefore, the reverse return process can be equivalent to the forward delivery process of transporting return goods, and at the same time, solve the distribution of the transportation volume of forward and reverse goods on the transportation path to achieve an integrated consideration of the forward - reverse network. Specifically, as Figure 6As shown in the figure, the forward goods demand process of customers in the original network basic structure remains unchanged, that is, the forward customers (numbered 9, 10, 11, 12) in the original forward network; the reverse goods return process of customers in the original network basic structure is equivalent to the forward delivery process of transporting return goods, and the customers initiating returns are converted into equivalent forward customers (numbered 13, 14, 15, 16) with the quantity of goods returned in the original reverse network as the goods demand; the forward and mixed transfer centers and customers (numbered 9, 10, 11, 12) are connected by the original forward transporter, representing the original forward transportation process, and the mixed and reverse transfer centers and customers (numbered 13, 14, 15, 16) are connected by the original reverse transporter, representing the converted forward transportation process; the obtained integrated forward and reverse network structure can simultaneously consider the distribution of the handling volumes of forward and reverse goods by the mixed transfer center, achieving integrated consideration of forward and reverse directions;

[0180] Step 3.7.2: Perform structure topology on the network equivalent in Step 3.7.1. The specific operation is as follows: Add a source point v S and a sink point v t , virtual nodes and virtual arcs to the network, and further convert the equivalent network into a single-source point - single-sink point network structure so that it can be solved by the minimum-cost maximum-flow algorithm.

[0181] Specifically, as Figure 6 shown, first add a source point v S as the starting point of the network and add a sink point v t as the ending point of the network. The quantities of forward and reverse goods to be transported are both sent from v S and end at v t ; secondly, add a forward aggregation node (numbered 3) and a reverse aggregation node (numbered 4) to split the goods, transport forward demand goods by the forward network, and transport reverse return goods by the reverse equivalent network; finally, add virtual nodes to the aggregation center, transfer center, and customers respectively, and represent the goods demand quantity limit and processing capacity quantity limit by the transport capacity of the virtual arcs between the corresponding nodes and virtual nodes; thus, all conversion processes of the network basic structure are completed, and the final converted integrated forward and reverse network topology structure is Figure 6 the structure shown, which can be solved by the minimum-cost maximum-flow algorithm;

[0182] Step 3.7.3: Use the minimum-cost maximum-flow algorithm to solve the integrated forward and reverse network topology structure obtained in Step 3.7.2 to obtain the actual goods transport volume under the network planning scheme;

[0183] Step 3.7.4: Calculate the network service level through the actual goods transport volume, and then obtain the target value of the network planning scheme.

[0184] Step 3.8: According to the objective values of the network planning schemes corresponding to each particle, record the optimal value that has appeared during the particle iteration process as the historical optimal value of the particle, and the corresponding particle is the historical optimal solution; and find the optimal objective value among all particles as the current global optimal value of the population, and the corresponding particle is the global optimal solution.

[0185] Step 3.9: Update the particle swarm, that is, update the network planning scheme, and check and repair the infeasible schemes after the update. The specific steps are as follows:

[0186] Step 3.9.1: Update the particle swarm according to the standard particle swarm optimization algorithm update formula. First, update the velocity of each particle in the population The update formula for the velocity vector is:

[0187]

[0188] Then update the position of each particle in the population The update formula for the position vector is:

[0189]

[0190] In the above formula, i represents the i-th particle in the population, D represents the D-th dimension of the particle, t represents the t-th generation, represents the particle velocity vector, represents the particle position vector, is the historical optimal solution of the particle, is the global optimal solution of the population, w is the inertia weight, c1 and c2 are learning factors, ξ and η are scaling factors, and the scaling factors take values from a uniform distribution U[0,1].

[0191] Step 3.9.2: Check and repair the infeasible schemes after the update, and the process is the same as that in Step 3.6; solve the objective value of the new network planning scheme, and the process is the same as that in Step 3.7;

[0192] Step 3.9.3: Introduce the simulated annealing operator, and use the Metropolis criterion of the simulated annealing operator to accept the scheme with a deteriorated objective value after the update with a certain probability. The specific implementation steps are as follows:

[0193] Step 3.9.3.1: Compare the change in the objective value of the network planning scheme before and after the update in Step 3.9.2. If the objective value of the new scheme is higher than that of the old scheme, replace it with the new scheme. If the objective value of the new scheme is lower than that of the old scheme, accept the replacement with the scheme with a deteriorated objective value after the update according to the Metropolis criterion. The calculation formula for the acceptance probability P is:

[0194]

[0195] Among them, T(t) is the temperature of each iteration of the simulated annealing operator, and the calculation formula of T(t) is as follows:

[0196]

[0197] Among them, μ is the temperature reduction coefficient, and f(t) is the global optimal value of the population particles at the t-th iteration.

