# Research on Optimization of Intelligent Logistics Agile Distribution Model in Supply Chain Networks

Authors: Yun Ping Ai; Dong Yan Liu; Jia-Bao Liu; Yun Liu
Journal: Mathematical Problems in Engineering
 (2022)

---

## Abstract

In the supply chain environment, agile distribution refined the division of operations, responded quickly to the customer needs of the mobile terminal, and promoted the construction of an intelligent logistics distribution system. In order to integrate the distribution resources of the distribution system of the logistics industry and maximize the overall benefits of distribution, this paper designs an intelligent logistics agile distribution model and optimizes the distribution strategy. Firstly, this paper puts forward a rationalization evaluation system based on the established logistics agile distribution model. Make full use of the fuzzy subsets of each level to quantify the fuzzy indexes to evaluate, and then comprehensively clarify the index attributes through the fuzzy transformation criteria to obtain the evaluation results. Secondly, aiming at the networked agile distribution organization form, the scientific location mathematical model of agile distribution center and the path mathematical model of the agile distribution are established. Finally, the uncertain influence of many objective conditions on distribution agility has been analyzed, and the dynamic optimization model of an agile distribution path with the concept of time window under random demand is constructed. Through the experimental analysis, the rationalization evaluation strategy and index of verification test results show that the model has significant optimization advantages, which not only improve the rationality and economic benefits of distribution, but also meet the time requirements of all users.


---

## Body

## 1. Introduction

The rapidly developing market economy gave birth to many production and service industries, among which the modern logistics industry is the most outstanding [1]. The logistics industry is the third profit source of enterprises. The development goal is to use the least cost in exchange for a high degree of user satisfaction. In recent years, the informatization construction in the field of logistics in China has gradually stepped into the “take-off” stage. As a special form of logistics activity, distribution is of great significance to social and economic development. This business aims at high security, high service level, and low cost, so it needs to comprehensively analyze the coupling relationship among efficiency, cost, and users and reasonably customize distribution lines [2].Based on the above background, many scholars at home and abroad have achieved relatively successful research results in logistics distribution, For example, Song et al. [3] built an emergency logistics distribution model by analyzing the psychological impact of material damage. However, Liu et al. [4] focused on the mode of distribution crowdsourcing task and carried out simulation and optimization analysis of the cold-chain logistics distribution model. At the same time, in the retailers’ supply chain environment, agile distribution can effectively improve the retailer’s credit rating. Through a large number of experiments, Jiang et al. concluded that for a given positive initial capital supply chain environment, the members’ profits will increase with the improvement of the retailer’s credit rating [5]. Iowan et al. constructed the agile distribution scheme of the information sharing mechanism to effectively counter the common bullwhip effect in customer service distribution. Since then, research on agile distribution has gradually developed in the direction of practicality and informatization [6]. Koch and Wäscher first build a mathematical model based on the minimum total warehouse area as the optimization objective, and then combine the grouping genetic algorithm and local search algorithm with further solution to the problem of agile distribution [7]. Jennifer et al. constructed a mathematical model with the minimum sum of transportation costs and inventory costs as the optimization objective [8]. On this basis, both inventory and transportation of route plans should be taken into account. Experiments effectively verified the effectiveness of the distribution path-planning algorithm. Li et al. studied the mathematical model of the vehicle distribution problem in multiple distribution centers and completed the experimental analysis with the improved ant colony algorithm, especially playing a positive role in energy conservation and emission reduction in the distribution process. From the perspective of market distribution business demand [9], ERICO et al. and others analyzed the route optimization of distribution vehicles caused by the random demand of consumers in the distribution system, forming the research field of random distribution vehicle routing problems [10]. With such effective technical support, the distribution costs of China’s logistics industry began to fall. Combined with the research results in recent years, it is not difficult to see that both emergency distribution and cold-chain distribution emphasize agility and efficiency, making agile distribution increasingly important in the smart logistics distribution system. The increasingly mature supply chain [11] provides opportunities for the logistics industry and promotes the formation of smart logistics concepts [12]. In addition, the formulation of a reasonable logistics distribution mode based on supply chain networks is conducive to the common progress and development of both. Therefore, taking the supply chain networks as the research background, this paper proposes an optimization method for the smart logistics agile distribution model to speed up the construction process of smart logistics, realize the agile distribution and meet users’ strict requirements on delivery time. The innovation of this method is to speed up the construction process of intelligent logistics, realize the agility of distribution, and meet the strict requirements of users for distribution time.


