CN118171789A - A time window low-carbon site selection inventory path optimization solution method and system - Google Patents

Abstract

The invention discloses a time window low-carbon site selection inventory path optimization solving method and system, relates to a genetic algorithm, and particularly relates to a low-carbon logistics center site selection inventory path planning model based on the genetic algorithm. In the invention, in the site selection inventory path network, various costs in a supply chain, customer service time punishment costs and carbon emission costs are comprehensively considered, a double-objective optimization model is established by taking total cost minimization and satisfaction maximization as optimization targets, an improved NSGA-II algorithm is utilized to process and obtain a Pareto optimal solution set, and an optimal reference decision scheme is selected by utilizing a Entropy-TOPSIS method. The invention establishes and solves the model for the site selection inventory path problem of the logistics center by considering carbon emission and time window constraint, and the used distributor demand is a random variable which accords with the actual situation, so that the calculation results of inventory cost, transportation cost, carbon cost and customer satisfaction function value are given, and the logistics cost of enterprises is further reduced.

Description

A time window low-carbon site selection inventory path optimization solution method and system

Technical Field

The present invention relates to a genetic algorithm, in particular to a low-carbon logistics center site selection inventory path planning model based on a genetic algorithm, in particular to a time window low-carbon site selection inventory path optimization solution method and system.

Background Art

At present, domestic and foreign scholars have studied the location and routing problems of logistics facilities from the perspectives of multi-cost, satisfaction and planning algorithms, and have achieved certain results. However, the general location and routing planning model schemes do not take into account carbon emissions and the time window constraints of distributors.

Summary of the invention

The purpose of the present invention is to provide a time window low-carbon site selection inventory path optimization solution method for the above-mentioned problem, in which the distributor demand used is a random variable that is more in line with the actual situation.

In order to achieve the above object, the technical solution adopted by the present invention is:

A time window low-carbon location inventory path optimization solution method includes the following contents:

Step S1: construct a location inventory path optimization model. The two objective optimization functions of the location inventory path with the minimum total cost and the highest customer satisfaction are:

minf ₁ =λ ₁ G+λ ₂ T _c +λ ₃ W _c +λ ₄ P _c +λ ₅ C _c (1);

Among them, the fixed construction cost of the distribution center site selection is

The transportation cost of the delivery vehicle is

The inventory cost is

The time penalty cost is max{ET' _j -t _j ,0} represents the advance arrival time when serving customer j, and max{t _j -LT _j ,0} represents the delay time when serving customer j;

The carbon emission cost of the delivery on the customer node (i, j) is Customer satisfaction is Capacity constraints of distribution centers: Vehicle carrying capacity constraints: Vehicle driving distance constraints: Constraints on the number of delivery vehicles: The starting and ending points of each vehicle’s delivery route are the same delivery center: Each customer can only be served once by a vehicle: Each distributor has a vehicle responsible for delivery: Time window constraints: In special cases of out-of-stock and insufficient transportation capacity, time window constraints: The order quantity from the distribution center is greater than the shipping quantity from the distribution center to the distributor: The transportation volume from the distribution center to the distributor meets the distributor's demand: x _hj z _hj ≥u _j ,h∈H;

A distributor is served by only one distribution center: Only by establishing a distribution center can we have a distribution route:

Step S2: using the entropy weight method to obtain the weights of fixed construction cost, transportation cost, inventory cost, time window penalty cost and carbon emission cost, which are λ ₁ , λ ₂ , λ ₃ , λ ₄ and λ ₅ respectively. The specific processing flow of step S2 is as follows:

Step 21. According to the fixed construction cost, transportation cost, inventory cost, time window penalty cost and carbon emission cost, and setting the preset weight of each cost to 1, the improved NSGA-II algorithm is used to calculate the Pareto optimal solution set A1 of the objective optimization function (1); Step 22. The Pareto optimal solution set A1 is forward-oriented, a forward-oriented matrix is constructed, and the entropy weight method is used to obtain the weights of the fixed construction cost, transportation cost, inventory cost, time window penalty cost and carbon emission cost, which are λ ₁ , λ ₂ , λ ₃ , λ ₄ and λ ₅ respectively.

Step S3: Substitute the weight of each cost into the objective optimization function (1), and use the improved NSGA-II algorithm to calculate the Pareto optimal solution set A2 of the two objective optimization functions (1) and (2).

Step S4: Based on the Pareto optimal solution set A2, the TOPSIS method is used to evaluate and rank the solutions in the Pareto optimal solution set A2, and the solution ranked first is selected as the optimal reference solution. The specific processing flow of step S4 is as follows:

Step 41, construct an evaluation matrix and perform normalization processing; there are t solutions in the Pareto optimal solution set A2, and the two objective functions are used to construct an evaluation index judgment matrix; Step 42, use the entropy weight method to calculate the entropy weight W _j of the j-th objective; Step 43, determine the comprehensive weight β _j of each objective function; Step 44, construct a weighted normalization matrix; Step 45, determine the ideal solution and the negative ideal solution; Step 46, calculate the proximity index R _t between the t-th solution in the Pareto optimal solution set A2 and the optimal level, and sort them in descending order, and then select the solution ranked first as the optimal reference solution; Among them, The maximum and minimum values of each index in the weighted standardization matrix are the ideal solutions and negative ideal solution Distance from the ideal solution Distance to negative ideal solution

Among them, the processing flow of the improved NSGA-II algorithm is as follows:

First, an initial population of size N is randomly generated. After non-dominated sorting, the first generation of offspring population is obtained through the three basic operations of genetic algorithm selection, crossover, and mutation; secondly, starting from the second generation, the parent population and the offspring population are merged to perform fast non-dominated sorting. At the same time, the crowding degree of individuals in each non-dominated layer is calculated, and appropriate individuals are selected to form a new parent population based on the non-dominated relationship and the crowding degree of the individuals; finally, a new offspring population is generated through the basic operations of the genetic algorithm. The dynamic crowding distance calculation formula of individual i in the improved NSGA-II algorithm is: in, Each objective function is f _m , where f _m (i+1) is the last digit of the objective function value after the individuals are sorted, and M is the number of objective functions.

