# Research on Partner Selection of High-Speed Railway Dynamic Logistics Alliance Based on the Dynamic Programming Model

Authors: Haixia Wu; Yinghui Wang; Pei Zhang; Jiang Yu; Yuxuan Du
Journal: Journal of Advanced Transportation
 (2023)

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## Abstract

Traditional railway transportation can no longer meet people’s demand for logistics services. This paper takes advantage of high speed to propose a high-speed railway dynamic logistics alliance based on a cloud platform to make up for the lack of transport capacity at both ends of the high-speed railway logistics trunk line. Selecting partners is crucial to the high-speed rail logistics alliance. This paper uses the methods of multiobjective fuzzy optimization and dynamic programming to conduct multistage optimization of high-speed railway dynamic logistics alliance partners. When the market demand changes, in order to optimize the overall interests of the alliance, this paper uses the efficiency profit field method to achieve the dynamic selection of alliance partners or potential partners. The case study shows that the establishment of the high-speed railway dynamic logistics alliance can optimize the interests of the members of the alliance, verify the effectiveness of the method, and provide a reference for the better development of high-speed railway logistics.


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## Body

## 1. Introduction

Railway freight transport is an important part of the modern transportation system. It plays a key role in the entire transportation field. China’s railway freight transport is one of the basic modes of land transportation. Between 2010 and 2021, the total annual freight volume reached over 3.9 billion tons. As a railway transportation mode with Chinese characteristics, high-speed rail logistics is constantly developing with the growth of the freight market.The first attempt at high-speed rail express transportation in China was implemented by the Guangzhou Railway Group on the Wuhan high-speed rail line. However, it was not until the promulgation of the interim measures for the administration of high-speed rail express transportation in 2013 that the high-speed rail enterprises involved in the express delivery business were equipped with corresponding document guidance. In the same year, the Beijing-Guangzhou line and the Beijing-Shanghai line also launched high-speed rail express trains. The partners included high-quality express enterprises such as SF Express and UPS. In 2016, China Railway Corporation provided high-speed rail express services. By 2020, the high-speed rail express business volume in China will increase by 40% year over year. There are 980 lines in China, covering more than 80 cities [1]. Such a vast freight market has created business opportunities for high-speed rail logistics. High-speed rail logistics has the outstanding advantages of “quickness, accurateness, and stability,” mainly transporting high-value-added products such as medical machinery and fresh products. Since the modern logistics system is a long industrial chain, high-speed rails can only realize part of the functions of this chain and cannot complete the logistics services at both ends of high-speed rails. It is difficult for high-speed rails to take the lead in the modern logistics market by doing it alone [1]. Therefore, based on its own advantages and disadvantages, the establishment of a high-speed rail dynamic logistics alliance led by high-speed rails is a great breakthrough against the status quo.A high-speed rail dynamic logistics alliance means that high-speed rail logistics enterprises temporarily cooperate with other enterprises to build a dynamic logistics alliance organization to grasp a certain market opportunity. Based on information network technology and through the integration of high-speed rail equipment, infrastructure, and superior logistics resources of cooperative enterprises, a temporary logistics network structural organization with complementary advantages, risks, and resource sharing is formed. The alliance responds to market challenges with its overall advantages, with a view to seizing market opportunities and increasing economic returns. It is a feasible and effective measure to form a high-speed rail dynamic logistics alliance, integrate the logistics resources of multiple enterprises, realize the complementary advantages between enterprises, and enhance market competitiveness, so as to achieve seizing market opportunities and increasing economic returns.


## 2. Literature Review

The preparation of a high-speed rail dynamic alliance based on a cloud platform has attracted some scholars’ attention. The construction of the alliance based on a cloud platform is essential to integrate the high-quality service resources of various enterprises into the cloud so that the reasonable scheduling and effective supervision of resources can be realized, thereby reducing the cost of related services and effectively improving the resource efficiency, safety, and timeliness of the service. The selection of alliance partners is essential to the survival and development of the alliance and is a key step in the alliance’s life cycle. Scholars have conducted a lot of research on logistics enterprise alliances and partner selection and have achieved rich results.For the research on the construction of dynamic alliances by logistics enterprises, Du and Qu [2] proposed a cross-border logistics alliance model based on information collaboration, built a three-way evolutionary game model of information collaboration between cross-border e-commerce platforms, domestic logistics enterprises, and foreign logistics enterprises, and conducted dynamic simulation analysis on the three-way information collaboration strategy; Luo et al. [3] built a quadratic programming model based on the square distance and least square method of interval numbers to minimize the sum of the square excess of the interval numbers of all players in the largest cooperative cold chain logistics alliance and then determined the income distribution value of each player in the alliance; Li et al. [4] proposed to apply “expressway + high-speed railway” as a fast intermodal transport mode to the multimodal transport of fresh products in view of the transport characteristics of small batches and the high timeliness of fresh products. Taking the lowest total cost as the goal, a high-speed rail service time window, and customer satisfaction as constraints, a combination model of road-rail intermodal transport route selection and transport mode for fresh products based on fuzzy demand is constructed; Jauhar et al. [5] proved that the efficiency of the third-party reverse logistics (3PRLP) may have an impact on the selection of third-party reverse logistics partners and the orders assigned to them through the two-stage method. The first stage includes a method combining data envelopment analysis and a differential evolution algorithm to improve discrimination and distinguish 3PRLPs according to efficiency. In the second stage, use the multiobjective model to allocate orders to 3PRLP. Two solutions are adopted to solve the proposed multiobjective model and find the Pareto optimal solution.Railway transportation is one of the main modern transportation modes. In order to transform traditional logistics into modern logistics, many experts have conducted research on high-speed rail logistics services. D’Acierno et al. [6, 7] and other scholars analyzed how to select the best strategy to minimize the impact on users when the railway system fails; Gallo et al. [8], taking into account the costs of all transportation systems (cars, buses, and railways) and external costs, proposed four different objective functions that can be used to assume that demand is elastic and study the design of regional railway frequency; Zhang et al. [9] proposed to build a modern logistics service system, strengthen the construction of freight brands, optimize the window period of transportation supply quality, embed the railway logistics park into the social logistics system, provide diversified logistics services, accelerate the construction of railway informatization, improve the soft power of railway logistics, and accelerate the transformation of railway freight to modern logistics; Rao et al. [10] used the double difference model to prove that the city where the enterprise is located has a significant impact on the distribution of suppliers after the high-speed railway is opened; Ren et al. [11] used the double difference tendency score matching method to prove that the opening of high-speed rail has promoted the development of the logistics industry in cities along the line on the whole; Han and Chao [12] analyzed the indirect freight effect of high-speed rail construction using the enterprise inventory cost as the starting point. According to the different transportation modes of enterprises, they built a triple-difference model. The results showed that the impact of high-speed rail on the inventory level increased with the increase in enterprises’ dependence on railway transportation.How to optimize the selection of dynamic alliance partners is the key to determining the quality of the alliance. There are many research methods for optimization in academia. This paper mainly discusses the literature review from the following two aspects: freight optimization and database use optimization.In freight optimization research, Wang et al. [13] established a multiobjective optimization model for a high-speed railway station emergency evacuation path with the goal of crowding degree and total evacuation time in the process of high-speed railway station emergency evacuation and solved it through an improved adaptive quantum ant colony algorithm. Ma and Liao [14] used a heuristic iterative algorithm to solve the integer programming model of high-speed rail express base location and scale optimization based on the service network. Wang and Wu [15] built an emergency logistics model based on cloud platforms and optimized the emergency logistics path based on cloud platforms through a genetic algorithm. Li [16] proposed a hybrid genetic algorithm combining the k-means algorithm and cluster analysis to solve the problem of multiparty collaborative logistics distribution path optimization. Camur et al. [17] used the new heuristic algorithm of the rolling time range to achieve the optimization frame of an efficient and sustainable logistics operation through transportation mode optimization and shipment integration. Song et al. [18] handled the optimization of emergency logistics through an in-depth learning model based on big data.On the optimization of database use, Crispim et al. [19] proposed using the TOPSIS method to sort and select candidate partners; Wang Daoqu [20] combined AHP and TOPSIS to achieve partner selection; Gong et al. [21] used the adaptive dynamic programming method to research and solve the online solution of the network multiagent pursuit and evasion game so that each agent can obtain the strategy to achieve Nash equilibrium in real time; Liang and Xu [22] established a finite-time domain Markov decision process model with the goal of maximizing the benefits of the hospital in terms of inspection equipment, and combined it with the dynamic programming theory to obtain the optimal reservation scheduling strategy of the system. In order to adapt the warehouse to the increasing variety and quantity of storage products, Djurdjević et al. [23] used the dynamic programming method to obtain the optimal allocation of products in different order-picking areas. In order to solve the optimal control problem in the full driving scenario of hybrid electric vehicles, Bao et al. [24] proposed an adaptive dynamic programming method to solve the interpolation error problem and obtained the solution without theoretical error at the cost of small driving cycle accuracy. Lan et al. [25] developed a heuristic algorithm combined with the dynamic programming algorithm to generate a task attribute list for each doctor when studying the doctor scheduling problem, so as to ensure the optimization of the solution. Hu et al. [26] proposed a multiobjective planning algorithm based on pruning rules to solve the problem of the dimension disaster of dynamic programming algorithms: prune the dominated state by pruning rules and reduce the search space to improve the calculation efficiency.Existing literature has conducted meaningful research and exploration on the general dynamic alliances of logistics enterprises and their partners selection of dynamic alliances. However, there is a lack of research on high-speed rail logistics enterprises as the core of dynamic alliances. It can be seen from the literature that the dynamic programming method has the advantage of being able to obtain the global optimal solution and is often used to solve optimization problems, but there are few articles on the optimization of the selection of alliance partners. Due to the problem of “dimension disaster” in dynamic programming, this paper proposes to conduct multistage optimization of high-speed railway dynamic logistics alliance partners with the goal of maximizing the overall profit of the alliance based on the realistic background that big data cloud platforms have been widely used, using the method of combining multiobjective fuzzy optimization and dynamic programming. When the market demand changes, in order to optimize the overall interests of the alliance, this paper uses the efficiency profit field method to achieve the dynamic selection of alliance partners or potential partners. In this way, the dynamic selection of partners and the dynamic entry and exit mechanisms of alliances can be formed.