[0198] Step 3.9.3.2: Generate a random number r belonging to U[0,1]. When P≥r, accept the solution with a deteriorated updated target value for replacement; when P<r, do not accept it.

[0199] Step 3.9.4: Introduce a crossover operator to further cross-update the new population updated in Step 3.9.3. The specific implementation steps are as follows:

[0200] Step 3.9.4.1: According to the target value sizes of the new solutions updated in Step 3.9.3, sort the particles in ascending order of the target value;

[0201] Step 3.9.4.2: Use the roulette wheel selection method to select the particles to perform the crossover operation from the population. To ensure that the population size remains unchanged before and after the crossover operation, it is executed Num times, and the selected particle group is denoted as group1;

[0202] Step 3.9.4.3: In the order in group1, every two particles are grouped for the crossover operation. The two particles performing the crossover operation are denoted as crowd1 and crowd2. The specific crossover operation is as follows: Traverse the two particles simultaneously in the order of each bit from front to back. Each time, generate a random number ε belonging to U[0,1] and compare it with the initially set crossover probability P c for comparison. When ε≥P c perform the crossover operation and swap the corresponding bit numbers of crowd1 and crowd2; when ε<P c do not perform the crossover operation and retain the original numbers of the corresponding bits of crowd1 and crowd2; finally, when all bit data have been traversed, a new pair of particles is obtained, denoted as crowd′1 and crowd′2; when the crossover operation has been performed on all particles in group1, the new particle population is denoted as group2;

[0203] Step 3.9.4.4: For the population group2, check and repair the infeasible solutions after the update, and the process is the same as in Step 3.6; solve the target value of the new network planning solution, and the process is the same as in Step 3.7.

[0204] Through Steps 3.3 to 3.9, a new network planning solution can be obtained by improving the particle swarm optimization algorithm.

[0205] Step 3.10: The iteration number t = t + 1, and execute Step 3.5;

[0206] Step 3.11: Output the global optimal solution of the population, and the global optimal solution is the optimal network planning scheme.

[0207] It should be understood that those skilled in the art, inspired by the technical concept of the present invention, can also make various improvements or transformations based on the above content without departing from the content of the present invention, and this still falls within the protection scope of the present invention.

[0208] To verify the performance advantages of the method of the present invention, two groups of different calculation examples are designed. Each group of calculation examples includes three different scales of 9 nodes, 14 nodes, and 24 nodes. The first group of calculation examples is labeled as "9-node - 1", "14-node - 1", "24-node - 1", and the second group of calculation examples is labeled as "9-node - 2", "14-node - 2", "24-node - 2". And five evaluation indicators are adopted: the optimal value (BS), the worst value (WS), the average value (Mean), the standard deviation percentage (SE), and the running time (Time) as the evaluation criteria. Among them, the formula for calculating the standard deviation percentage (SE) is as follows:

[0209]

[0210] In the formula, N is the number of data samples, x iIt is the result of the i-th numerical experiment. Among the above five evaluation indicators, BS, WS, and the Mean value reflect the accuracy of the algorithm's solution results. The larger the value, the better the algorithm performance. The SE value reflects the algorithm's stability, and the Time value reflects the algorithm's time consumption. The smaller the values of both, the better the performance. Based on the above five evaluation indicators, the algorithm proposed in the present invention is compared and analyzed with existing algorithms with better effects. Specifically, five algorithms are compared: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Particle Swarm Optimization algorithm embedded with Crossover strategy (C-PSO), Particle Swarm Optimization algorithm embedded with Simulated Annealing strategy (SA-PSO), and Particle Swarm Optimization algorithm embedded with Simulated Annealing and Crossover dual strategies (SAC-PSO). The experimental comparison results are shown in Table 1. Incorporating the simulated annealing operator enables the standard particle swarm algorithm to jump out of local optima, and incorporating the crossover operator further improves the algorithm's optimization ability. Both strategies can improve the solution accuracy. Therefore, the improved particle swarm algorithm incorporating the dual operators has the optimal solution ability compared to the other four algorithms. The experimental results verify the effectiveness and superiority of the improved particle swarm algorithm proposed in the present invention.