Due to the adoption of the above technical solution, the present invention has the following beneficial effects:

In the site selection inventory path network, the present invention comprehensively considers various costs in the supply chain, customer service time penalty costs and carbon emission costs, takes total cost minimization and satisfaction maximization as optimization goals, establishes a dual-objective optimization model, uses the improved NSGA-II algorithm to obtain the Pareto optimal solution set, and then uses the Entropy-TOPSIS method to select the optimal reference decision plan. The present invention establishes and solves the model for the site selection inventory path problem of the logistics center while considering carbon emissions and time window constraints. The distributor demand used is a random variable that is more in line with the actual situation. The calculation results of inventory cost, transportation cost, carbon cost, and customer satisfaction function value are given, which further reduces the logistics cost of the enterprise.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of the solution method of the present invention. FIG. 2 is a LIRP supply chain diagram of multiple vehicles of the present invention. FIG. 3 is a time window penalty cost function diagram of the present invention. FIG. 4 is a customer satisfaction function diagram of the present invention. FIG. 5 is a schematic diagram of the basic coding rules of the improved NSGA-II algorithm of the present invention. FIG. 6 is a schematic diagram of the complete individual coding of the improved NSGA-II algorithm of the present invention. FIG. 7 is a schematic diagram of the initialization of a single individual of the improved NSGA-II algorithm of the present invention. FIG. 8 is a flowchart of the competition selection of the improved NSGA-II algorithm of the present invention. FIG. 9 is a schematic diagram of the cross-coding of the single-cycle destruction segment coding of the improved NSGA-II algorithm of the present invention. FIG. 10 is a schematic diagram of the cross-coding of the double-individual multi-cycle whole segment of the improved NSGA-II algorithm of the present invention. FIG. 11 is a schematic diagram of the cross-coding of the single-body cycle segment of the improved NSGA-II algorithm of the present invention. FIG. 12 is a schematic diagram of the single-cycle gene position exchange variation of the improved NSGA-II algorithm of the present invention. FIG. 13 is a schematic diagram of the variation of increasing vehicles at cycle a of the improved NSGA-II algorithm of the present invention. FIG. 14 is a schematic diagram of the variation of reducing vehicles at cycle b of the improved NSGA-II algorithm of the present invention. Figure 15 is a population merging and optimization flowchart of the improved NSGA-II algorithm of the present invention. Figure 16 is a flowchart of the improved NSGA-II algorithm of the present invention. Figure 17 is a Pareto optimal solution set curve with a weight of 1 for the solution example of the present invention. Figure 18 is a Pareto optimal solution set curve with weighted total cost and satisfaction for the solution example of the present invention. Figure 19 is a roadmap of the optimal allocation plan for the solution example of the present invention. Figure 20 is a schematic diagram of the carbon emission cost and customer satisfaction of the solution example of the present invention as the carbon quota increases. Figure 21 is a schematic diagram of the carbon emission cost and total cost of the solution example of the present invention as the carbon quota increases. Figure 22 is a graph of the carbon emission cost of the solution example of the present invention as the carbon quota increases.

DETAILED DESCRIPTION

The specific implementation of the invention is further described below with reference to the accompanying drawings.

Example 1

As shown in FIG1 , the method for optimizing the low-carbon location inventory path of the time window of the present invention includes steps S1 to S4 , which will be described in detail below.

1. Optimization model establishment

The present invention starts from a logistics model in which a factory is connected to various potential distribution logistics centers, and the distribution logistics centers then deliver the goods to various distributors. It optimizes the selection and order quantity of the distribution logistics centers, and the path from the distribution logistics centers to the distributors. It establishes a model and a solution algorithm for the site selection and inventory path problem of the logistics center while considering carbon emissions and time window constraints.

The following issues need to be addressed in model building: 1. How to consider the time window factor and the time penalty strategy; 2. How to calculate the carbon emission cost; 3. How to establish a comprehensive optimization target for the total cost that takes into account carbon emissions and time window factors; 4. How to reasonably arrange the delivery route to reduce energy consumption and carbon emissions; 5. How to design an algorithm to solve the model.

When the distributor places an order on the factory platform, the distribution logistics center will first analyze the distributor's order information and perform corresponding ordering, picking, packaging and other operations, then reasonably allocate and determine the delivery tasks of each delivery person, and finally call a certain number of delivery vehicles to arrange appropriate driving routes for a series of distributor addresses to deliver the goods intact within the customer's expected delivery time period. Under the time window constraints and specified constraints, a certain distribution center is selected from the alternative distribution logistics centers, and the transportation volume from the factory to the distribution logistics center, that is, the order volume of the distribution center, is given. Then, the transportation volume and optimal or suboptimal path of multi-vehicle distribution from the distribution center to each distributor are found to meet the minimum total cost. As shown in Figure 1, it is a multi-vehicle LIRP supply chain diagram.

In order to construct the mathematical model, the following assumptions are made: (1) The research object is the location path problem considering inventory. (2) It is assumed that only a single type of cold chain food is selected; because cold chain food involves a wide range of areas, the temperature control, shelf life, and fragility of various types of food are different. (3) Each customer is served by a single distribution center. (4) Each developed distribution center provides one delivery service to the customer point it serves every working day, and all developed distribution centers have the same annual working days. (5) The demand of each customer point is independent and normally distributed. (6) It is assumed that the delivery vehicles of the same store are of uniform specifications. That is, the capacity, service life, fuel consumption, and speed of each vehicle during transportation are the same. (7) Carbon emissions in transportation, inventory, and facility construction are considered. (8) The total carbon emissions of the supply chain are subject to constraints. (9) Any emergencies that occur during delivery are not considered, such as changes in production demand at the vehicle production center, traffic control, weather reasons, etc. (10) The time window factor is considered in delivery, and it is assumed that the associated penalty cost and time have a certain linear correlation function relationship. (11) Each delivery route is served by only one vehicle, and the transport vehicles are of the same model. (12) The total demand of customer points on any delivery route cannot exceed the vehicle's load capacity, and the delivery vehicle departs from the distribution center and returns to the distribution center after completing the task.

Next, the model parameters and their definitions are required. The following is a description of the model parameters and symbols, including the meaning of the parameters, decision variables and carbon emission coefficients.