## 3. Analysis of Partners Selection of High-Speed Rail Dynamic Logistics Alliance

### 3.1. The Formation of High-Speed Rail Dynamic Logistics Alliance

High-speed rail logistics dynamic alliance is task-oriented. It uses cloud platforms as the infrastructure. The specific formation process of the alliance is that after the cloud platform owned by the high-speed rail logistics enterprise obtains the customer’s transportation demands, based on the characteristics of the task, among all the partners that the high-speed rail logistics enterprise can obtain, the enterprise that best meets the overall profit maximization will be selected and formed into the alliance to serve the transportation. Through the formation process, it can be seen that the alliance with high-speed rail logistics enterprises as the core emerges with tasks. Different partners are determined according to different cooperation goals, and sometimes it is necessary to run multiple alliances simultaneously at the same time. This requires the use of cloud platforms to efficiently and orderly process large amounts of data and realize information sharing and collaboration among alliance members. The cloud platforms have powerful distributed processing and storage capabilities, so they can quickly process the information between the partners of the dynamic logistics alliance and realize real-time information sharing between alliance members. Meanwhile, because of the large amount of storage, the stored information is more comprehensive and specific and contributes to the overall optimization of the alliance, which avoids the problem that traditional information systems can only issue decisions based on one-sided information [27].


### 3.2. The  Partners Selection Process of High-Speed Rail Dynamic Logistics Alliance

In the formation of a high-speed rail dynamic logistics alliance, partner selection is extremely important as a link throughout. This paper divides the partner selection for the alliance based on a cloud platform into three phases.Phase I is the classification of partners. Before the transportation task is launched, the cloud platform will classify the partners based on the information collected from high-speed rail logistics enterprise partners combined with various quantitative and qualitative indicators so that when the demand for the alliance’s construction arises, feasible enterprises can be selected efficiently.Phase II is the selection of partners. To allow the alliance partners to collaborate to achieve the effect of “1 + 1 > 2,” a comprehensive evaluation was carried out on the basis of the classification of the proposed cooperative enterprises according to the logistics and transportation stages in the classification of partners so as to achieve the globally optimal goal [28, 29]. Phase II is divided into the following two steps:Step one is to comprehensively consider the quantitative and qualitative indicators that need to be evaluated in the partners’ selection of the alliance and determine the relative superiority of each candidate enterprise in each link based on the multiobjective fuzzy optimization model.Step two is to use the basic idea of the dynamic programming method: first, divide the target logistics tasks completed by the alliance’s plan into stages according to the various links that need to be completed and transform the partners’ selection into a multistaged optimal combination decision; second, by adopting the method of maximizing the sum of the relative superiority of the decision sequence, calculate and solve the optimal combination of the alliance partners.Phase III is the dynamic selection of partners. When the market demand changes and the selected partner combination is not sufficient to meet the market demand, the alliance members are dynamically replaced through the efficiency profit field model by setting the critical point for entering and exiting the alliance. Enterprises that meet the conditions will enter the alliance organization, and those that do not meet the conditions will exit.


## 3.1. The Formation of High-Speed Rail Dynamic Logistics Alliance

High-speed rail logistics dynamic alliance is task-oriented. It uses cloud platforms as the infrastructure. The specific formation process of the alliance is that after the cloud platform owned by the high-speed rail logistics enterprise obtains the customer’s transportation demands, based on the characteristics of the task, among all the partners that the high-speed rail logistics enterprise can obtain, the enterprise that best meets the overall profit maximization will be selected and formed into the alliance to serve the transportation. Through the formation process, it can be seen that the alliance with high-speed rail logistics enterprises as the core emerges with tasks. Different partners are determined according to different cooperation goals, and sometimes it is necessary to run multiple alliances simultaneously at the same time. This requires the use of cloud platforms to efficiently and orderly process large amounts of data and realize information sharing and collaboration among alliance members. The cloud platforms have powerful distributed processing and storage capabilities, so they can quickly process the information between the partners of the dynamic logistics alliance and realize real-time information sharing between alliance members. Meanwhile, because of the large amount of storage, the stored information is more comprehensive and specific and contributes to the overall optimization of the alliance, which avoids the problem that traditional information systems can only issue decisions based on one-sided information [27].


## 3.2. The  Partners Selection Process of High-Speed Rail Dynamic Logistics Alliance

In the formation of a high-speed rail dynamic logistics alliance, partner selection is extremely important as a link throughout. This paper divides the partner selection for the alliance based on a cloud platform into three phases.Phase I is the classification of partners. Before the transportation task is launched, the cloud platform will classify the partners based on the information collected from high-speed rail logistics enterprise partners combined with various quantitative and qualitative indicators so that when the demand for the alliance’s construction arises, feasible enterprises can be selected efficiently.Phase II is the selection of partners. To allow the alliance partners to collaborate to achieve the effect of “1 + 1 > 2,” a comprehensive evaluation was carried out on the basis of the classification of the proposed cooperative enterprises according to the logistics and transportation stages in the classification of partners so as to achieve the globally optimal goal [28, 29]. Phase II is divided into the following two steps:Step one is to comprehensively consider the quantitative and qualitative indicators that need to be evaluated in the partners’ selection of the alliance and determine the relative superiority of each candidate enterprise in each link based on the multiobjective fuzzy optimization model.Step two is to use the basic idea of the dynamic programming method: first, divide the target logistics tasks completed by the alliance’s plan into stages according to the various links that need to be completed and transform the partners’ selection into a multistaged optimal combination decision; second, by adopting the method of maximizing the sum of the relative superiority of the decision sequence, calculate and solve the optimal combination of the alliance partners.Phase III is the dynamic selection of partners. When the market demand changes and the selected partner combination is not sufficient to meet the market demand, the alliance members are dynamically replaced through the efficiency profit field model by setting the critical point for entering and exiting the alliance. Enterprises that meet the conditions will enter the alliance organization, and those that do not meet the conditions will exit.


## 4. Methods and Models for Partners Selection of the High-Speed Rail Dynamic Logistics Alliance

### 4.1. Multiobjective Fuzzy Optimization Method

Suppose that the high-speed rail dynamic logistics alliance needs to go throughs links to complete a target logistics task and an appropriate partner must be selected in each link to complete the task. Suppose that the collection of candidate partners for all links is T=t1,t2,…tn, where ts=ts1,ts2,…,tsn is the collection of candidate partners for the sth,s=1,2…S link. Suppose that there are a total of m indicators in the evaluation indicator system selected by the partner and G=g1,g2,…,gm is the collection of the m qualitative and quantitative evaluation targets. Let 1 to h be the quantitative evaluation indicator and h+1 to m be the qualitative evaluation indicator. The m target feature matrices of ts collection in the sth link are(1)Xs=x11sx12s⋯x1tssx21sx22s⋯x2tss⋯⋯⋯⋯xm1sxm2s⋯xmtss=xijs.In equation (1), s=1,2,…,S; i=1,2,…,m; j=1,2,…,ts; element xijs represents the evaluation value of jth candidate partner tsj in the sth link with the ith quantitative target gi.