[0211] Table 1 Comparison of algorithm results

[0212]

[0213] Obviously, the above embodiments are only a part of the embodiments of the present invention, rather than all embodiments. The above embodiments are only used to explain the present invention and do not constitute a limitation on the protection scope of the present invention. Based on the above embodiments, all other embodiments obtained by those skilled in the art without creative efforts, that is, all modifications, equivalent replacements, and improvements made within the spirit and principle of this application, fall within the protection scope required by the present invention.

Claims

1. A method for planning a forward and reverse logistics network considering supply and demand satisfaction comprehensively, characterized in that, The method includes the following steps: Step 1: Collect data related to logistics planning; Step 2: Determine the decision variables and the satisfaction expressions of both the supply and demand sides. Combine the logistics planning-related data with the satisfaction expressions of both the supply and demand sides, and consider the forward and reverse networks integrally. Taking suppliers, transfer centers, and customers as nodes, and the connecting lines between suppliers and transfer centers, and between transfer centers and customers as paths, establish a forward and reverse integrated network planning model; Step 3: Use the improved particle swarm optimization algorithm to solve the forward and reverse integrated network planning model to obtain a logistics network planning scheme.

2. The forward and reverse logistics network planning method according to claim 1, characterized in that, The logistics planning-related data includes: 1) Information on potential market suppliers, including the locations and supply capabilities of suppliers; 2) Information on transfer centers, including the locations, types, cargo handling capabilities, fixed construction costs, and unit cargo handling costs of transfer centers; 3) Customer information, including the locations, demands, returns, and service level requirements of customers; 4) Information on transportation routes, including the routes between suppliers and transfer centers, and between transfer centers and customers, as well as the cargo transportation capabilities, construction costs, and unit cargo handling costs on the routes; 5) Information on logistics carriers, including the types, transportation capabilities, operating costs, and unit cargo transportation costs of carriers; 6) Information on the investment costs of logistics enterprises, including the cost budgets for network construction and operation; The types of transfer centers include 3 types: forward transfer centers, reverse transfer centers, and hybrid transfer centers.

3. The positive and reverse logistics network planning method according to claim 2, characterized in that, Sort and classify the supplier information to construct a supplier set; sort and classify the transfer center information to construct a forward transfer center set, a reverse transfer center set, and a hybrid transfer center set respectively; integrate all available logistics carrier information to construct a logistics carrier set; sort and classify the customer information to construct a customer set, and in the customer set, use the scenario planning method to sort and classify the customer demands and return information according to different scenarios.

4. The positive and reverse logistics network planning method according to claim 3, characterized in that The satisfaction expressions of both the supply and demand sides include: The customer satisfaction expression is: The supplier satisfaction expression is: Where m j represents the service level of the forward network for different customers; C represents the set of customers, V represents the set of transfer centers, V ij represents the set of forward logistics carriers between nodes in the forward network, R represents the set of customer demands corresponding to different scenarios; N jr represents the actual cargo demand of customers under different scenarios; Z ijkr represents the actual cargo transportation volume of the k-th carrier between nodes in the forward network under different scenarios; n represents the service level of the reverse network to the suppliers, S represents the set of suppliers, and L pg represents the set of reverse logistics carriers between nodes in the reverse network, θ represents the customer return ratio, and Z qpkr represents the actual cargo transportation volume of the k-th carrier between nodes in the reverse network under different scenarios; m l represents the customer service level reference point; n l represents the supplier service level reference point; λ, α, and β are prospect theory parameters.