Model parameters:

N: a factory node is recorded as N=0; H: the set of potential locations of distribution logistics centers; J: the set of distributors; K: the set of all distribution vehicles; g _h : the fixed construction cost of potential distribution center h, h∈H; d _ij : the distance between node i and node j, i,j∈N∪H∪J; i _h : the inventory holding cost of each unit product of distribution logistics center h; α: the probability of out-of-stock operation, 1-α is the corresponding service level; z _α : safety stock coefficient; L: order lead time; μ _j : the average demand of distributor j during the cycle; σ _j : the standard deviation of demand during the cycle of distributor j; c _h : the maximum storage capacity service capacity of distribution center h; C ^CAP : the carbon quota allocated in the supply chain; C ₁ : the fixed cost of distribution vehicles, which is independent of vehicle load and vehicle driving distance; FC _ij : the energy consumption cost of distribution vehicles; T _c : the transportation cost of distribution vehicles; [ET _j ',LT _j ']: the expected delivery time window of distributor j in the customer satisfaction function; α ₁ : the penalty cost per unit time for a vehicle to arrive at distributor j before time ET _j '; α ₂ : the penalty cost per unit time for a vehicle to arrive at distributor j after time LT _j '; [eT _j ,lT _j ]: the acceptable delivery time window for distributor j in the customer satisfaction function; P _c : penalty cost; ρ: fuel consumption per unit distance; Q _X : vehicle load; ρ(Q _ij ): fuel consumption per unit distance of a delivery vehicle carrying Q _ij , goods, when driving from node i to node j; Q ₀ : dead weight of the delivery vehicle; Q _k : maximum load of the delivery vehicle; ρ ₀ : fuel consumption per unit distance when empty; ρ ^* : fuel consumption per unit distance when fully loaded; Q _c : total carbon emissions during delivery; p ₂ : unit price of fuel; ω: represents the carbon emission coefficient; C _c : carbon emission cost; _Ce : carbon tax, the environmental cost of consuming unit carbon emissions; D : maximum driving distance of the delivery vehicle.

Model decision variables:

x _h : the order quantity from the factory to the distribution center DC _h ; x _hj : the transportation quantity allocated to distributor j by the distribution center DC _h ;

Then, the objective function is designed as follows.

(1) The fixed construction cost of the distribution center site selection is

(2) Transportation costs

The transportation cost is mainly composed of two parts. The first is the fixed cost of the distribution vehicle, which is the cost of dispatching the vehicle, set as a constant C ₁ , including the fixed loss of the vehicle, the salary of the distribution staff and other costs related to the use of the vehicle, which is unrelated to the vehicle load and the distance traveled by the vehicle. Second, although there are previous documents that measure the vehicle travel transportation cost by multiplying the unit distance cost by the distance, under normal circumstances, the longer the vehicle travels, the greater the carrying capacity, and the higher the transportation cost, but the unit distance cost is not as easy to obtain directly as the fuel consumption on the road. In addition, the main power of cold chain vehicle transportation, whether it is refrigeration or operation, is fuel. Therefore, the transportation cost of the present invention takes into account the energy consumption cost FC _ij of the distribution vehicle.

Assuming that the unit distance fuel consumption ρ of the customer node (i, j) section is linearly related to the vehicle load Q _X, it can be expressed as:

ρ(Q _X )＝a(Q ₀ +Q _X )+b

Given the deadweight Q ₀ and the maximum load Q _k of the delivery vehicle, we can obtain:

ρ ₀ = aQ ₀ + b

ρ ^* ＝a(Q ₀ +Q _k )+b

It turns out that:

It can be concluded that the vehicle fuel consumption per unit distance ρ(Q _X ) is:

The energy cost FC _ij generated in the delivery of node (i, j) can be obtained:

in,

Therefore, the transportation cost _Tc of the distribution vehicle can be expressed as:

(3) Inventory costs

The ordering cost is The inventory cost is Assuming that the demands of each distributor are independent and follow a standard normal distribution, the demand of the distribution center with order lead time, i.e., the safety stock point, is The order point of the distribution center is Then the inventory cost is

(4) Time Window Penalty Cost Function

The relationship between penalty cost and delivery time is shown in Figure 3. Assume that the horizontal axis represents the delivery time t _j , the vertical axis P _j (t _j ) represents the penalty cost, α ₁ , α ₂ (α ₁ , α ₂ ≥ 0) are the penalty coefficients in the time window [eT _j , ET _j '] and the time window [LT _j ', lT _j ], respectively, where α ₂ ≥ α ₁ , M represents infinite penalty cost, that is, when the delivery time exceeds the time window range acceptable to the customer, the customer will refuse to accept the goods, and the penalty cost is infinite at this time.

From this we can conclude that the time window penalty function is:

Then the penalty cost _Pc can be quantified by the time penalty function, which is specifically expressed as:

Among them, max{ET' _j -t _j ,0} represents the advance arrival time when serving customer j, and max{t _j -LT _j ,0} represents the delay time when serving customer j.

(5) Carbon emission cost function

Carbon emissions are generated by burning fuel. The fuel consumption of delivery vehicles is not only related to the distance traveled by the delivery vehicles, but also to the load capacity of the vehicles.

The total carbon emissions during distribution, Q _c , is expressed as:

Therefore, the carbon emission cost mainly describes the environmental cost of carbon emissions generated by vehicles during the delivery process. Carbon emission cost = carbon tax * (carbon emissions - carbon quota). The carbon emission cost C _c in the delivery of the customer node (i, j) section is expressed as:

(6) Customer Satisfaction Function

Assume that S = 1, which means out of stock and insufficient transportation capacity occur. In this special case, the delivery time window acceptable to customers is [eT _j , lT _j ]. The horizontal axis represents the delivery time t _j , and the vertical axis V(t _j ) represents the customer satisfaction function. The relationship between customer satisfaction and delivery time is shown in Figure 4.

From this we can derive the customer satisfaction function as:

The dual-objective optimization model of minimizing total cost and maximizing customer satisfaction is established for the above objective function as follows:

minf ₁ ＝λ ₁ G+λ ₂ T _c +λ ₃ W _c +λ ₄ P _c +λ ₅ C _c (1)

The objective function constraints are as follows:

(1) The capacity constraints of the distribution center are:

(2) Vehicle carrying capacity constraints are:

(3) The vehicle driving distance constraint is:

(4) Constraints on the number of delivery vehicles:

(5) The starting point and end point of each vehicle’s delivery route are the same distribution center:

(6) Each customer can only be served once by one vehicle:

(7) Each distributor has a vehicle responsible for delivery:

(8) The time window constraint is:

(9) Time window constraints in special circumstances such as shortage of goods or insufficient transportation capacity:

(10) The order quantity from the distribution center is greater than the transportation quantity from the distribution center to the distributor:

(11) The transportation volume from the distribution center to the distributor meets the distributor’s demand: x _hj z _hj ≥u _j ,h∈H.