#### 4.1.1. Analysis of Relative Superiority of Qualitative Targets [27, 30]

According to fuzziness and relativity, setrijs as the relative superiority of the eigenvalues of the sample indicator i with respect to the fuzzy concept [31]. The equations are as follows:(1)
If the indicatorgi belongs to the smaller the better, then(2)rijs=mins,jxijsxijs,(2)
If the indicatorgi belongs to the higher the better, then(3)rijs=xijsmaxs,jxijs.The nondimensional relative superiority matrix of the quantitative targets is as follows:(4)Rs1=r11s1r12s1⋯r1ns1r21s1r22s1⋯r2ns1⋯⋯⋯⋯rh1s1rh1s1⋯rhns1=rijs1.In equation (4), s=1,2,…,S; i=1,2,…,h; j=1,2,…,n; 0≤rijs1≤1; rijs1 represents the relative superiority matrix of the jth candidate plan in the sth link with the ith quantitative target.


#### 4.1.2. Analysis of Relative Superiority of Qualitative Targets [27, 30]

Through binary comparison of the superiority of each qualitative target of different candidate partners, sort and compare in turn, determine the mood operator, and then obtain the relative superiority matrix of qualitative targets according to Tables1. The specific steps are as follows.Table 1
The relationship between mood operator, quantitative scale, and relative superiority.
Mood operatorsSameSlightlyA bit more than slightlyA bit less than obviouslyObviouslyRemarkablyQuiteQuite a lotEspeciallyExtremelyIncomparablyQuantitative scale0.500.550.600.650.700.750.800.850.900.951.000.5250.5750.6250.6750.7250.7750.8250.8750.9250.975Relative superiority1.00.8180.6670.5380.4290.3330.250.1760.1110.05300.9050.7390.600.4810.3790.290.2120.10.9250.975The qualitative ranking scale of superiority obtained by binary comparison takes values between 0, 0.5, and 1.0. The following equation can be obtained:(5)eqpsgi=1,tsqis superior totsp,0.5,tsqandtsphave the same superiorty,0,tsqis n ferior totsp.Equation (5) represents the qualitative ranking scale of the superiority binary comparison between the candidate partner and the candidate partner in the sth link with the quantitative target. If the superiority of the partner for the qualitative target is greater than the superiority of the partner for the qualitative target and then, if both superiorities are the same, then eqpsgi=epqsgi=0.5. The binary comparison matrix can be derived as follows:(6)Esgi=e11s,e12s,…,e1nse21s,e22s,…,e2nsem1s,em1s,…,emns=eqpsgi.Whentsj, Esgi is the superiority ranking consistency scale matrix. If eqpsgi≠0.5, the ranking is required to be recalculated. When Esgi meets the criteria, sort the rows and columns from the largest to the smallest, and then obtain the relative superiority matrix of qualitative indicators according to the mood operator in Table 2, as shown in the equation (5).(7)Rs2=rh+11s2rh+12s2⋯rh+1ns2rh+21s2rh+22s2⋯rh+2ns2⋯⋯⋯⋯rm1s2rm2s2⋯rmns2=rijs2.Table 2
Related concepts and meaning of the efficiency profit field of the alliance.
NoConceptMeaning1Source of profit fieldOThe high-speed rail dynamic logistics alliance2Efficiency profit fieldThe profit range generated by the high-speed rail dynamic logistics alliance due to its high efficiency3Profit qualityMProfits that the enterprise can generate4The strength of profit fieldEThe size of the profits that can be generated by the alliance using various logistics resources5The radius of profit fieldrThe radiation range of different strength of profit field6Profit attractionFGThe attraction of various advantages of the alliance to the proposed cooperative enterprises7Willingness resistanceFWThe opportunity cost of the proposed cooperative enterprises joining the alliance (namely, the maximum profit given up by the enterprises choosing to join the alliance) and the risk cost (the cost of joining the alliance)8Profit distanceDThe gap between the comprehensive capabilities of the enterprises and the ideal service requirements of the alliance9Profit distance thresholdεThe maximum profit distance that the alliance can acceptIn the abovementioned equation,rijs2 represents the relative superiority matrix of the jth candidate plan in the sth link with the ith quantitative target.ThroughRs1 and Rs2, the relative superiority matrix of all quantitative and qualitative evaluation targets of the candidate partners in the sth link is as follows:(8)Rs=r11s1r12s1⋯r1ns1r21s1r22s1⋯r2ns1⋯⋯⋯⋯rh1s1rh2s1⋯rhns1rh+11s2rh+12s2⋯rh+1ns2⋯⋯⋯⋯rm1s2rm2s2⋯rmns2=rijs.In equation (8), s=1,2,…,S; i=1,2,…,m; j=1,2,…,n; 0≤rijs≤1; rijs represents the relative superiority matrix of the jth candidate plan in the sth link with the ith quantitative target.


#### 4.1.3. Analysis of Target Weight Vector

Different factors have different effects on target selection. To ensure that target selection is reliable and evidence-based, imitate the abovementioned method of determining the superiority of qualitative and quantitative targets to determine the proportion of each factor. That is, the “importance” of the fuzzy concept replaces the concept’s “excellence” in order to obtain the relative superiority degree of each target to the importance. After normalization, the weight vector of the target can be obtained as follows:(9)ws=w1s,w2s,…,wmsΤ,∑i=1mwis=1,(10)wi=1−α1i/α1i∑i=1m1−α1i/α1i,0.5≤α1i≤1,i=1,2,…,m.α1i is the importance scale calculated according to the relationship between the mood operator and the quantitative scale, and the relative superiority degree is obtained after the qualitative indicator uses the binary comparison method to obtain the superiority ranking consistency scale matrix.


#### 4.1.4. Determination of the Relative Superiority of Candidate Partners [27, 30]

To facilitate comparison, the reference benchmark must be unified. According to the relativity of optimization, the maximum value of the relative superiority of each indicator of candidate partners in all S links can be taken as the superior solution of the decision vector, and the minimum value as the inferior solution, which are represented, respectively, asa=a1,a2,…,amT and b=b1,b2,…,bmT. Therefore, in the sth link, for the determined comprehensive relative superiority matrix and the target weight vector, according to the basic theory of fuzzy optimization [32], the comprehensive relative superiority ujs of all evaluation objectives of the candidate partner in the sth link can be obtained as follows:(11)ujs=11+∑i=1mwisai−rijs/∑i=1mwisrijs−bi2.In the given equationj=1,2,…,n; s=1,2,…,S.The main purpose of the fuzzy optimization stage of candidate partners is to select candidates in a unified and comparable form through the fuzzy optimization method and to determine the relative superiority of candidate enterprises in each link.


### 4.2. Dynamic Programming Method

(1)
Construction of a Decision Matrix [27, 30]. According to the dynamic programming method, a problem needs to be considered as being composed of different stages. Therefore, S logistic links are regarded as S stages; Ts is defined as the state collection in dynamic programming, representing the collection of candidate partners in the sth stage, in which; represents the decision of the sthstage; represents the relative superiority of the candidate partners in the sthstage, which is determined by the decision of this stage and the state of the previous stage. Using the multiobjective fuzzy optimization method in 4.1, the relative superiority of candidate partners’ decision matrix in the sth stage is obtained as follows:(12)ϕs=ϕsts−11,ts1ϕsts−11,ts2⋯ϕsts−11,tsnϕsts−12,ts1ϕsts−12,ts2⋯ϕsts−12,tsn⋯⋯⋯⋯ϕsts−1n−1,ts1ϕsts−1n−1,ts2⋯ϕsts−1n−1,tsn.In the given equation, ϕtts−1i,tsji=1,2,…,n−1;j=1,2,…,n represents the relative superiority of the candidate partners tsj when the state in the stage s−l is Ts−1 and the decision is in the sth stage.(2)
Solution of Optimal Partner Combination [33]. According to the dynamic programming theory and the principle of maximum superiority, determine the objective function of the dynamic programming model and select the objective function of the fuzzy optimization dynamic programming with the largest sum of the relative superiority in S stages. The function is as follows:(13)f=max∑s=1Sujs.According to the abovementioned dynamic programming objective function and the dynamic programming optimization principle, the recursive equations of the relative superiority of candidate partners are obtained as follows:(14)fs∗=maxujs+fs−1∗,f1∗=uj1.In the given equation, fs∗ represents the maximum value of the sum of relative superiority of candidate partners in s stages; ujs represents the relative superiority of the candidate tsj in the sth stage; and fs−1∗ represents the maximum value of the sum of relative superiority of the candidate partner in the previous stage s−l of the sth stage.Through continuous recursion of equation (14), the optimal solution (or optimal partner combination) at each stage is d=d1∗,d1∗,…,dS∗.The dynamic programming method is used to select partners, which corresponds to the second stage of partner selection, namely, the optimal selection stage, that is, to compare all the combinations of all proposed cooperative enterprises one by one. The purpose is to select the globally optimal plan through comparison, so as to determine the partners of the alliance.