## 2. Smart Logistics Agile Distribution Model in Supply Chain Networks

### 2.1. Rationalization Evaluation of Agile Logistics Distribution in the Supply Chain Networks

The data adopts the distribution data of a local logistics park. The data network structure mainly includes the distribution center, the service time, time period, congestion time, and location, driving speed, departure times, and other information of the distribution center. For reasonable evaluation, based on the representativeness and scientific principles, analytic hierarchy process [13] is adopted to establish the rationalization evaluation system of agile logistics distribution as shown in Table 1 and optimize the distribution model scientifically and reasonably.Table 1
Intelligent logistics agile distribution rationalization evaluation system.
Rule layerIndex layerObjective factorsThe relevant provisionsForce majeure conditionMacro market factorsInfrastructureDistribution centerTransportation routeLogistics networkIndustry marketDegree of concernStaff qualityNormative degreeRelevant technical supportRisk controlRisk awarenessRisk warningThere are many constraints on agile distribution. The changeable distribution environment and complex market background cannot accurately quantify the logistics distribution. For these kinds of multiple-criteria decision-making (MCDM) or MCGDM problems [14], the process of constructing the decision matrix should be carried out in a single decision-making stage. In most practical decision-making problems, including multiple viewpoints does not involve collecting evaluation from a group of experts in multiple periods. Therefore, according to the following steps, first establish a reasonable evaluation strategy for fuzzy synthesis, use different levels of fuzzy subsets to quantitatively deal with fuzzy indicators, and then clarify the attributes through the comprehensive treatment of fuzzy transformation criteria, obtain more objective evaluation results, which provide a reference basis for optimizing the distribution model, and improve the actual distribution effect.(1)
Indicator set: based on the evaluation system, a setU = {U1, U2, …, Un} composed of n factors is obtained. According to the correlation, it is divided into m parts, then there is a subset Uk = {Uk1, Uk2, …, Ukn} and subset ordinal number k = 1, 2, …, m.(2)
Result set E: Zhen et al. proposed a PHFLTSs coding method based on the concept of proportional interval T2 hesitant fuzzy set (Pit2 HFS). The mathematical form of Pit2 HFS is strictly defined. The distance measurement, scoring function, and operation rules are given. The decision model has been developed to provide linguistic decision-making under uncertainty and has potential application prospects in real life [15]. This paper proposes that the first result of the rationalization evaluation of the agile distribution scheme is E1, and so on, the second evaluation result is E2, and finally all the rationalization evaluation results set E = {E1, E2, …, En} of logistics agile distribution are obtained.(3)
Weight set: establish the weight judgment matrix of each indicator through an analytic hierarchy process, make the CI value of the following consistency indicators less than 0.1, and allocate the weight values reasonably:(1)CI=λ−nn−1.In formula (1), the maximum characteristic root of each expert under the weight determination matrix is λ.The geometric average and normalization of all column vectors in the judgment matrix have been performed to obtain the weight vectorV of the corresponding vector.(4)
Fuzzy decision matrix: assume that the subscriptj in the evaluation result Ej (j = 1, 2, …, m) represents the evaluation grade of the result set, to obtain the subcase of the fuzzy subset of E. As for the fuzzy evaluation result, Ei = {Ei1, Ei2, …, Ein}(i = 1, 2, …, n) of index i, when the j-grade evaluation result is obtained, it is represented by Eij, then the fuzzy decision matrix U′, namely the fuzzy correlation from index set U to result set E, is expressed as follows:(2)Uij′=nijkm.In formula (2), nijk represents the number of experts whose evaluation index i is Ek level.(5)
Comprehensive evaluation matrix: the fuzzy decision matrix of criterion layer and index layer are respectively multiplied with their corresponding weight vectors to construct comprehensive evaluation matrixF′ and B′;(6)
Combined with the principle of the fuzziest membership degree [16], the weighted average method was used to select the reasonable fuzzy evaluation results of the index layer. The first two components are max B′ and sec B′, which are found in the result set. After the maximum membership degree ∑i=1nB′ has been obtained by the following formula, the fuzzy comprehensive evaluation has completed according to its value:(3)a=n∗maxB′−∑i=1nB′2n−1∗secB′.As shown in equation (3), the method of fuzzy membership function transforms the fuzzy time window into the level of customers’ satisfaction with the delivery time. This method mainly uses the weighted average method to evaluate the rationality of the distribution scheme comprehensively. The effective range of membership value is a≥0.5. Otherwise, the membership degree fails. As shown below, the range of A value is between zero and one, and the closer it is to one, the more reasonable the distribution scheme is:(4)A=∑j=1nBijj∑j=1nBijj.In formula (4), Bij refers to the comprehensive evaluation matrix when the evaluation level of index i is j.