(12) A distributor is served by only one distribution center:

(13) Only by establishing a distribution center can we have a distribution route:

2. Optimization model solution

2.1 Improved NSGA-II algorithm process steps

As mentioned above, the relationship between the sum of carbon cost, site selection cost, transportation cost and inventory cost and the two optimization objectives of customer satisfaction in the constructed multi-objective optimization model is a contradictory one. Solving this type of problem requires the application of a multi-objective optimization algorithm. The improved NSGA-II has a better ability to solve the formulated model, so better decisions can be made according to the decision maker's priorities. In addition, the improved NSGA-II provides a set of Pareto optimal solutions as the final result, which provides decision makers with multiple options. The improved design of NSGA-II is as follows:

(1) Coding scheme

In the genetic algorithm, individuals represent solutions to the problem, so the result needs to contain the following information: (i) The first-cycle vehicle distribution path solution; the first-cycle vehicle distribution volume solution. (ii) The second-cycle vehicle distribution path solution; the second-cycle vehicle distribution volume solution. (iii) Continue, the genetic algorithm iterates until the nth iteration. The nth-cycle vehicle distribution path problem studies the nth-cycle vehicle distribution volume solution.

Based on the above principles, the following basic coding rules can be obtained:

First, each individual is divided into several segments according to the number of cycles; then each segment is divided into a routing segment and a distribution segment. The route segment code directly uses the sales point number to represent the vehicle distribution sequence, and the distribution volume segment code directly uses the distribution volume of the corresponding sales point.

As shown in Figure 5, the distribution path plan and distribution volume plan from the first cycle to the third cycle are shown from top to bottom. Among them: the blue (dark gray under grayscale) gene position represents the sales point code; the yellow (light gray under grayscale) gene position represents the distribution volume corresponding to the previous sales point; the green (gray under grayscale) gene position represents the distribution center code, and its corresponding distribution volume position is represented by inf. As shown in Figure 6, in a complete individual code, the two red (black under grayscale) gene positions at the end respectively record the two function values of the objective function A and B calculated by the distribution center under the solution provided by this individual.

(2) Initialize the population

First, for the convenience of algorithm design and the improvement of operation efficiency, this model divides the sales points according to the nearest principle of the distribution center before designing the solution to the problem. As a result, the LIRP problem of multiple distribution centers and multiple sales points is transformed into the LIRP problem of multiple sales points of a single distribution center. After the division, each distribution center is responsible for a fixed number of sales points, and the distribution centers do not affect each other. The costs and risks can also be calculated separately, which greatly reduces the complexity of the model and the operation efficiency of the algorithm. The specific division process is as follows:

For each sales point, calculate the straight-line distance between it and all distribution centers, then traverse these distances and search for the minimum value. The distribution center node corresponding to the shortest distance is the distribution center responsible for the sales point. Then add this sales point to the responsible node set of the distribution center. In this way, by traversing each sales point in a loop, we can get the set of sales points that each distribution center is responsible for.

The above is the code of the first cycle of the individual. The specific process can be referred to Figure 7. Then it is looped according to the number of cycles (for example, each individual is set to contain T cycles), and the population size (for example, the population size is 200) is nested. Finally, a population matrix with 200 rows and x columns is obtained. In this matrix, each row of data represents an individual, and each individual has T cycle segment codes and 2 function value gene bits. Among them, x is given by the following formula:

x＝(length _routing +length _{shipping quantity} )×T

(3) Select crossover mutation

(i) Select crossover mutation

The tournament is organized based on the existing population, and excellent individuals are extracted from the parent population of all individuals and added to the mating pool. This step simulates the process of individuals in a population competing for sexual rights when a species reaches the breeding season in nature. Individuals who are not excellent due to genetic advantages have no right to participate in the crossover and recombination output of the next generation. As the entire population develops in the direction of continuous evolution, the algorithm also continuously explores better solutions on the existing basis. The entire process of the competitive selection method is shown in Figure 8.

(ii) Crossover recombination strategy

Combined with the model established in this paper, the main objectives of the cross-reorganization in the algorithm are the change of delivery route, the change of delivery volume and the change of delivery vehicle selection.

a) Code crossover of single-cycle destruction segments: This method requires randomly selecting two parent individuals in each cycle and randomly selecting an intersection point on their path codes or delivery quantity codes. At this time, due to the individual codes at the time of initialization, the code lengths of the two selected cycles must be the same. It is only necessary to find an intersection in the two codes. Finally, the path segment or distribution segment where the boundary segment is located is cross-coded, and the codes of all non-distribution center locations are exchanged before the intersection. Figure 9 is a schematic diagram of this process.

b) Double-individual multi-cycle whole-segment crossover: This method randomly selects n cycles from all individual cycles, takes the boundary of the path segment code or distribution segment code as the crossover point, and directly exchanges the path segment code or distribution segment code of the non-distribution center location of the two parent individuals in these n cycles. Assuming there are n cycles in total, select the 1st and nth cycles for crossover, as shown in Figure 10.

c) Single-body cycle segment crossover: This method requires a single parent individual to cross over and recombine itself, specifically, a single parent individual randomly rearranges its cycle numbers to obtain a sequence of randomly arranged cycles, and then re-fills the path segment and delivery volume segment codes of each cycle in this sequence order. This method is equivalent to rearranging the cycle sequence of the individual to obtain the offspring individual, without disrupting the combination of the path segment and delivery volume segment codes. In the model, this means that only the inventory cost and penalty cost have changed, while the transportation cost has not changed. The crossover diagram is shown in Figure 11.

(iii) Mutation strategy

Mutation is an important method in genetic algorithms to escape from local optimality and avoid the limitation of solution space. As mentioned above, the model established in this paper needs to obtain these three search directions when generating offspring: changes in delivery routes, changes in delivery volume, and changes in delivery vehicle selection. The three methods of cross-recombination mentioned above have more fully realized the changes in delivery routes and delivery volume, but have not realized the changes in delivery vehicle selection. This is mainly because the changes in delivery vehicle selection are mainly for a single individual and are suitable for mutation operations. Combined with the encoding method, this paper gives the following mutation methods.

a) Single-cycle gene position exchange mutation: This mutation method requires that two gene positions are randomly selected for exchange in the path segment or delivery segment code of an individual in one cycle, which means that the exchange can only occur in the same cycle. This is mainly because when gene positions are exchanged in different cycles, even if they belong to the same path segment code, there will be repeated sales points in the path segment after the exchange. Fundamentally, it is caused by the model limiting that each sales point is only allowed to be visited once in each cycle. However, this problem will not occur when gene positions are exchanged in the same cycle. Of course, the exchange can also only occur in one code, and the genes in the path segment and the delivery segment cannot be exchanged. The above restrictions make the range of variation smaller, which is also one of the reasons for setting a larger variation probability. The specific crossover process is shown in Figure 12.

b) Vehicle selection mutation: This mutation method focuses on changing the selection of vehicles in each cycle delivery plan provided at the time of initialization, that is, the change of the distribution center gene position in the chromosome. It can be roughly divided into two directions: adding a vehicle and reducing a vehicle. Adding a vehicle is equivalent to reducing the workload of the previous vehicle at the insertion point, and the separated part is handled by the newly added vehicle. Reducing a vehicle is equivalent to adding the workload of the vehicle to the previous vehicle at the deletion point. Of course, whether adding or reducing vehicles, the premise for such mutation is that there are gene positions available for mutation, which are specifically divided into the following three situations.