### 4.3. Construction of Efficiency Profit Field Model

Enterprises construct a high-speed rail dynamic logistics alliance to meet the needs of the modern logistics market and to obtain profits while ensuring the efficient completion of logistics tasks. In the dynamic partners’ selection, this paper makes innovations based on the concept and model of the profit field. Since the outstanding advantage of the alliance is high efficiency, this paper adds the “unit logistics service time” indicator that reflects efficiency when constructing an efficiency profit field model to show the different proportions of various influencing factors in partners selection. Influencing factors are reflected in the number of indicators. The specific indicators are shown in Tables3 and 4.Table 3
Indicators for influencing factors of SC.
FactorsIndicatorsLevel12345Quality of logistics serviceLogistics resource conditionsLogistics service capabilitiesLogistics service scaleLogistics service rangeLoss rate of goodsLogistics service priceEfficiency of logistics serviceTime to complete the taskLogistics service flexibilityLogistics service securityLogistics service convenienceInformation technology levelInformation infrastructureInformation network systemInformation securityEnterprise compatibilityCompatibilityTable 4
Indicators for influencing factors of RP.
FactorsIndicatorsLevel12345Enterprise reputationProduct reputationFinancial reputationService reputationCompetitive reputationCommercial reputationBanks reputationBusiness performanceProfit marginBusiness volumeOperating time


#### 4.3.1. Profit Distance

The profit distanceD is mainly affected by the comprehensive service strength (SC) and the enterprises’ operation status (RP). The specific values of SC and RP are derived from the indicator system in Tables 3 and 4, where each indicator is divided into 5 grades using a 5-point system. The 1 to 5 grades correspond to 1 to 5 points. The full score of the SC including 12 measurement indicators is 70 points, and the full score of the RP including 9 measurement indicators is 45 points. The higher the score is, the more popular it is. The grade value of each measurement indicator is determined by the threshold value of the superiority of each target of the enterprise calculated above. Therefore, the equation for calculating the enterprise’s profit distance is(15)DT=70−SC2+45−BC2.In the given equation,70−SC represents the comprehensive service distance and 45−RP represents the distance of the enterprise’s operation status.


#### 4.3.2. Profit Attraction [34]

The quality of the alliance and the proposed cooperative enterprises is determined by the types of logistics resources they own and market demand. This paper uses the vectorL to represent the set of n logistics resources. In the equation, li (li≥0) represents the number of resources i; vector Y represents the set of resource utilization. The resource utilization rate is expressed by whether the enterprise can provide the resource. yi=0 means the enterprise cannot provide resources, and yi=1 means the enterprise can provide resources. Since market demand is dynamically changing, the alliance and the proposed cooperative enterprises have different resource supply capabilities in different time periods. Thus, the time vector T=t1,t2,…,tn is introduced.The equation of the resource qualityP of the alliance is(16)PT=L×Y1,=∑i=1nliy1i.Suppose the collection of resource income of the alliance is. Different resources provide different incomes. Therefore,n resources provide n kinds of incomes, which is expressed by a vector as(17)λ=λ1,λ2,…,λn.In the equation, represents the resource income corresponding to resource. The profit quality is(18)MT=λTPT.The calculation of the profit quality of the proposed cooperative enterprise is similar to that of the alliance:(19)pT=∑i=1nli∗y2i.In the given equation,p represents the resource quality of the proposed cooperative enterprises, m represents the profit quality of the proposed cooperative enterprises, and μ=μ1,μ2,…,μn represents the collection of the resource income of the proposed cooperative enterprise.


#### 4.3.3. Willingness Resistance

The willingness resistance is expressed by the sum of risk costC∗ and the opportunity cost C of the proposed cooperative enterprise joining the alliance as(20)FTW=CT+CT∗.Suppose the profit increase of the proposed cooperative enterprises after joining the alliance isZT, and ∂ represents the increase in profit per unit resource of the enterprise after joining the alliance under current market condition. Then,(21)∂=ZTPT+pT.The strength of the profit field is(22)ET=∂TMTDT2.The calculation formula of the profit attraction FG is(23)FTG=ET×mT,=∂TMT×mTDT2.


#### 4.3.4. Construction of Efficiency Profit Field Model

Based on the abovementioned analysis, the efficiency profit field model of the alliance is determined, as shown in Figure1. The dotted circles in Figure 1 represent the radiation range of different profit field strengths; r is the profit radius, and π represents the enterprises in different profit circles. The construction of the efficiency profit field model is as follows:(24)maxMT.Figure 1
Efficiency profit field model.The constraints are(25)DT≤εT(26)FTW≤FTG.The objective function equation (24) indicates that the alliance has the greatest profit quality. The constraint equation (25) shows that the profit distance of the enterprise should be smaller than the profit distance threshold of the alliance, where εT represents the profit distance threshold. The constraint equation (26) illustrates that the profit attraction of the alliance is greater than the enterprise’s willingness resistance. The dual constraints of equations (25) and (26) form the trigger point for the proposed cooperative enterprises to enter into and exit from the alliance, which reflects the two-way choice between the alliance and the enterprise.


#### 4.3.5. Mechanism of Dynamic Selection

When market demand changes, to ensure the alliance’s advantage in the market, the alliance will adjust its internal alliance members. During the whole process, the profit quality and the strength of the alliance will change correspondently. The change in profit quality is(27)Mt+1=Mt+menter−mexit.The profit field, then, turns into(28)Et+1=∂t+1Mt+menter+mexitDt+12.The willingness resistance of the enterprise is given as follows:(29)Ft+1W=ηmt+1.After entering the algorithm program of the above method into the cloud platform’s background system, the leader of the alliance only needs to use the client side of the cloud platform to complete the automated selection of partners.


## 4.1. Multiobjective Fuzzy Optimization Method

Suppose that the high-speed rail dynamic logistics alliance needs to go throughs links to complete a target logistics task and an appropriate partner must be selected in each link to complete the task. Suppose that the collection of candidate partners for all links is T=t1,t2,…tn, where ts=ts1,ts2,…,tsn is the collection of candidate partners for the sth,s=1,2…S link. Suppose that there are a total of m indicators in the evaluation indicator system selected by the partner and G=g1,g2,…,gm is the collection of the m qualitative and quantitative evaluation targets. Let 1 to h be the quantitative evaluation indicator and h+1 to m be the qualitative evaluation indicator. The m target feature matrices of ts collection in the sth link are(1)Xs=x11sx12s⋯x1tssx21sx22s⋯x2tss⋯⋯⋯⋯xm1sxm2s⋯xmtss=xijs.In equation (1), s=1,2,…,S; i=1,2,…,m; j=1,2,…,ts; element xijs represents the evaluation value of jth candidate partner tsj in the sth link with the ith quantitative target gi.


### 4.1.1. Analysis of Relative Superiority of Qualitative Targets [27, 30]

According to fuzziness and relativity, setrijs as the relative superiority of the eigenvalues of the sample indicator i with respect to the fuzzy concept [31]. The equations are as follows:(1)
If the indicatorgi belongs to the smaller the better, then(2)rijs=mins,jxijsxijs,(2)
If the indicatorgi belongs to the higher the better, then(3)rijs=xijsmaxs,jxijs.The nondimensional relative superiority matrix of the quantitative targets is as follows:(4)Rs1=r11s1r12s1⋯r1ns1r21s1r22s1⋯r2ns1⋯⋯⋯⋯rh1s1rh1s1⋯rhns1=rijs1.In equation (4), s=1,2,…,S; i=1,2,…,h; j=1,2,…,n; 0≤rijs1≤1; rijs1 represents the relative superiority matrix of the jth candidate plan in the sth link with the ith quantitative target.