### 2.2. Agile Distribution Organization Model of Networked Logistics

The supply chain networks have a great impact on the organization of agile logistics distribution, and the limitation of distribution time and logistics radius makes it gradually show a networked topology. Therefore, based on the most simplified assumptions, a mathematical model of scientific site selection has been established to improve the organization of agile distribution.The total construction fundsα, variable total funds β, and total distribution funds Q of logistics centers and distribution points in the supply chain are known (consisting of freight from supplier to logistics center, logistics center to customer, logistics center to distribution point, and distribution point to customer.). Taking the sum ρ of user needs not covered by the agile distribution radius as the service level of the networked distribution organization, the most optimal location model of the networked logistics agile distribution organization is as follows:(5)Minf=α+β+Q+ωρ.The following equations describe the constraints of the model:(6)Hι=∑φ∈J′qφyιφ2,Hι<γi′,∑φ∈I′HφZi′+∑φ∈Jqφ≤∑ι∈IZιγι,∑ι∈I′yιφ2=1,1−Zι∑φ∈Jyιφ1=0,1−Zi′∑φ∈Jyιφ2=0,1≤∑ι∈IZι≤p,1≤∑ι∈I′Zi′≤p′,Zι,Zi′∈0,1,yιφ1,yιφ2∈0,1,Zιφ1,Zιφ2∈0,1.In formula (6), f refers to the overall distribution cost of the supply chain; ω refers to the service level evaluation weight; ι and φ refer to the serial number of the distribution center and the user’s serial number. Ht,Hφ refers to the average annual delivery volume of the corresponding distribution center and users; I,I′ refer to the location collection of the logistics center and the distribution center; J,J′ refer to the set of users served by the corresponding center. qφ refer to the user φ′s annual average delivery demand; ytφ1,ytφ2 refer to whether the user φ is from the logistics center ι, the distribution center ι provides services; rι and rι′ refer to the inventory capacity of the two centers. Zt and Zt′ refer to whether a logistics center and distribution center are set up at the serial number ι; ρ and ρ′ refer to the number of locations of the two centers; and Ztφ1,Ztφ2 is used to determine whether the delivery distance between the two centers and the user meets the agile delivery standard.


### 2.3. Networked Logistics Agile Distribution Task Model

In order to reduce the computational complexity and simplify the assumptions, a mathematical model of agile distribution tasks has been established to speed up distribution efficiency and improve service levels under the premise of minimizing distribution costs.Based on the goal of minimizing distribution costs, the following agile distribution task models are established by using the following equation:(7)minZ=∑μ∈S′∪L∑φ∈S′∪L∑κ∈DXμφκCμφ+∑φ∈LPφ.The constraint equations are as follows:(8)∑μ∈Lgyμκ≤W,∑κ∈D∑μ∈S′∪LXμφκ=1,∀φ∈L;∑κ∈D∑φ∈S′∪LXμφκ=1,∀μ∈L,∑μ,φ∈S′∪LXμφκ≤NL−1,tφ=∑κ∈D∑μ∈S′∪LXμφκtμ+tμ′+tμφ,∀φ∈L,Xμφκtφ−tμ≥0,∀μ,φ∈LPφ=tφ>Tφb,btφ−Tφb,tφ≤Tφb,0.As shown in equation (8), Z represents the cost of completing the delivery task. Cuφ represents the delivery cost between the user’s μ and φ. L represents the user set that dispatches the delivery task; NL refers to the number of the user set; W represents the delivery vehicle volume; g represents the demand for each user; and S′ represents the collection of designated distribution centers. tu,tφ, tυφ represent the transportation time between use μ, φ and the two users, respectively from the center. tu′ represents the service time of user μ. Pφ represents the penalty fee for not delivering on time. Tφb represents the latest delivery time given by the user φ. D represents the number of transport vehicles in the distribution center, and b represents the penalty coefficient. yuk has used to determine whether the transport vehicle κ provides delivery services for the user μ. xuφk is used to determine whether the delivery route of the transport vehicle κ for users μ to φ; ∀ represents the universal quantifier.