Case 1: If only one vehicle is called in a certain period segment code, that is, there is no distribution center gene position in the path segment and delivery volume segment code, then this segment code cannot undergo a mutation that reduces the number of vehicles, but can only undergo a mutation that increases the number of vehicles. When this mutation occurs in period a, its schematic diagram is shown in Figure 13.

Case 2: If the number of vehicles in a certain period segment code has reached the upper limit of the number of vehicles, then this segment code cannot mutate to increase the number of vehicles, and can only mutate to reduce the number of vehicles. When this mutation occurs in period b, its schematic diagram is shown in Figure 14.

Case 3: If the number of vehicles called in a certain period segment code is greater than 1 but less than the upper limit, then this segment code can arbitrarily change the vehicle selection.

The above restrictions are proposed because the chromosomes of existing individuals have determined the coding length when they are initialized. If the mutation breaks this length limit, the chromosomes of the entire population will be disordered. Only when there are non-upper limit redundant bits at the end of the path segment code (that is, the third case in the above restrictions), there is room for any vehicle selection mutation. Adding a vehicle can move the subsequent coding backward and remove a redundant bit; reducing a vehicle can move the subsequent coding forward and add a redundant bit. Of course, the subsequent delivery segment coding needs to be adjusted accordingly according to the path segment coding.

(4) Population merging and optimization

From the above, we know that after the selection, crossover and mutation process, a parent population and a child population generated by mating of the parent population are selected according to the initial population. However, in the actual use of the algorithm, the problems we need to solve are often very complex, which means that the excellence of an individual is a better solution obtained by the combination of all genes on its chromosomes, but it cannot be proved that all chromosomes of an excellent individual are excellent, or that its excellence is brought by a certain part of the chromosomes. Therefore, after two excellent individuals undergo crossover, recombination and mutation, it can only be said that there is a greater probability of obtaining a better individual, but it cannot be completely guaranteed that a better individual will be produced. In order to solve this problem, the NSGA-II algorithm introduces an elite selection strategy. The specific operation is to merge the child population obtained by the previous operation with the initial population, so as to obtain an intermediate population with a size twice the original size, and then perform non-dominated sorting and crowding calculation operations on this population, and finally take the individuals with the highest non-dominated sorting from top to bottom to fill the set population size, so as to finally obtain the second generation population after reproduction. Its process is shown in Figure 15.

(5) Crowding calculation

In the algorithm, the quality of individuals is judged by the crowding operator. However, the resulting crowding operator may deviate from the actual density of individuals. If so, high-density individuals may be retained in the next generation, leading to a local optimum. In order to improve the uniformity of individual distribution, diversify the population distribution, and enhance the global search capability, the dynamic crowding distance is introduced. The algorithm is as follows:

1). Let parameter n _d = 0, n∈1...N.

2).for each objective function f _m :

① Sort the individuals of this level according to the objective function, record is the maximum value of the individual objective function value f _m , is the minimum value of the individual objective function value f _m . ② For the crowding degree 1 _d and N _d of the two boundaries after sorting, set them to ∞. ③ Then, calculate the dynamic crowding distance of individual i according to the formula: in, f _m (i+1) is the last digit of the objective function value after the individuals are sorted, and M is the number of objective functions.

3). End.

Therefore, the improved NSGA-II algorithm process steps are as follows: first, randomly generate an initial population of size N, and after non-dominated sorting, obtain the first generation of offspring population through the three basic operations of selection, crossover, and mutation of the genetic algorithm as described above; second, starting from the second generation, merge the parent population with the offspring population, perform fast non-dominated sorting, and use the crowding distance formula to calculate the crowding degree of individuals in each non-dominated layer, and select appropriate individuals to form a new parent population based on the non-dominated relationship and the crowding degree of the individuals; finally, generate a new offspring population through the basic operations of the genetic algorithm: and so on, until the condition for the end of the program is met (whether Gen is less than the maximum number of generations). The process of the algorithm is shown in Figure 16.

2.2 Dual-objective decision-making

The Entropy-TOPSIS method is used to determine the optimal reference solution by calculating the proximity index of each solution in the Pareto solution set to the optimal level, thereby helping decision makers select a Pareto solution that balances multiple objectives as the optimal reference solution.

Therefore, the optimization model solution process is as follows:

First, for costs, they have the same dimension. The entropy weight method can be used to assign weights to the five costs, namely, fixed cost, transportation cost, inventory cost, time window penalty cost, and carbon emission cost, which are recorded as λ ₁ , λ ₂ , λ ₃ , λ ₄ , and λ ₅ . The calculation steps of the entropy weight method are as follows:

(1) Determine whether there are negative numbers in the input matrix. If there are, re-normalize it to a non-negative interval. Assume that there are t solutions in the Parero optimal solution set, and the forward matrix composed of 5 evaluation indicators (i.e. 5 cost data, and forward (maximization)) is as follows:

Then, the standardized matrix is recorded as Z, and each element in Z is:

Determine whether there are negative numbers in the Z matrix. If so, another standardization method needs to be used for X. Standardize the matrix X once to get The matrix is standardized as follows:

(2) Calculate the proportion of the i-th sample under the j-th indicator and regard it as the probability used in the relative entropy calculation. There are t evaluation objects and 5 evaluation indicators. The non-negative matrix obtained after the previous step is:

Calculate the probability matrix P, where the calculation formula for each element p _ij in P is as follows:

Easy to verify: That is to ensure that the probability of each indicator is 1.

(3) Calculate the information entropy of each indicator, calculate the information utility value, and normalize it to obtain the entropy weight of each indicator. For the jth indicator, the calculation formula for its information entropy is:

(4) Information utility is worth defining: d _j = 1-e _j , then the larger the information utility value is, the more information it corresponds to. The information utility value is normalized to obtain the entropy weight of each indicator:

Then, the obtained weights are substituted into the objective function f ₁ , and the improved NSGA-II algorithm is used again to calculate the Pareto optimal solution set. Taking the two optimization objectives as evaluation indicators, the entropy weight method is introduced to calculate the objective weights of the two indicators, which effectively weakens the influence of the less reliable solutions at both ends of the Pareto optimal solution set on the objective weighting.

Finally, the TOPSIS method is used to evaluate and rank the solutions of the Pareto optimal solution set. The following will give the specific steps of the Entropy-TOPSIS method to select the optimal solution.