5. The forward and reverse logistics network planning method according to claim 4, characterized in that The establishment of the forward and reverse integrated network planning model includes: (a) Taking the network planning scheme that can maximize the minimum level of the satisfaction of both the supply and demand sides as the goal of the forward and reverse integrated network planning problem considering the forward and reverse networks integrally, construct an objective function, and the expression is: (b) According to when a certain transfer center is selected, at least one of the incoming path and the outgoing path adjacent to the transfer center node is selected; when a certain transfer center node is not selected, all the paths connected to it cannot be selected; construct the forward and reverse integrated network structure constraints, and the expression is: Among them, W is the set of all nodes, V p is the set of forward transfer centers, V m is the set of mixed transfer centers, V n is the set of reverse transfer centers, K ij is the set of all carriers between the nodes of the forward and reverse networks, x ijk , y j are both decision variables. x ijk represents whether the k-th carrier between nodes is selected, and y j represents whether a transfer center is to be selected; (c) According to the sum of the various costs incurred by the overall network should be less than or equal to the total investment budget size, construct the network investment cost constraints, and the expression is as follows: In the formula, the first term represents the fixed construction cost of the transfer center; the second term represents the fixed operating cost of the carriers between nodes; the third term represents the handling cost of the transfer center for goods during the operation of the forward network; the fourth term represents the handling cost of the transfer center for goods during the operation of the reverse network; the fifth term represents the transportation cost of goods during the network operation, and the sum of the cost is less than or equal to the upper limit of the investment budget; F represents the upper limit of the maximum investment cost of the logistics enterprise, B j represents the fixed construction cost of the transfer center, C j represents the unit handling cost of the transfer center for goods, b ijk represents the fixed operating cost of the k-th carrier between nodes, c ijk represents the unit transportation cost of the k-th carrier between nodes; (d) Considering that the cargo transportation volume of the forward network should be less than or equal to the upper limit of the cargo supply quantity of the supplier, construct the supplier supply quantity constraints, and the expression is: Among them, SA i represents the upper limit of the supplier's goods supply quantity; (e) Considering that in different demand scenarios, the customer cargo demand quantity is less than or equal to the cargo transportation volume of the forward network, construct the forward network transportation volume constraints, and the expression is: (f) Considering that the quantity of customer returns should be greater than or equal to the quantity of goods transported back in the reverse network, a constraint on the quantity of goods transported in the reverse network is constructed, and the expression is: (g) Considering that under any demand scenario, the upper limit of the goods transportation capacity of the transporter should be greater than or equal to the actual quantity of goods transported on the transportation route, a constraint on the transportation capacity of the logistics transporter is constructed, and the expression is: where h ijk represents the transportation capacity of the k-th transporter between nodes; (h) Considering that under any demand scenario, the actual quantity of goods processed at the transfer center should be less than its maximum goods processing capacity, a constraint on the processing capacity of the transfer center is constructed, and the expression is: Among which Q j represents the upper limit of the cargo handling capacity of the transfer center; (i) Considering that for any transfer center, the quantity of inflowing goods should be equal to the quantity of outflowing goods, a network flow balance constraint is constructed, and the expression is: (j) Taking the selection of transfer centers, the selection of logistics transporters, and the actual quantity of goods transported by the logistics transporters as decision variables, a constraint on the decision variables of the problem is constructed. The actual quantity of goods transported by the logistics transporters should be a non-negative integer, and the selection of transfer centers and logistics transporters should be {0, 1} variables. The expression is:

6. The forward and reverse logistics network planning method according to claim 5, characterized in that, Step 3 further includes the following steps: Step 3.1: Based on the relevant data of logistics planning, number the network nodes in the order of suppliers, transfer centers, and customers, and connect the logistics transportation routes between the nodes in the forward and reverse logistics networks in the order of node numbers to determine the basic structure of the forward and reverse networks; Step 3.2: Based on the relevant data of logistics planning, determine the number of available logistics transporters on each transportation route in the network structure, and then determine the range of values of the number of available transporters; When there are m alternative carriers between node pairs, the value range of the number of available carriers for each transportation route is [0, 2 m - 1]; Step 3.3: Set the maximum number of iterations and initial parameters of the improved particle swarm algorithm; Step 3.4: Initialize a particle population with the number Num, and randomly initialize the information of each particle according to the range of values of the number of available transporters; The information of each particle specifically includes: a position vector of length L a velocity vector of length L where the position vector represents the network planning scheme corresponding to the current particle, x iL ∈[0, 2 m - 1]; the velocity vector represents the improvement direction of the network planning scheme corresponding to the current particle, v iL ∈[1 - 2 m , 2 m - 1]; L represents the number of node pairs for which the decision-making carrier needs to select a situation; Step 3.5: Determine whether the number of algorithm iterations has reached the maximum number of iterations T. If so, execute Step 3.11; otherwise, execute the next step; Step 3.6: Each particle represents a network planning scheme, and check and repair the infeasible schemes among them; The infeasible schemes are divided into two types: the selection of transporters exceeds the range of values and the network is not connected; For the first type of infeasible scheme, it is repaired by taking the boundary value: when the current value exceeds the upper limit of the value range, the upper limit value of the range is used to replace the current value; when the current value is lower than the lower limit of the value range, the lower limit value of the range is used to replace the current value; For the second type of infeasible scheme, there are three cases: ① The supplier is not connected to the network, that is, the supplier in the forward network cannot ship goods normally or the supplier in the reverse network cannot receive returns normally; ② The customer is not connected to the network, that is, the customer in the forward network cannot receive goods normally or the customer in the reverse network cannot return goods normally; ③ The in - end or out - end of the transfer center is not connected to the network, that is, the transfer center cannot transfer goods normally; The repair strategies for the infeasible schemes in the above three cases are as follows: Check whether there is a situation where the supplier is not connected to the network. If so, check the transfer centers connected to the supplier in the basic network structure and randomly select one or some transfer centers to connect; Check whether the customer is disconnected from the network. If so, check the transfer centers connected to the customer in the basic network structure and randomly select one or some of them to connect; Finally, check whether there is an inbound or outbound end of the transfer center that is disconnected from the network. If the transfer center has no inbound end, check the suppliers connected to the transfer center in the basic network structure and randomly select one or some of them to connect; if the transfer center has no outbound end, check the customers connected to the transfer center in the basic network structure and randomly select one or some of them to connect; Step 3.7: Transform the basic network structure, introduce the minimum-cost maximum-flow algorithm, and calculate the objective value of the network planning scheme; Step 3.8: According to the objective value of the network planning scheme corresponding to each particle, record the optimal objective value that appears during the particle iteration as the historical optimal value of the particle, and the corresponding particle is the historical optimal solution; and find the optimal objective value among all particles as the current global optimal value of the population, and the corresponding particle is the global optimal solution; Step 3.9: Update the particle swarm, that is, update the network planning scheme, and check and repair the infeasible scheme after the update; Step 3.10: The iteration number t = t + 1, and execute Step 3.5; Step 3.11: Output the global optimal solution of the population, and the global optimal solution is the optimal network planning scheme.