## 2.1. Rationalization Evaluation of Agile Logistics Distribution in the Supply Chain Networks

The data adopts the distribution data of a local logistics park. The data network structure mainly includes the distribution center, the service time, time period, congestion time, and location, driving speed, departure times, and other information of the distribution center. For reasonable evaluation, based on the representativeness and scientific principles, analytic hierarchy process [13] is adopted to establish the rationalization evaluation system of agile logistics distribution as shown in Table 1 and optimize the distribution model scientifically and reasonably.Table 1
Intelligent logistics agile distribution rationalization evaluation system.
Rule layerIndex layerObjective factorsThe relevant provisionsForce majeure conditionMacro market factorsInfrastructureDistribution centerTransportation routeLogistics networkIndustry marketDegree of concernStaff qualityNormative degreeRelevant technical supportRisk controlRisk awarenessRisk warningThere are many constraints on agile distribution. The changeable distribution environment and complex market background cannot accurately quantify the logistics distribution. For these kinds of multiple-criteria decision-making (MCDM) or MCGDM problems [14], the process of constructing the decision matrix should be carried out in a single decision-making stage. In most practical decision-making problems, including multiple viewpoints does not involve collecting evaluation from a group of experts in multiple periods. Therefore, according to the following steps, first establish a reasonable evaluation strategy for fuzzy synthesis, use different levels of fuzzy subsets to quantitatively deal with fuzzy indicators, and then clarify the attributes through the comprehensive treatment of fuzzy transformation criteria, obtain more objective evaluation results, which provide a reference basis for optimizing the distribution model, and improve the actual distribution effect.(1)
Indicator set: based on the evaluation system, a setU = {U1, U2, …, Un} composed of n factors is obtained. According to the correlation, it is divided into m parts, then there is a subset Uk = {Uk1, Uk2, …, Ukn} and subset ordinal number k = 1, 2, …, m.(2)
Result set E: Zhen et al. proposed a PHFLTSs coding method based on the concept of proportional interval T2 hesitant fuzzy set (Pit2 HFS). The mathematical form of Pit2 HFS is strictly defined. The distance measurement, scoring function, and operation rules are given. The decision model has been developed to provide linguistic decision-making under uncertainty and has potential application prospects in real life [15]. This paper proposes that the first result of the rationalization evaluation of the agile distribution scheme is E1, and so on, the second evaluation result is E2, and finally all the rationalization evaluation results set E = {E1, E2, …, En} of logistics agile distribution are obtained.(3)
Weight set: establish the weight judgment matrix of each indicator through an analytic hierarchy process, make the CI value of the following consistency indicators less than 0.1, and allocate the weight values reasonably:(1)CI=λ−nn−1.In formula (1), the maximum characteristic root of each expert under the weight determination matrix is λ.The geometric average and normalization of all column vectors in the judgment matrix have been performed to obtain the weight vectorV of the corresponding vector.(4)
Fuzzy decision matrix: assume that the subscriptj in the evaluation result Ej (j = 1, 2, …, m) represents the evaluation grade of the result set, to obtain the subcase of the fuzzy subset of E. As for the fuzzy evaluation result, Ei = {Ei1, Ei2, …, Ein}(i = 1, 2, …, n) of index i, when the j-grade evaluation result is obtained, it is represented by Eij, then the fuzzy decision matrix U′, namely the fuzzy correlation from index set U to result set E, is expressed as follows:(2)Uij′=nijkm.In formula (2), nijk represents the number of experts whose evaluation index i is Ek level.(5)
Comprehensive evaluation matrix: the fuzzy decision matrix of criterion layer and index layer are respectively multiplied with their corresponding weight vectors to construct comprehensive evaluation matrixF′ and B′;(6)
Combined with the principle of the fuzziest membership degree [16], the weighted average method was used to select the reasonable fuzzy evaluation results of the index layer. The first two components are max B′ and sec B′, which are found in the result set. After the maximum membership degree ∑i=1nB′ has been obtained by the following formula, the fuzzy comprehensive evaluation has completed according to its value:(3)a=n∗maxB′−∑i=1nB′2n−1∗secB′.As shown in equation (3), the method of fuzzy membership function transforms the fuzzy time window into the level of customers’ satisfaction with the delivery time. This method mainly uses the weighted average method to evaluate the rationality of the distribution scheme comprehensively. The effective range of membership value is a≥0.5. Otherwise, the membership degree fails. As shown below, the range of A value is between zero and one, and the closer it is to one, the more reasonable the distribution scheme is:(4)A=∑j=1nBijj∑j=1nBijj.In formula (4), Bij refers to the comprehensive evaluation matrix when the evaluation level of index i is j.