Step 1: Construct an evaluation matrix and perform normalization. There are t solutions in the Pareto optimal solution set. The two objective functions are used to construct an evaluation index judgment matrix. Step 2: Use the entropy weight method to calculate the entropy weight W _j of the jth objective. Step 3: Determine the comprehensive weight β _j of each objective function. Step 4: Construct a weighted normalization matrix. Step 5: Determine the ideal solution and the negative ideal solution. The maximum and minimum values of the indicators in the weighted normalization matrix are used to represent the ideal solution. and negative ideal solution Step 6: Calculate the closeness index R _t of the t-th solution in the Pareto optimal solution set to the optimal level, and sort it in descending order (the larger the R _t , the closer it is to the optimal level): Among them, the distance to the ideal solution is d ⁺ : Distance d ^- from the negative ideal solution:

3. Decision-making Case

As described above, the optimization model construction and solution process are described. The following will further illustrate the decision results with specific actual cases. The MATLAB2021a programming software was used for the experiment. The system is Windows 10 Home Chinese version. The hardware environment is 11th Gen Intel(R)Core(TM)i7-1165G7@2.80GHz and memory is 16G (The algorithm was executed on a laptop, with an Intel(R)Core TM(TM)i7-8550U CPU@1.80GHz1.99GHz processor and 8GB RAM of memory.). The parameter settings are as follows: number of iterations 500, population size 200.

Taking an enterprise in Jinan City, Shandong Province as an example, the logistics distribution network is optimized according to the specific development situation and optimization needs of the enterprise. The main business categories of W enterprise include fruits and vegetables, poultry, eggs and dairy products, and its business covers multiple urban areas in S City. Strive to scientifically plan the logistics distribution system, effectively improve supply efficiency and ensure product quality. Information about factories, potential distribution centers and distributors is shown in Tables 1 and 2 below. Experiments were conducted on 8 potential distribution centers and 40 distributors. The rated load of each vehicle is 300, the carbon quota allocated to the carbon quota supply chain C ^CAP = 200, the inventory holding cost i _h = 4, the probability of out-of-stock operation α = 0.05, the safety stock coefficient z _α = 0.95, the order lead time L = 7 days, the unit order price is p = 9 yuan, the fixed cost of the distribution vehicle C ₁ = 100, the unit time penalty cost α ₁ = 60, α ₂ = 90, the unit distance fuel consumption when empty ρ ₀ = 0.122, the number of cars K = 16, the unit distance fuel consumption when fully loaded ρ ^* = 0.388, the carbon emission coefficient ω = 0.0028, the carbon tax _Ce = 0.0075, the maximum driving distance of the transport vehicle D = 1600 kilometers, the average speed during transportation is 50 km/h, and the rated load is 200. All weights in the objective function (1) are set to 1. Therefore, the Pareto optimal solution set obtained by the improved NSGA-II is shown in Figure 17.

Table 1: Factory and alternative distribution center information

Table 2: Distributor information

From the Pareto solution set, we can see that:

(i) There is a certain correlation between the two objectives of total cost and customer satisfaction.

(ii) As total costs increase, customer satisfaction generally shows an upward trend. In the process of optimizing the logistics distribution network, enterprises usually cannot guarantee customer service levels and distribution efficiency when pursuing low costs. Customer satisfaction is often low and delivery time (delivery time can be seen from penalty costs) is longer.

(iii) In pursuit of higher customer satisfaction, in order to meet the customer's expected time window as much as possible, the total cost is usually increased, and the delivery time may also increase due to the need for scheduling. Therefore, enterprises need to combine inventory capacity, distribution capacity and the actual needs of distributors, and comprehensively weigh logistics costs and customer satisfaction to choose the appropriate decision-making plan based on the company's business strategy and market positioning.

Therefore, companies need to combine inventory capacity, distribution capacity, and the actual needs of dealers, and choose the correct decision-making plan based on the company's business strategy and market positioning, comprehensively weighing logistics costs, and customer satisfaction.

According to the above numerical experiments, we can get the Pareto optimal solution set of fixed cost, transportation cost, inventory cost, time window penalty cost, and carbon emission cost. These cost solution sets are forward-oriented to form the forward-oriented matrix X. The weights of fixed cost, transportation cost, inventory cost, time window penalty cost, and carbon emission cost are obtained by using the entropy weight method:

λ ₁ =0.0035, λ ₂ =0.0013, λ ₃ =0.0681, λ ₄ =0.8746, λ ₅ =0.0524

Based on the solution set of the established model, it can be observed that the maximum number of vehicles required is 11. To optimize cost and time, the number of vehicles is reduced from 16 to 11, saving 31% of the fixed cost of vehicle usage.

Then, the obtained weights are reintegrated into the model to generate a new Pareto optimal solution set. The optimization result is shown in Figure 18, which shows the new Pareto optimal solution set considering the updated vehicle constraints.

A new forward matrix X with two objective functions as indicators is constructed from the new Pareto optimal solution set. The Entropy-TOPSIS method is used to obtain the top 10 decisions in the Pareto optimal solution set, as shown in Table 3 below.

Table 3: The first 10 solutions in the Pareto optimal solution set

The solution ranked first is taken as the best solution for the LIRP supply chain, as shown in Table 4 below. Figure 19 shows the optimal allocation solution roadmap.

Table 4: Best Practices

In the best solution, the transportation cost is 129.46 less than the average transportation cost, a reduction of 7.01%; the inventory cost is 4 less than the average inventory cost, a reduction of 0.2%; the time window penalty cost is 80.66 less, a reduction of 52.71%; and the carbon emission cost is 6.15 less, a reduction of 4.29%.

In order to ensure the insufficient or sufficient conditions of carbon quotas under any solution, we set a smaller value (20kg) as the insufficient carbon quota, increase it in steps of 20kg, and use a larger value (280kg) as the sufficient carbon quota to conduct experiments respectively. Figure 20 shows the trend of carbon emission cost and total cost with the change of carbon quotas. Figure 21 shows the trend of carbon emission cost and customer satisfaction with the increase of carbon quotas. Figure 22 shows the trend of carbon emission cost with the increase of carbon quotas. It can be clearly seen from the trend chart that carbon quota is a key variable that affects the difference between carbon emission and economic cost targets, while the impact on customer satisfaction is relatively small. As can be seen from Figure 22, as the carbon quota increases from 20 to 280, the economic cost decreases.