7. The forward and reverse logistics network planning method according to claim 6, characterized in that, The said Step 3.7 further includes the following steps: Step 3.7.1: In the basic network structure, equivalent the reverse return process to the forward delivery process of transporting return goods to obtain a forward and reverse integrated network; Step 3.7.2: Perform structural topology on the forward and reverse integration network: Add a source point v to the network S , a sink point v t , virtual nodes and virtual arcs, and further convert the equivalent network into a single-source point - single-sink point network structure so that it can be solved by the minimum cost maximum flow algorithm; Step 3.7.3: Use the minimum-cost maximum-flow algorithm to solve the forward and reverse integrated network topology structure obtained in Step 3.7.2 to obtain the actual cargo transportation volume under the network planning scheme; Step 3.7.4: Calculate the network service level through the actual cargo transportation volume, and then obtain the objective value of the network planning scheme.

8. The forward and reverse logistics network planning method according to claim 6, wherein Step 3.9 further includes the following steps: Step 3.9.1: Update the particle swarm according to the standard particle swarm algorithm update formula; Step 3.9.2: Check and repair the infeasible network planning scheme after the update, and the process is the same as Step 3.6; solve the objective value of the new network planning scheme, and the process is the same as Step 3.7; Step 3.9.3: Introduce the simulated annealing operator, and use the Metropolis criterion of the simulated annealing operator to accept the scheme with a deteriorated objective value after the update with a certain probability; Step 3.9.4: Introduce the crossover operator to further cross-update the new population updated in Step 3.9.

3.

9. The forward and reverse logistics network planning method according to claim 8, characterized in that The said Step 3.9.3 further includes the following steps: Step 3.9.3.1: Compare the change in the objective value of the network planning scheme before and after the update. If the objective value of the new scheme is higher than that of the old scheme, replace it with the new scheme. If the objective value of the new scheme is lower than that of the old scheme, accept the replacement with a deteriorated objective value after the update according to the Metropolis criterion with a certain probability. The calculation formula of the acceptance probability P is: where, T(t) is the temperature of each iteration of the simulated annealing operator, and the calculation formula of T(t) is as follows: where, μ is the cooling coefficient, and f(t) is the global optimal value of the population particles at the t-th iteration; Step 3.9.3.2: Generate a random number r belonging to U[0,1]. When P≥r, accept the solution with a deteriorated objective value after replacement as the updated one; when P<r, do not accept it.

10. The forward and reverse logistics network planning method according to claim 8, wherein Step 3.9.4 further includes the following steps: Step 3.9.4.1: Sort the particles in ascending order of the objective value according to the objective value of the new solution updated in Step 3.9.

3. Step 3.9.4.2: Use the roulette wheel selection method to select the particles to perform the crossover operation from the population. After Num selections, the particle swarm composed of the selected particles is denoted as group1. Step 3.9.4.3: Perform the crossover operation by dividing every two particles in group1 into a group. After performing the crossover operation on all particles in group1, the new particle population is denoted as group2. Step 3.9.4.4: For the population group2, check and repair the infeasible solutions after the update, and the process is the same as Step 3.6; solve the objective value of the new network planning solution, and the process is the same as Step 3.7.

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