## 2.2. Agile Distribution Organization Model of Networked Logistics

The supply chain networks have a great impact on the organization of agile logistics distribution, and the limitation of distribution time and logistics radius makes it gradually show a networked topology. Therefore, based on the most simplified assumptions, a mathematical model of scientific site selection has been established to improve the organization of agile distribution.The total construction fundsα, variable total funds β, and total distribution funds Q of logistics centers and distribution points in the supply chain are known (consisting of freight from supplier to logistics center, logistics center to customer, logistics center to distribution point, and distribution point to customer.). Taking the sum ρ of user needs not covered by the agile distribution radius as the service level of the networked distribution organization, the most optimal location model of the networked logistics agile distribution organization is as follows:(5)Minf=α+β+Q+ωρ.The following equations describe the constraints of the model:(6)Hι=∑φ∈J′qφyιφ2,Hι<γi′,∑φ∈I′HφZi′+∑φ∈Jqφ≤∑ι∈IZιγι,∑ι∈I′yιφ2=1,1−Zι∑φ∈Jyιφ1=0,1−Zi′∑φ∈Jyιφ2=0,1≤∑ι∈IZι≤p,1≤∑ι∈I′Zi′≤p′,Zι,Zi′∈0,1,yιφ1,yιφ2∈0,1,Zιφ1,Zιφ2∈0,1.In formula (6), f refers to the overall distribution cost of the supply chain; ω refers to the service level evaluation weight; ι and φ refer to the serial number of the distribution center and the user’s serial number. Ht,Hφ refers to the average annual delivery volume of the corresponding distribution center and users; I,I′ refer to the location collection of the logistics center and the distribution center; J,J′ refer to the set of users served by the corresponding center. qφ refer to the user φ′s annual average delivery demand; ytφ1,ytφ2 refer to whether the user φ is from the logistics center ι, the distribution center ι provides services; rι and rι′ refer to the inventory capacity of the two centers. Zt and Zt′ refer to whether a logistics center and distribution center are set up at the serial number ι; ρ and ρ′ refer to the number of locations of the two centers; and Ztφ1,Ztφ2 is used to determine whether the delivery distance between the two centers and the user meets the agile delivery standard.


## 2.3. Networked Logistics Agile Distribution Task Model

In order to reduce the computational complexity and simplify the assumptions, a mathematical model of agile distribution tasks has been established to speed up distribution efficiency and improve service levels under the premise of minimizing distribution costs.Based on the goal of minimizing distribution costs, the following agile distribution task models are established by using the following equation:(7)minZ=∑μ∈S′∪L∑φ∈S′∪L∑κ∈DXμφκCμφ+∑φ∈LPφ.The constraint equations are as follows:(8)∑μ∈Lgyμκ≤W,∑κ∈D∑μ∈S′∪LXμφκ=1,∀φ∈L;∑κ∈D∑φ∈S′∪LXμφκ=1,∀μ∈L,∑μ,φ∈S′∪LXμφκ≤NL−1,tφ=∑κ∈D∑μ∈S′∪LXμφκtμ+tμ′+tμφ,∀φ∈L,Xμφκtφ−tμ≥0,∀μ,φ∈LPφ=tφ>Tφb,btφ−Tφb,tφ≤Tφb,0.As shown in equation (8), Z represents the cost of completing the delivery task. Cuφ represents the delivery cost between the user’s μ and φ. L represents the user set that dispatches the delivery task; NL refers to the number of the user set; W represents the delivery vehicle volume; g represents the demand for each user; and S′ represents the collection of designated distribution centers. tu,tφ, tυφ represent the transportation time between use μ, φ and the two users, respectively from the center. tu′ represents the service time of user μ. Pφ represents the penalty fee for not delivering on time. Tφb represents the latest delivery time given by the user φ. D represents the number of transport vehicles in the distribution center, and b represents the penalty coefficient. yuk has used to determine whether the transport vehicle κ provides delivery services for the user μ. xuφk is used to determine whether the delivery route of the transport vehicle κ for users μ to φ; ∀ represents the universal quantifier.