Therefore, as mentioned above, the present invention comprehensively considers various costs in the supply chain, customer service time penalty costs and carbon trading mechanisms in the site selection inventory path network, takes total cost minimization and satisfaction maximization as optimization goals, and establishes a LIRP dual-objective optimization model. According to the characteristics of multi-objective problems, this application designs an improved NSGA-II algorithm, and verifies the effectiveness of the constructed model and algorithm through decision-making case experiments. Finally, since there is a certain correlation between the total distribution cost and customer satisfaction, the Entropy-TOPSIS method is used to weigh the relationship between the two for decision makers, and comprehensively consider and select the optimal reference decision plan. In practical applications, the distribution network needs to face large-scale data information, and the intelligent algorithm will further optimize the large-scale examples efficiently.

From the perspective of low-carbon economy and market competition, the site selection inventory and vehicle path problems of the logistics center must pay attention to carbon emissions and time window constraints. The carbon emissions will be considered to be correlated with fuel consumption and driving distance, and finally the carbon emission cost function will be established according to the carbon trading mechanism. A multi-objective 0-1 hybrid nonlinear programming model that meets the normal distribution of customer demand and time window constraints is proposed. With the goal of reducing carbon emissions, the logistics cost of the enterprise is saved, and the customer experience is improved in terms of time. The model is solved by an improved non-dominated sorting genetic algorithm (NSGA-II) with an elite strategy. Considering cost factors, non-allowed inventory shortages, carbon emissions and other factors, as well as random variables under the condition of considering customer demand, the entropy weight method is used to obtain the weights of the total fixed cost, transportation cost, inventory cost, penalty cost and carbon emission cost, thereby establishing a nonlinear programming model for the site selection inventory path problem. The hybrid intelligent algorithm is compiled using MATLAB software to obtain the optimal order quantity of the distribution center, the location of the distribution center, the number of distribution vehicles of the distribution center and the path allocation. The calculation results of the inventory cost, transportation cost, carbon cost and customer satisfaction function value are given, which further reduces the logistics cost of the enterprise. Since IMNSGA-II is a Pareto optimal solution set, decision makers need to choose appropriate strategies from it and need to give an objective ranking. The Entropy-TOPSIS method is used to provide objective choices for decision makers by giving a ranking of the solution set.

Example 2

Based on the steps S1 to S4 of the location inventory path optimization solution method in the aforementioned embodiment 1, a low-carbon location inventory path optimization solution system for a time window can be formed, which is briefly described as follows. For any incomplete description, please refer to the aforementioned embodiment 1. The location inventory path optimization solution system includes a server, etc., specifically a processor and a memory, etc., and a computer program is stored on the memory, which is executed by the processor to implement the steps S1 to S4 of the location inventory path optimization solution method.

The site selection inventory path optimization solution system includes: a model building module: used to build a site selection inventory path optimization model, which has two objective optimization functions (1) and (2) of minimizing the total cost and maximizing customer satisfaction; a weight obtaining module: used to obtain the weights of fixed construction cost, transportation cost, inventory cost, time window penalty cost and carbon emission cost by using the entropy weight method, which are λ ₁ , λ ₂ , λ ₃ , λ ₄ and λ ₅ respectively; a solution set obtaining module: used to substitute the weight of each cost into the objective optimization function (1), and use the improved NSGA-II algorithm to calculate the Pareto optimal solution set A2 of the two objective optimization functions (1) and (2); a solution selection module: used to evaluate and rank each solution of the Pareto optimal solution set A2 by using the TOPSIS method according to the Pareto optimal solution set A2, and select the solution ranked first as the optimal reference solution.

It should be pointed out that the examples of the above-mentioned embodiments can be preferably combined with one or more of them according to actual needs, and multiple examples use a set of illustrations of combined technical features, which will not be described one by one here.

The above descriptions are detailed descriptions and illustrations of the preferred embodiments of the present invention, but these descriptions are not intended to limit the scope of protection required by the present invention. All equivalent changes or modified modifications achieved under the technical teachings suggested by the present invention should fall within the scope of patent protection covered by the present invention.

Claims (10)