### 4.1.2. Analysis of Relative Superiority of Qualitative Targets [27, 30]

Through binary comparison of the superiority of each qualitative target of different candidate partners, sort and compare in turn, determine the mood operator, and then obtain the relative superiority matrix of qualitative targets according to Tables1. The specific steps are as follows.Table 1
The relationship between mood operator, quantitative scale, and relative superiority.
Mood operatorsSameSlightlyA bit more than slightlyA bit less than obviouslyObviouslyRemarkablyQuiteQuite a lotEspeciallyExtremelyIncomparablyQuantitative scale0.500.550.600.650.700.750.800.850.900.951.000.5250.5750.6250.6750.7250.7750.8250.8750.9250.975Relative superiority1.00.8180.6670.5380.4290.3330.250.1760.1110.05300.9050.7390.600.4810.3790.290.2120.10.9250.975The qualitative ranking scale of superiority obtained by binary comparison takes values between 0, 0.5, and 1.0. The following equation can be obtained:(5)eqpsgi=1,tsqis superior totsp,0.5,tsqandtsphave the same superiorty,0,tsqis n ferior totsp.Equation (5) represents the qualitative ranking scale of the superiority binary comparison between the candidate partner and the candidate partner in the sth link with the quantitative target. If the superiority of the partner for the qualitative target is greater than the superiority of the partner for the qualitative target and then, if both superiorities are the same, then eqpsgi=epqsgi=0.5. The binary comparison matrix can be derived as follows:(6)Esgi=e11s,e12s,…,e1nse21s,e22s,…,e2nsem1s,em1s,…,emns=eqpsgi.Whentsj, Esgi is the superiority ranking consistency scale matrix. If eqpsgi≠0.5, the ranking is required to be recalculated. When Esgi meets the criteria, sort the rows and columns from the largest to the smallest, and then obtain the relative superiority matrix of qualitative indicators according to the mood operator in Table 2, as shown in the equation (5).(7)Rs2=rh+11s2rh+12s2⋯rh+1ns2rh+21s2rh+22s2⋯rh+2ns2⋯⋯⋯⋯rm1s2rm2s2⋯rmns2=rijs2.Table 2
Related concepts and meaning of the efficiency profit field of the alliance.
NoConceptMeaning1Source of profit fieldOThe high-speed rail dynamic logistics alliance2Efficiency profit fieldThe profit range generated by the high-speed rail dynamic logistics alliance due to its high efficiency3Profit qualityMProfits that the enterprise can generate4The strength of profit fieldEThe size of the profits that can be generated by the alliance using various logistics resources5The radius of profit fieldrThe radiation range of different strength of profit field6Profit attractionFGThe attraction of various advantages of the alliance to the proposed cooperative enterprises7Willingness resistanceFWThe opportunity cost of the proposed cooperative enterprises joining the alliance (namely, the maximum profit given up by the enterprises choosing to join the alliance) and the risk cost (the cost of joining the alliance)8Profit distanceDThe gap between the comprehensive capabilities of the enterprises and the ideal service requirements of the alliance9Profit distance thresholdεThe maximum profit distance that the alliance can acceptIn the abovementioned equation,rijs2 represents the relative superiority matrix of the jth candidate plan in the sth link with the ith quantitative target.ThroughRs1 and Rs2, the relative superiority matrix of all quantitative and qualitative evaluation targets of the candidate partners in the sth link is as follows:(8)Rs=r11s1r12s1⋯r1ns1r21s1r22s1⋯r2ns1⋯⋯⋯⋯rh1s1rh2s1⋯rhns1rh+11s2rh+12s2⋯rh+1ns2⋯⋯⋯⋯rm1s2rm2s2⋯rmns2=rijs.In equation (8), s=1,2,…,S; i=1,2,…,m; j=1,2,…,n; 0≤rijs≤1; rijs represents the relative superiority matrix of the jth candidate plan in the sth link with the ith quantitative target.


### 4.1.3. Analysis of Target Weight Vector

Different factors have different effects on target selection. To ensure that target selection is reliable and evidence-based, imitate the abovementioned method of determining the superiority of qualitative and quantitative targets to determine the proportion of each factor. That is, the “importance” of the fuzzy concept replaces the concept’s “excellence” in order to obtain the relative superiority degree of each target to the importance. After normalization, the weight vector of the target can be obtained as follows:(9)ws=w1s,w2s,…,wmsΤ,∑i=1mwis=1,(10)wi=1−α1i/α1i∑i=1m1−α1i/α1i,0.5≤α1i≤1,i=1,2,…,m.α1i is the importance scale calculated according to the relationship between the mood operator and the quantitative scale, and the relative superiority degree is obtained after the qualitative indicator uses the binary comparison method to obtain the superiority ranking consistency scale matrix.


### 4.1.4. Determination of the Relative Superiority of Candidate Partners [27, 30]

To facilitate comparison, the reference benchmark must be unified. According to the relativity of optimization, the maximum value of the relative superiority of each indicator of candidate partners in all S links can be taken as the superior solution of the decision vector, and the minimum value as the inferior solution, which are represented, respectively, asa=a1,a2,…,amT and b=b1,b2,…,bmT. Therefore, in the sth link, for the determined comprehensive relative superiority matrix and the target weight vector, according to the basic theory of fuzzy optimization [32], the comprehensive relative superiority ujs of all evaluation objectives of the candidate partner in the sth link can be obtained as follows:(11)ujs=11+∑i=1mwisai−rijs/∑i=1mwisrijs−bi2.In the given equationj=1,2,…,n; s=1,2,…,S.The main purpose of the fuzzy optimization stage of candidate partners is to select candidates in a unified and comparable form through the fuzzy optimization method and to determine the relative superiority of candidate enterprises in each link.


## 4.1.1. Analysis of Relative Superiority of Qualitative Targets [27, 30]

According to fuzziness and relativity, setrijs as the relative superiority of the eigenvalues of the sample indicator i with respect to the fuzzy concept [31]. The equations are as follows:(1)
If the indicatorgi belongs to the smaller the better, then(2)rijs=mins,jxijsxijs,(2)
If the indicatorgi belongs to the higher the better, then(3)rijs=xijsmaxs,jxijs.The nondimensional relative superiority matrix of the quantitative targets is as follows:(4)Rs1=r11s1r12s1⋯r1ns1r21s1r22s1⋯r2ns1⋯⋯⋯⋯rh1s1rh1s1⋯rhns1=rijs1.In equation (4), s=1,2,…,S; i=1,2,…,h; j=1,2,…,n; 0≤rijs1≤1; rijs1 represents the relative superiority matrix of the jth candidate plan in the sth link with the ith quantitative target.