## 3. Intelligent Logistics Agile Distribution Optimization Technology

According to the uncertain influence of many objective conditions on the agile distribution, the concept of time window [17] has been used as a constraint to optimize the agile distribution model and improve the customer’s satisfaction with the distribution time [18].


### 3.1. Technical Model

The objective function expression of the technology model based on the concept of time windows has shown the following equation:(9)minT=d∑φ∈LmaxTφa−Tφκ,0+e∑φ∈LmaxTφκ−Tφb,0,,minZ=∑μ∈S′∪L∑φ∈S′∪L∑κ∈DXμφκCμφ+∑φ∈LPφ.Among them,d represents the number of smart logistics agile distribution centers, e represents the annual average distribution demand, and L represents the unit penalty cost for the delayed distribution. minT, which is to complete the distribution task in the time window, minZ, which is to minimize the distribution cost.It is mainly aimed at the random demand business of market consumers. How can the distribution center respond quickly and meet the needs of customers with high quality according to the demand time of consumers? In fact, this problem can transform into a distributed, agile distribution path with a time window under random demand. The constraint equations of the time window model have been shown in the following equation:(10)∑φ∈LXμφκ=∑μ∈LXφμκ≤1,∑φ∈S′∪Lyμκg≤W,∑μ∈S′∪L∑φ∈S′∪LSφμXφμκ≤F,Tφκ′=Tμκ′+tφμκTμκ′,Tφκ=Tφκ′,Tφκ′≥TφaTφκ′,Tφκ′<Tφa.where W represents the unit penalty cost incurred by the transport vehicle due to early arrival; Sφu represents the distribution distance between user’s φ and μ; F represents the farthest distribution distance of each vehicle. tφμκ represents the time when the transport vehicle κ immediately goes to user φ and the service end time of the user μ; Tφα represents the upper limit of service time window given by user φ; and Tφk′, represents the arrival time and service time for user φ and vehicle κ, respectively.It is necessary to decide to select the appropriate matching object for trading within the time required by logistics agile distribution. As the service resources and trading objects entering the platform change with the passage of time, the decision-making benefits and corresponding risks will vary in different time periods, which brings difficulties to the decision-making in the concept of the time window. The technical model based on the concept of the time window can effectively solve this problem.


### 3.2. Optimization

Based on the attribute characteristics of agile distribution and many uncertain factors [19, 20], on the premise of simplifying assumptions, the optimization objectives (i.e., the minimization of total distribution cost is expressed as minζ1 and the maximization of agile distribution time is expressed as maxζ2) are set up, and the dynamic optimization model of agile distribution with time window is established. The functional equations have been shown in the following equation:(11)minζ1=minf+minZ,maxζ2=∑s∈S′∑φ∈Ltφsκ′−tφsκ.The constraints of the agile distribution optimization model have been shown in the following equations (12):(12)s=tφικ2×yιμ2×Rιmin,s′=tφικ′2×yιμ2×Rιmax,where tφικ′2 represents the allowable lead-time of distribution for user φ. tφικ2 represents the estimated lead-time of delivery of transport vehicle k. yιμ2 indicates whether user u has been served by distribution center ι. Rιmin and Rιmax indicate that the center ι stores extreme values. The model completes the agile distribution in a time window and optimizes the operation mode, which needs to control the demand of the time window into constraints and establish an optimization model to obtain the optimal operation. To sum up, complete the optimization research of an intelligent logistics agile distribution model in the supply chain environment.