1. A time window low-carbon site selection inventory path optimization solution method, characterized by including the following contents: Step S1: construct a location inventory path optimization model. The two objective optimization functions of the location inventory path with the minimum total cost and the highest customer satisfaction are: minf ₁ =λ ₁ G+λ ₂ T _c +λ ₃ W _c +λ ₄ P _c +λ ₅ C _c (1); Among them, the fixed construction cost of the distribution center site selection is The transportation cost of the delivery vehicle is The inventory cost is The time penalty cost is max{ET _j '-t _j ,0} represents the advance arrival time when serving customer j, and max{t _j -LT _j ,0} represents the delay time when serving customer j; The carbon emission cost of the delivery on the customer node (i, j) is Customer satisfaction is Capacity constraints of distribution centers: Vehicle carrying capacity constraints: Vehicle driving distance constraints: Constraints on the number of delivery vehicles: The starting and ending points of each vehicle’s delivery route are the same delivery center: Each customer can only be served once by a vehicle: Each distributor has a vehicle responsible for delivery: Time window constraints: In special cases of out-of-stock and insufficient transportation capacity, time window constraints: The order quantity from the distribution center is greater than the shipping quantity from the distribution center to the distributor: The transportation volume from the distribution center to the distributor meets the distributor's demand: x _hj z _hj ≥u _j ,h∈H; A distributor is served by only one distribution center: Only by establishing a distribution center can we have a distribution route: Step S2: using the entropy weight method to obtain the weights of fixed construction cost, transportation cost, inventory cost, time window penalty cost and carbon emission cost, which are λ ₁ , λ ₂ , λ ₃ , λ ₄ and λ ₅ respectively; Step S3, substituting the weight of each cost into the objective optimization function (1), and using the improved NSGA-II algorithm to calculate the Pareto optimal solution set A2 of the two objective optimization functions (1) and (2); Step S4: According to the Pareto optimal solution set A2, the TOPSIS method is used to evaluate and rank the solutions of the Pareto optimal solution set A2, and the solution ranked first is selected as the optimal reference solution. 2. The method for optimizing the low-carbon inventory path in a time window according to claim 1 is characterized in that the specific processing flow of step S2 is as follows: Step 21, based on the fixed construction cost, transportation cost, inventory cost, time window penalty cost and carbon emission cost, and setting the preset weight of each cost to be 1, the improved NSGA-II algorithm is used to calculate the Pareto optimal solution set A1 of the objective optimization function (1); Step 22: Forward the Pareto optimal solution set A1, construct a forward matrix, and use the entropy weight method to obtain the weights of fixed construction cost, transportation cost, inventory cost, time window penalty cost and carbon emission cost, which are λ ₁ , λ ₂ , λ ₃ , λ ₄ and λ ₅ respectively. 3. The method for optimizing the low-carbon inventory path in a time window according to claim 1, wherein the specific processing flow of step S4 is as follows: Step 41, construct an evaluation matrix and perform normalization processing; the Pareto optimal solution set A2 has t solutions in total, and the two objective functions are used to construct an evaluation index judgment matrix; Step 42: Calculate the entropy weight W _j of the j-th target using the entropy weight method; Step 43, determining the comprehensive weight β _j of each objective function; Step 44, construct a weighted normalization matrix; Step 45, determine the ideal solution and the negative ideal solution; Step 46: Calculate the closeness index R _t between the t-th solution in the Pareto optimal solution set A2 and the optimal level, sort them in descending order, and then select the solution ranked first as the optimal reference solution; wherein, The maximum and minimum values of each index in the weighted standardization matrix are the ideal solutions and negative ideal solution Distance from the ideal solution Distance to negative ideal solution 4. The method for optimizing the low-carbon inventory path selection in a time window according to claim 1 is characterized in that the processing flow of the improved NSGA-II algorithm is as follows: Firstly, an initial population of size N is randomly generated. After non-dominated sorting, the first generation offspring population is obtained through the three basic operations of selection, crossover and mutation of genetic algorithm. Secondly, starting from the second generation, the parent population and the offspring population are merged to perform fast non-dominated sorting. At the same time, the crowding degree of individuals in each non-dominated layer is calculated, and suitable individuals are selected to form a new parent population according to the non-dominated relationship and the crowding degree of individuals. Finally, a new offspring population is generated through the basic operations of genetic algorithm. 5. A time window low-carbon location inventory path optimization solution method according to claim 4, characterized in that: the dynamic crowding distance calculation formula of individual i in the improved NSGA-II algorithm is: in, Each objective function is f _m , where f _m (i+1) is the last digit of the objective function value after the individuals are sorted, and M is the number of objective functions. 6. A time window low-carbon site selection inventory path optimization solution system, characterized by including the following contents: Model building module: used to build a location inventory path optimization model. The two objective optimization functions of the location inventory path with the minimum total cost and the highest customer satisfaction are: minf ₁ =λ ₁ G+λ ₂ T _c +λ ₃ W _c +λ ₄ P _c +λ ₅ C _c (1); Among them, the fixed construction cost of the distribution center site selection is The transportation cost of the delivery vehicle is The inventory cost is The time penalty cost is max{ET _j '-t _j ,0} represents the advance arrival time when serving customer j, and max{t _j -LT _j ,0} represents the delay time when serving customer j; The carbon emission cost of the delivery on the customer node (i, j) is Customer satisfaction is Capacity constraints of distribution centers: Vehicle carrying capacity constraints: Vehicle driving distance constraints: Constraints on the number of delivery vehicles: The starting and ending points of each vehicle’s delivery route are the same delivery center: Each customer can only be served once by a vehicle: Each distributor has a vehicle responsible for delivery: Time window constraints: In special cases of out-of-stock and insufficient transportation capacity, time window constraints: The order quantity from the distribution center is greater than the shipping quantity from the distribution center to the distributor: The transportation volume from the distribution center to the distributor meets the distributor's demand: x _hj z _hj ≥u _j ,h∈H; A distributor is served by only one distribution center: Only by establishing a distribution center can we have a distribution route: Obtaining weight module: used to obtain the weights of fixed construction cost, transportation cost, inventory cost, time window penalty cost and carbon emission cost by using entropy weight method, which are λ ₁ , λ ₂ , λ ₃ , λ ₄ and λ ₅ respectively; Solution set acquisition module: used to substitute the weight of each cost into the objective optimization function (1), and use the improved NSGA-II algorithm to calculate the Pareto optimal solution set A2 of the two objective optimization functions (1) and (2); Solution selection module: It is used to evaluate and sort the solutions of Pareto optimal solution set A2 using TOPSIS method, and select the solution ranked first as the optimal reference solution. 7. A time window low-carbon site selection inventory path optimization solution system according to claim 6, characterized in that: the specific processing flow of the weight acquisition module is as follows: Step 21, based on the fixed construction cost, transportation cost, inventory cost, time window penalty cost and carbon emission cost, and setting the preset weight of each cost to be 1, the improved NSGA-II algorithm is used to calculate the Pareto optimal solution set A1 of the objective optimization function (1); Step 22: Forward the Pareto optimal solution set A1, construct a forward matrix, and use the entropy weight method to obtain the weights of fixed construction cost, transportation cost, inventory cost, time window penalty cost and carbon emission cost, which are λ ₁ , λ ₂ , λ ₃ , λ ₄ and λ ₅ respectively. 8. The low-carbon location inventory path optimization solution system for a time window according to claim 6 is characterized in that: the specific processing flow of the selected solution module is as follows: Step 41, construct an evaluation matrix and perform normalization processing; the Pareto optimal solution set A2 has t solutions in total, and the two objective functions are used to construct an evaluation index judgment matrix; Step 42: Calculate the entropy weight W _j of the j-th target using the entropy weight method; Step 43, determining the comprehensive weight β _j of each objective function; Step 44, construct a weighted normalization matrix; Step 45, determine the ideal solution and the negative ideal solution; Step 46: Calculate the closeness index R _t between the t-th solution in the Pareto optimal solution set A2 and the optimal level, sort them in descending order, and then select the solution ranked first as the optimal reference solution; wherein, The maximum and minimum values of each index in the weighted standardization matrix are the ideal solutions and negative ideal solution Distance from the ideal solution Distance to negative ideal solution 9. The low-carbon location inventory path optimization solution system of time window according to claim 6 is characterized in that: the processing flow of the improved NSGA-II algorithm is as follows: Firstly, an initial population of size N is randomly generated. After non-dominated sorting, the first generation offspring population is obtained through the three basic operations of selection, crossover and mutation of genetic algorithm. Secondly, starting from the second generation, the parent population and the offspring population are merged to perform fast non-dominated sorting. At the same time, the crowding degree of individuals in each non-dominated layer is calculated, and suitable individuals are selected to form a new parent population according to the non-dominated relationship and the crowding degree of individuals. Finally, a new offspring population is generated through the basic operations of genetic algorithm. 10. A time window low-carbon location inventory path optimization solution system according to claim 9, characterized in that: the dynamic crowding distance calculation formula of individual i in the improved NSGA-II algorithm is: n _di = n _d / lg (1/V _i ); wherein, Each objective function is f _m , where f _m (i+1) is the last digit of the objective function value after the individuals are sorted, and M is the number of objective functions.