## 4.1.2. Analysis of Relative Superiority of Qualitative Targets [27, 30]

Through binary comparison of the superiority of each qualitative target of different candidate partners, sort and compare in turn, determine the mood operator, and then obtain the relative superiority matrix of qualitative targets according to Tables1. The specific steps are as follows.Table 1
The relationship between mood operator, quantitative scale, and relative superiority.
Mood operatorsSameSlightlyA bit more than slightlyA bit less than obviouslyObviouslyRemarkablyQuiteQuite a lotEspeciallyExtremelyIncomparablyQuantitative scale0.500.550.600.650.700.750.800.850.900.951.000.5250.5750.6250.6750.7250.7750.8250.8750.9250.975Relative superiority1.00.8180.6670.5380.4290.3330.250.1760.1110.05300.9050.7390.600.4810.3790.290.2120.10.9250.975The qualitative ranking scale of superiority obtained by binary comparison takes values between 0, 0.5, and 1.0. The following equation can be obtained:(5)eqpsgi=1,tsqis superior totsp,0.5,tsqandtsphave the same superiorty,0,tsqis n ferior totsp.Equation (5) represents the qualitative ranking scale of the superiority binary comparison between the candidate partner and the candidate partner in the sth link with the quantitative target. If the superiority of the partner for the qualitative target is greater than the superiority of the partner for the qualitative target and then, if both superiorities are the same, then eqpsgi=epqsgi=0.5. The binary comparison matrix can be derived as follows:(6)Esgi=e11s,e12s,…,e1nse21s,e22s,…,e2nsem1s,em1s,…,emns=eqpsgi.Whentsj, Esgi is the superiority ranking consistency scale matrix. If eqpsgi≠0.5, the ranking is required to be recalculated. When Esgi meets the criteria, sort the rows and columns from the largest to the smallest, and then obtain the relative superiority matrix of qualitative indicators according to the mood operator in Table 2, as shown in the equation (5).(7)Rs2=rh+11s2rh+12s2⋯rh+1ns2rh+21s2rh+22s2⋯rh+2ns2⋯⋯⋯⋯rm1s2rm2s2⋯rmns2=rijs2.Table 2
Related concepts and meaning of the efficiency profit field of the alliance.
NoConceptMeaning1Source of profit fieldOThe high-speed rail dynamic logistics alliance2Efficiency profit fieldThe profit range generated by the high-speed rail dynamic logistics alliance due to its high efficiency3Profit qualityMProfits that the enterprise can generate4The strength of profit fieldEThe size of the profits that can be generated by the alliance using various logistics resources5The radius of profit fieldrThe radiation range of different strength of profit field6Profit attractionFGThe attraction of various advantages of the alliance to the proposed cooperative enterprises7Willingness resistanceFWThe opportunity cost of the proposed cooperative enterprises joining the alliance (namely, the maximum profit given up by the enterprises choosing to join the alliance) and the risk cost (the cost of joining the alliance)8Profit distanceDThe gap between the comprehensive capabilities of the enterprises and the ideal service requirements of the alliance9Profit distance thresholdεThe maximum profit distance that the alliance can acceptIn the abovementioned equation,rijs2 represents the relative superiority matrix of the jth candidate plan in the sth link with the ith quantitative target.ThroughRs1 and Rs2, the relative superiority matrix of all quantitative and qualitative evaluation targets of the candidate partners in the sth link is as follows:(8)Rs=r11s1r12s1⋯r1ns1r21s1r22s1⋯r2ns1⋯⋯⋯⋯rh1s1rh2s1⋯rhns1rh+11s2rh+12s2⋯rh+1ns2⋯⋯⋯⋯rm1s2rm2s2⋯rmns2=rijs.In equation (8), s=1,2,…,S; i=1,2,…,m; j=1,2,…,n; 0≤rijs≤1; rijs represents the relative superiority matrix of the jth candidate plan in the sth link with the ith quantitative target.


## 4.1.3. Analysis of Target Weight Vector

Different factors have different effects on target selection. To ensure that target selection is reliable and evidence-based, imitate the abovementioned method of determining the superiority of qualitative and quantitative targets to determine the proportion of each factor. That is, the “importance” of the fuzzy concept replaces the concept’s “excellence” in order to obtain the relative superiority degree of each target to the importance. After normalization, the weight vector of the target can be obtained as follows:(9)ws=w1s,w2s,…,wmsΤ,∑i=1mwis=1,(10)wi=1−α1i/α1i∑i=1m1−α1i/α1i,0.5≤α1i≤1,i=1,2,…,m.α1i is the importance scale calculated according to the relationship between the mood operator and the quantitative scale, and the relative superiority degree is obtained after the qualitative indicator uses the binary comparison method to obtain the superiority ranking consistency scale matrix.


## 4.1.4. Determination of the Relative Superiority of Candidate Partners [27, 30]

To facilitate comparison, the reference benchmark must be unified. According to the relativity of optimization, the maximum value of the relative superiority of each indicator of candidate partners in all S links can be taken as the superior solution of the decision vector, and the minimum value as the inferior solution, which are represented, respectively, asa=a1,a2,…,amT and b=b1,b2,…,bmT. Therefore, in the sth link, for the determined comprehensive relative superiority matrix and the target weight vector, according to the basic theory of fuzzy optimization [32], the comprehensive relative superiority ujs of all evaluation objectives of the candidate partner in the sth link can be obtained as follows:(11)ujs=11+∑i=1mwisai−rijs/∑i=1mwisrijs−bi2.In the given equationj=1,2,…,n; s=1,2,…,S.The main purpose of the fuzzy optimization stage of candidate partners is to select candidates in a unified and comparable form through the fuzzy optimization method and to determine the relative superiority of candidate enterprises in each link.


## 4.2. Dynamic Programming Method

(1)
Construction of a Decision Matrix [27, 30]. According to the dynamic programming method, a problem needs to be considered as being composed of different stages. Therefore, S logistic links are regarded as S stages; Ts is defined as the state collection in dynamic programming, representing the collection of candidate partners in the sth stage, in which; represents the decision of the sthstage; represents the relative superiority of the candidate partners in the sthstage, which is determined by the decision of this stage and the state of the previous stage. Using the multiobjective fuzzy optimization method in 4.1, the relative superiority of candidate partners’ decision matrix in the sth stage is obtained as follows:(12)ϕs=ϕsts−11,ts1ϕsts−11,ts2⋯ϕsts−11,tsnϕsts−12,ts1ϕsts−12,ts2⋯ϕsts−12,tsn⋯⋯⋯⋯ϕsts−1n−1,ts1ϕsts−1n−1,ts2⋯ϕsts−1n−1,tsn.In the given equation, ϕtts−1i,tsji=1,2,…,n−1;j=1,2,…,n represents the relative superiority of the candidate partners tsj when the state in the stage s−l is Ts−1 and the decision is in the sth stage.(2)
Solution of Optimal Partner Combination [33]. According to the dynamic programming theory and the principle of maximum superiority, determine the objective function of the dynamic programming model and select the objective function of the fuzzy optimization dynamic programming with the largest sum of the relative superiority in S stages. The function is as follows:(13)f=max∑s=1Sujs.According to the abovementioned dynamic programming objective function and the dynamic programming optimization principle, the recursive equations of the relative superiority of candidate partners are obtained as follows:(14)fs∗=maxujs+fs−1∗,f1∗=uj1.In the given equation, fs∗ represents the maximum value of the sum of relative superiority of candidate partners in s stages; ujs represents the relative superiority of the candidate tsj in the sth stage; and fs−1∗ represents the maximum value of the sum of relative superiority of the candidate partner in the previous stage s−l of the sth stage.Through continuous recursion of equation (14), the optimal solution (or optimal partner combination) at each stage is d=d1∗,d1∗,…,dS∗.The dynamic programming method is used to select partners, which corresponds to the second stage of partner selection, namely, the optimal selection stage, that is, to compare all the combinations of all proposed cooperative enterprises one by one. The purpose is to select the globally optimal plan through comparison, so as to determine the partners of the alliance.


## 4.3. Construction of Efficiency Profit Field Model

Enterprises construct a high-speed rail dynamic logistics alliance to meet the needs of the modern logistics market and to obtain profits while ensuring the efficient completion of logistics tasks. In the dynamic partners’ selection, this paper makes innovations based on the concept and model of the profit field. Since the outstanding advantage of the alliance is high efficiency, this paper adds the “unit logistics service time” indicator that reflects efficiency when constructing an efficiency profit field model to show the different proportions of various influencing factors in partners selection. Influencing factors are reflected in the number of indicators. The specific indicators are shown in Tables3 and 4.Table 3
Indicators for influencing factors of SC.
FactorsIndicatorsLevel12345Quality of logistics serviceLogistics resource conditionsLogistics service capabilitiesLogistics service scaleLogistics service rangeLoss rate of goodsLogistics service priceEfficiency of logistics serviceTime to complete the taskLogistics service flexibilityLogistics service securityLogistics service convenienceInformation technology levelInformation infrastructureInformation network systemInformation securityEnterprise compatibilityCompatibilityTable 4
Indicators for influencing factors of RP.
FactorsIndicatorsLevel12345Enterprise reputationProduct reputationFinancial reputationService reputationCompetitive reputationCommercial reputationBanks reputationBusiness performanceProfit marginBusiness volumeOperating time


### 4.3.1. Profit Distance

The profit distanceD is mainly affected by the comprehensive service strength (SC) and the enterprises’ operation status (RP). The specific values of SC and RP are derived from the indicator system in Tables 3 and 4, where each indicator is divided into 5 grades using a 5-point system. The 1 to 5 grades correspond to 1 to 5 points. The full score of the SC including 12 measurement indicators is 70 points, and the full score of the RP including 9 measurement indicators is 45 points. The higher the score is, the more popular it is. The grade value of each measurement indicator is determined by the threshold value of the superiority of each target of the enterprise calculated above. Therefore, the equation for calculating the enterprise’s profit distance is(15)DT=70−SC2+45−BC2.In the given equation,70−SC represents the comprehensive service distance and 45−RP represents the distance of the enterprise’s operation status.