## 3.1. Technical Model

The objective function expression of the technology model based on the concept of time windows has shown the following equation:(9)minT=d∑φ∈LmaxTφa−Tφκ,0+e∑φ∈LmaxTφκ−Tφb,0,,minZ=∑μ∈S′∪L∑φ∈S′∪L∑κ∈DXμφκCμφ+∑φ∈LPφ.Among them,d represents the number of smart logistics agile distribution centers, e represents the annual average distribution demand, and L represents the unit penalty cost for the delayed distribution. minT, which is to complete the distribution task in the time window, minZ, which is to minimize the distribution cost.It is mainly aimed at the random demand business of market consumers. How can the distribution center respond quickly and meet the needs of customers with high quality according to the demand time of consumers? In fact, this problem can transform into a distributed, agile distribution path with a time window under random demand. The constraint equations of the time window model have been shown in the following equation:(10)∑φ∈LXμφκ=∑μ∈LXφμκ≤1,∑φ∈S′∪Lyμκg≤W,∑μ∈S′∪L∑φ∈S′∪LSφμXφμκ≤F,Tφκ′=Tμκ′+tφμκTμκ′,Tφκ=Tφκ′,Tφκ′≥TφaTφκ′,Tφκ′<Tφa.where W represents the unit penalty cost incurred by the transport vehicle due to early arrival; Sφu represents the distribution distance between user’s φ and μ; F represents the farthest distribution distance of each vehicle. tφμκ represents the time when the transport vehicle κ immediately goes to user φ and the service end time of the user μ; Tφα represents the upper limit of service time window given by user φ; and Tφk′, represents the arrival time and service time for user φ and vehicle κ, respectively.It is necessary to decide to select the appropriate matching object for trading within the time required by logistics agile distribution. As the service resources and trading objects entering the platform change with the passage of time, the decision-making benefits and corresponding risks will vary in different time periods, which brings difficulties to the decision-making in the concept of the time window. The technical model based on the concept of the time window can effectively solve this problem.


## 3.2. Optimization

Based on the attribute characteristics of agile distribution and many uncertain factors [19, 20], on the premise of simplifying assumptions, the optimization objectives (i.e., the minimization of total distribution cost is expressed as minζ1 and the maximization of agile distribution time is expressed as maxζ2) are set up, and the dynamic optimization model of agile distribution with time window is established. The functional equations have been shown in the following equation:(11)minζ1=minf+minZ,maxζ2=∑s∈S′∑φ∈Ltφsκ′−tφsκ.The constraints of the agile distribution optimization model have been shown in the following equations (12):(12)s=tφικ2×yιμ2×Rιmin,s′=tφικ′2×yιμ2×Rιmax,where tφικ′2 represents the allowable lead-time of distribution for user φ. tφικ2 represents the estimated lead-time of delivery of transport vehicle k. yιμ2 indicates whether user u has been served by distribution center ι. Rιmin and Rιmax indicate that the center ι stores extreme values. The model completes the agile distribution in a time window and optimizes the operation mode, which needs to control the demand of the time window into constraints and establish an optimization model to obtain the optimal operation. To sum up, complete the optimization research of an intelligent logistics agile distribution model in the supply chain environment.


## 4. Experimental Analysis

Select two distribution centers of a small or medium-sized smart logistics enterprise as the experimental objects. And apply the smart logistics agile distribution model in the supply chain environment to the experimental object, Two distribution centers of a small and medium-sized intelligent logistics enterprise are selected as experimental objects, and suppliers, distribution roads, of the two centers and their covered users are abstractly processed to obtain the connected undirected graph shown in Figure1. The figure shows the main parameters, such as supplier, distribution center, the number of users, and the time limit for delivery required by users (including the allowed lead-time). Other relevant parameters affecting delivery agility are shown in Table 2.Figure 1
Topology of agile distribution network.Table 2
The index data of the agile distribution.
IndexNumberNumber of transport vehicles2Delivery cost/yuan0.3Driving speed per hour/km60Penalty fee per minute delayed10Penalty fee per minute in advance5Fixed fee/RMB100Penalty factor0.1Each distribution center is equipped with a transport vehicle. Simulation software has been used to simulate the agile distribution scheme before and after optimization in this supply chain, as shown in Figure2. The solid red line represents the vehicle distribution path starting from distribution center No. 1, and the dotted green line represents the vehicle distribution path distributed by distribution center No. 2.Figure 2
Schematic diagram of agile distribution scheme (a) before and (b) after optimization.
(a)(b)Based on the rationalization evaluation system, the weights of indicators at different levels have been defined, as shown in Table3.(1)
By improving the established logistics agile evaluation system of logistics distribution rationalization and introducing the fuzzy comprehensive rationalization evaluation strategy, a more offline effect was obtained. The evaluation values of the distribution scheme before and after optimization are 0.56 and 0.98, which has nearly doubled.(2)
The growth rate shows that the optimized distribution scheme path is more scientific and reasonable.(3)
The distribution organization model improves the organizational form of agile distribution as a whole by scientifically selecting the address of the distribution center.(4)
Time window technology endows the distribution task model with flexibility and dynamics; so that the two objectives of distribution time requirements and distribution cost minimization are realized.Table 3
Smart logistics agile distribution rationalization evaluation system.
Rule layerIndex layerObjective factors = 0.2Relevant regulations = 0.06Force majeure conditions = 0.03Macro market factors = 0.11Infrastructure = 0.4Distribution center = 0.15Transportation line = 0.2Logistics network = 0.05Industry market = 0.2Attention = 0.03Quality of staff = 0.07Standardc = 0.03Technical support = 0.07Risk control = 0.2Risk awareness = 0.1Risk warning = 0.1All the above have improved the rationality of agile distribution to a certain extent. Combined with the distribution time of each user shown in Figure2, it found that before optimization, only the distribution service of a distribution center 2 had been completed within the time window given by the user, while the optimized distribution scheme met the distribution time requirements of all users, further verifying the effectiveness and superiority of the optimization method. In order to comprehensively test the optimization advantages of the distribution model, the changes in the index values before and after the optimization of the distribution plan are compared from the perspectives of the length of the distribution path, the length of the distribution service, and the distribution cost, as shown in Figure 3.Figure 3
Schematic diagram of index values before and after optimization.According to the results of the indicators in Figure3, the total delivery distance, total cost, and total time before optimization are 70.1 kilometers, 222.22 yuan, and 1.064 hours, respectively, while the total value of each indicator after optimization is 67.8 kilometers, 200.38 yuan, and 1.252 hours. After comparison, it was found that although the optimized delivery service time increased slightly, the delivery route length and delivery cost was significantly reduced. This is because the fuzzy comprehensive evaluation of the rational evaluation method helps to provide a good optimization direction, introduces the concept of the time window, and makes up for the shortcomings of the distribution task model in achieving agile distribution. The best solution has been obtained through dynamic optimization, and the distribution has been greatly reduced. Time and cost have improved the economic efficiency of logistics enterprises.


## 5. Conclusion

With the rapid progress of modern logistics, innovative distribution technology has attracted more and more attention and has become a research topic of great practical significance and theoretical value. Agile distribution, as the lifeblood and development booster of the logistics industry, plays an important role in meeting the strict distribution time limit requirements of users. This paper proposes an optimization method for the intelligent logistics agile distribution model to speed up the construction process of intelligent logistics, realize the agility of distribution, meet the strict requirements of users for distribution time, and enrich the supply chain mode of logistics agile distribution. Secondly, from the perspective of management, the time and space position of goods and vehicles in the process of supply, storage, circulation, processing, and delivery are inseparable from the lean coordination of managers. Therefore, it mainly aims at the random demand business of market consumers. How can the distribution center respond quickly and meet the needs of customers with high quality according to the demand time of consumers? Its essence is the distributed, agile distribution path problem with a time window under random demand. Each station is required to have a service time window, and vehicles can serve the station only after the time window has opened.(1)
When the distribution service vehicles arrive at the distribution station, the service demand of the station has exceeded the cumulative number of vehicles at this time. After the distribution vehicle reaches its own capacity, it returns to the distribution center for unloading loading. At this time, it meets some of the service needs of the station and then continues to serve.(2)
When the distribution service vehicle arrives at a distribution station, the service demand of the station plus the cumulative demand of the front station on the path is exactly equal to the vehicle capacity. The vehicle cannot continue to move forward for service, return to the distribution center for unloading loading, and then return to the next station for service.(3)
It has been agreed that when the vehicle fails in service at the distribution station, the vehicle shall return to the distribution center to unload (load) the goods, and then continue to return to the original path to complete the task. It has been assumed that a service failure on each distribution service path can only occur once at most.Agile distribution is in the early stages of research, and there is still much room for improvement. The details are as follows: we should deeply explore the random conditions such as road traffic and user dynamic demand, and establish constraints and optimization objectives that better fit the actual situation. We should try to expand the research scope of agile distribution by combining relatively mature technologies such as information processing, geographic information systems, and global positioning systems, to fundamentally restrain many uncertain factors of logistics and realize agile distribution; The time window in this model belongs to the hard time window, which only considers the distribution of single goods. However, in the real supply chain, there are many kinds and large quantities of goods, and the time window is mainly mixed. In the next stage, we will further optimize this kind of time window.



---

*Source: 4225202-2022-04-14.xml*