### 4.3.2. Profit Attraction [34]

The quality of the alliance and the proposed cooperative enterprises is determined by the types of logistics resources they own and market demand. This paper uses the vectorL to represent the set of n logistics resources. In the equation, li (li≥0) represents the number of resources i; vector Y represents the set of resource utilization. The resource utilization rate is expressed by whether the enterprise can provide the resource. yi=0 means the enterprise cannot provide resources, and yi=1 means the enterprise can provide resources. Since market demand is dynamically changing, the alliance and the proposed cooperative enterprises have different resource supply capabilities in different time periods. Thus, the time vector T=t1,t2,…,tn is introduced.The equation of the resource qualityP of the alliance is(16)PT=L×Y1,=∑i=1nliy1i.Suppose the collection of resource income of the alliance is. Different resources provide different incomes. Therefore,n resources provide n kinds of incomes, which is expressed by a vector as(17)λ=λ1,λ2,…,λn.In the equation, represents the resource income corresponding to resource. The profit quality is(18)MT=λTPT.The calculation of the profit quality of the proposed cooperative enterprise is similar to that of the alliance:(19)pT=∑i=1nli∗y2i.In the given equation,p represents the resource quality of the proposed cooperative enterprises, m represents the profit quality of the proposed cooperative enterprises, and μ=μ1,μ2,…,μn represents the collection of the resource income of the proposed cooperative enterprise.


### 4.3.3. Willingness Resistance

The willingness resistance is expressed by the sum of risk costC∗ and the opportunity cost C of the proposed cooperative enterprise joining the alliance as(20)FTW=CT+CT∗.Suppose the profit increase of the proposed cooperative enterprises after joining the alliance isZT, and ∂ represents the increase in profit per unit resource of the enterprise after joining the alliance under current market condition. Then,(21)∂=ZTPT+pT.The strength of the profit field is(22)ET=∂TMTDT2.The calculation formula of the profit attraction FG is(23)FTG=ET×mT,=∂TMT×mTDT2.


### 4.3.4. Construction of Efficiency Profit Field Model

Based on the abovementioned analysis, the efficiency profit field model of the alliance is determined, as shown in Figure1. The dotted circles in Figure 1 represent the radiation range of different profit field strengths; r is the profit radius, and π represents the enterprises in different profit circles. The construction of the efficiency profit field model is as follows:(24)maxMT.Figure 1
Efficiency profit field model.The constraints are(25)DT≤εT(26)FTW≤FTG.The objective function equation (24) indicates that the alliance has the greatest profit quality. The constraint equation (25) shows that the profit distance of the enterprise should be smaller than the profit distance threshold of the alliance, where εT represents the profit distance threshold. The constraint equation (26) illustrates that the profit attraction of the alliance is greater than the enterprise’s willingness resistance. The dual constraints of equations (25) and (26) form the trigger point for the proposed cooperative enterprises to enter into and exit from the alliance, which reflects the two-way choice between the alliance and the enterprise.


### 4.3.5. Mechanism of Dynamic Selection

When market demand changes, to ensure the alliance’s advantage in the market, the alliance will adjust its internal alliance members. During the whole process, the profit quality and the strength of the alliance will change correspondently. The change in profit quality is(27)Mt+1=Mt+menter−mexit.The profit field, then, turns into(28)Et+1=∂t+1Mt+menter+mexitDt+12.The willingness resistance of the enterprise is given as follows:(29)Ft+1W=ηmt+1.After entering the algorithm program of the above method into the cloud platform’s background system, the leader of the alliance only needs to use the client side of the cloud platform to complete the automated selection of partners.


## 4.3.1. Profit Distance

The profit distanceD is mainly affected by the comprehensive service strength (SC) and the enterprises’ operation status (RP). The specific values of SC and RP are derived from the indicator system in Tables 3 and 4, where each indicator is divided into 5 grades using a 5-point system. The 1 to 5 grades correspond to 1 to 5 points. The full score of the SC including 12 measurement indicators is 70 points, and the full score of the RP including 9 measurement indicators is 45 points. The higher the score is, the more popular it is. The grade value of each measurement indicator is determined by the threshold value of the superiority of each target of the enterprise calculated above. Therefore, the equation for calculating the enterprise’s profit distance is(15)DT=70−SC2+45−BC2.In the given equation,70−SC represents the comprehensive service distance and 45−RP represents the distance of the enterprise’s operation status.


## 4.3.2. Profit Attraction [34]

The quality of the alliance and the proposed cooperative enterprises is determined by the types of logistics resources they own and market demand. This paper uses the vectorL to represent the set of n logistics resources. In the equation, li (li≥0) represents the number of resources i; vector Y represents the set of resource utilization. The resource utilization rate is expressed by whether the enterprise can provide the resource. yi=0 means the enterprise cannot provide resources, and yi=1 means the enterprise can provide resources. Since market demand is dynamically changing, the alliance and the proposed cooperative enterprises have different resource supply capabilities in different time periods. Thus, the time vector T=t1,t2,…,tn is introduced.The equation of the resource qualityP of the alliance is(16)PT=L×Y1,=∑i=1nliy1i.Suppose the collection of resource income of the alliance is. Different resources provide different incomes. Therefore,n resources provide n kinds of incomes, which is expressed by a vector as(17)λ=λ1,λ2,…,λn.In the equation, represents the resource income corresponding to resource. The profit quality is(18)MT=λTPT.The calculation of the profit quality of the proposed cooperative enterprise is similar to that of the alliance:(19)pT=∑i=1nli∗y2i.In the given equation,p represents the resource quality of the proposed cooperative enterprises, m represents the profit quality of the proposed cooperative enterprises, and μ=μ1,μ2,…,μn represents the collection of the resource income of the proposed cooperative enterprise.


## 4.3.3. Willingness Resistance

The willingness resistance is expressed by the sum of risk costC∗ and the opportunity cost C of the proposed cooperative enterprise joining the alliance as(20)FTW=CT+CT∗.Suppose the profit increase of the proposed cooperative enterprises after joining the alliance isZT, and ∂ represents the increase in profit per unit resource of the enterprise after joining the alliance under current market condition. Then,(21)∂=ZTPT+pT.The strength of the profit field is(22)ET=∂TMTDT2.The calculation formula of the profit attraction FG is(23)FTG=ET×mT,=∂TMT×mTDT2.


## 4.3.4. Construction of Efficiency Profit Field Model

Based on the abovementioned analysis, the efficiency profit field model of the alliance is determined, as shown in Figure1. The dotted circles in Figure 1 represent the radiation range of different profit field strengths; r is the profit radius, and π represents the enterprises in different profit circles. The construction of the efficiency profit field model is as follows:(24)maxMT.Figure 1
Efficiency profit field model.The constraints are(25)DT≤εT(26)FTW≤FTG.The objective function equation (24) indicates that the alliance has the greatest profit quality. The constraint equation (25) shows that the profit distance of the enterprise should be smaller than the profit distance threshold of the alliance, where εT represents the profit distance threshold. The constraint equation (26) illustrates that the profit attraction of the alliance is greater than the enterprise’s willingness resistance. The dual constraints of equations (25) and (26) form the trigger point for the proposed cooperative enterprises to enter into and exit from the alliance, which reflects the two-way choice between the alliance and the enterprise.


## 4.3.5. Mechanism of Dynamic Selection

When market demand changes, to ensure the alliance’s advantage in the market, the alliance will adjust its internal alliance members. During the whole process, the profit quality and the strength of the alliance will change correspondently. The change in profit quality is(27)Mt+1=Mt+menter−mexit.The profit field, then, turns into(28)Et+1=∂t+1Mt+menter+mexitDt+12.The willingness resistance of the enterprise is given as follows:(29)Ft+1W=ηmt+1.After entering the algorithm program of the above method into the cloud platform’s background system, the leader of the alliance only needs to use the client side of the cloud platform to complete the automated selection of partners.


## 5. Case Analysis

### 5.1. Case I

Assuming that a high-speed rail logistics enterprise collects a batch of supply information through the cloud platform. To seize the opportunity, the enterprise prepares to form a high-speed rail dynamic logistics alliance. Through analysis, it is learned that, in addition to high-speed rail trunk line transportation, three stages are needed to complete this logistics task. The enterprise plans to select one company to cooperate with at each stage. The selected cooperative companies are SF Express, JD.com, YTO Express, and Yunda Express. The first-stage companies collected from society through the cloud platform are represented byT11,T12,T13,T14; the second-stage companies are represented by T21,T22,T23; the third-stage companies are represented by T31,T32,T33,T34. The specific evaluation indicators for selection are information technology level (the information technology input is expressed by the amount of capital input), operation efficiency (expressed by the task completion time), logistics service level, enterprise compatibility, and business performance, which are expressed by G=g1,g2,g3,g4,g5. The level of input resources and work efficiency are quantitative indicators; the smaller the better, and the rest are qualitative indicators. The specific evaluation indicator data are shown in Table 5.Table 5
Indicator data information of candidate companies [33].
Candidate companiesInformation technology level/10,000Operation efficiency/hourLogistics service levelCompany compatibilityBusiness performanceThe first stageT1110.25.3ExcellentFairRelatively goodT1212.54.2PassGoodFairT137.96Relatively goodGoodGoodT1410.94.7FairFairGoodThe second stageT217.35.3FairFairRelatively goodT225.84.2Relatively goodRelatively goodGoodT2310.83.8Relatively goodFairFairThe third stageT31123PassRelatively goodFairT3285.6Relatively goodFairGoodT338.73ExcellentRelatively goodGoodT3476.5FairGoodFairTable5 shows the data information of the simulation candidate company and uses the model in the previous chapter to select partners.Take this case as a dynamic programming problem and divide the stages according to the links. It is divided into three stages.The first stage is to determine the relative superiority of the quantitative target using formula (2); the relative superiority of the quantitative target matrix of the four companies in the first stage is obtained as follows:(30)R11=0.7750.6321.0000.7250.7921.0000.7000.894.The second stage is to determine the relative superiority of the qualitative target, taking the logistics service level as an example. After binary comparison among the four companies, the following consistent scaling matrix is obtained:(31)E1=T11T12T13T140.511100.500010.510100.5T11T12T13T14∑eij3.50.52.51.5order1423.According to the superiority rankingT11>T13>T14>T12, which means that T11 is better than T13, T13 is better than T14, and T14 is better than T12. According to Table 5, the relative superiority of the logistics service levels of the four companies is(32)r11=T11,T12,T13,T14=1.000,0.429,0.667,0.538.Similarly, the relative superiority of the other two qualitative indicators can be obtained as follows:(33)r21=T11,T12,T13,T14=0.5380.4291.0001.000,r31=T11,T12,T13,T14=0.4290.6671.0000.429,Based on the abovementioned results, the relative superiority matrix of all quantitative and qualitative evaluation targets in the first stage can be obtained as follows:(34)R1=0.7750.6321.0000.7250.8831.0000.7000.7831.0000.4290.6670.5380.5380.4291.0001.0000.4290.6671.0000.429.Take the target weight vectorω1=ω11,ω12,ω13,ω14,ω15,T=0.32,0.24,0.17,0.12,0.15T. Assuming ai=1 and bi=0, through the equation (11), the relative superiority of the four enterprises in the first stage is u11=0.9071, u21=0.9018, u31=0.9780, and u41=0.8440.According to the above steps, the relative superiority matrix of the second and third stages is obtained as follows:(35)ϕ2=0.81240.78560.83030.80120.92140.81020.90120.82780.82830.75980.68190.7391,ϕ3=0.74010.80790.86570.85270.76820.77060.71960.69380.88090.92960.86690.9381.By using equation (14) for recursive calculation, the best optimal combination is (see appendix) as follows:(36)d=T11,T22,T34,f=max∑s=13ujs=2.7676.That is, the first stage selects enterpriseT11, the second stage selects enterprise T22, and the third stage selects enterprise T34 to form the partner combination of the alliance.Through the calculation, it can be concluded that the combination of the optimal candidate enterprises at each stage is not the globally optimal combination: in the first stage,T13 (0.9779); in the second stage, T21 (0,8186); and in the third stage, T32 (0.836 0). The combined superiority of the three stages is fd1=2.7581<f, which is not the optimal combination. Therefore, the choice of the alliance should be based on the whole process rather than the optimal combination of various stages. This will maximize the benefits of the alliance.


### 5.2. Case II

Assuming that the market changes at timet, and the partners in the first link of the alliance operation in case I should be updated. High-speed rail logistics enterprises have collected the resource information of the three enterprises through the client side of the cloud platform. It is known that the resource status of the cooperative enterprises and the proposed external cooperative enterprises in the first link of the alliance are shown in Table 6, among which E1 is the enterprise in the alliance and E2, E3, and E4 are the proposed external cooperative enterprises. To ensure that the resources of the proposed external enterprises that have cooperated are reasonably matched with the needs of the alliance, the profit distance to meet the requirements is set to be 7.Table 6
Resource status of enterprises in the alliance and proposed cooperative enterprises.
EnterpriseThe number of medium truckThe number of large trucksE15050E25050E3120120E4150150The resource utilization rate of the alliance and the proposed cooperative enterprise is shown in Table7.Table 7
Resource utilization rate of the alliance and proposed cooperative enterprises.
EnterprisesMedium truck utilization rateLarge truck utilizationAlliance0.980.98E20.750.79E30.840.87E40.820.88Using the random scoring criteria, the SC and RP of the enterprises in the alliance and external partners are obtained as shown in Table8. At the same time, equation (15) is used to calculate the profit distance between the enterprises in the alliance and the external ones at time t, as shown in Table 9.Table 8
Scores of enterprises’ SC and RP.
EnterprisesComprehensive serviceBusiness conditionsE14327E23519E33926E44627Table 9
Profit distance of each enterprise.
EnterprisesProfit distanceE17.616E218.601E311.705E45.000As shown in Table10, the profit attraction and willingness resistance of E2, E3, and E4 are calculated by the equations (16), (17), and (20).Table 10
Profit attraction and willingness resistance of the proposed cooperative enterprises.
EnterprisesAttraction of profitWill resistanceE26.23034.012E324.90025.504E4141.5874.393Combining the results of Tables9 and 10, according to the equations (21) and(22), the change of the partner at time t can be obtained, if the profit distance of enterprise E1 is greater than the ideal profit distance of 7, E1 will exit from the alliance; if the profit distances of enterprises E2 and E3 are greater than the ideal profit distance of 7, they will not choose to enter into the alliance; if the profit distance of enterprise E4 is less than the ideal profit distance of 7 and its profit attraction is greater than willingness resistance, E4 will choose to enter into the alliance, which will realize the dynamic replacement of partners in the alliance.The dynamic replacement of partners at timet is shown in Figure 2. At time t, the alliance dynamically selects partners; E1 exits the alliance while E4 enters.Figure 2
Dynamic changes of alliance partner at timet (a) before selection and (b) after selection.
(a)(b)


## 5.1. Case I

Assuming that a high-speed rail logistics enterprise collects a batch of supply information through the cloud platform. To seize the opportunity, the enterprise prepares to form a high-speed rail dynamic logistics alliance. Through analysis, it is learned that, in addition to high-speed rail trunk line transportation, three stages are needed to complete this logistics task. The enterprise plans to select one company to cooperate with at each stage. The selected cooperative companies are SF Express, JD.com, YTO Express, and Yunda Express. The first-stage companies collected from society through the cloud platform are represented byT11,T12,T13,T14; the second-stage companies are represented by T21,T22,T23; the third-stage companies are represented by T31,T32,T33,T34. The specific evaluation indicators for selection are information technology level (the information technology input is expressed by the amount of capital input), operation efficiency (expressed by the task completion time), logistics service level, enterprise compatibility, and business performance, which are expressed by G=g1,g2,g3,g4,g5. The level of input resources and work efficiency are quantitative indicators; the smaller the better, and the rest are qualitative indicators. The specific evaluation indicator data are shown in Table 5.Table 5
Indicator data information of candidate companies [33].
Candidate companiesInformation technology level/10,000Operation efficiency/hourLogistics service levelCompany compatibilityBusiness performanceThe first stageT1110.25.3ExcellentFairRelatively goodT1212.54.2PassGoodFairT137.96Relatively goodGoodGoodT1410.94.7FairFairGoodThe second stageT217.35.3FairFairRelatively goodT225.84.2Relatively goodRelatively goodGoodT2310.83.8Relatively goodFairFairThe third stageT31123PassRelatively goodFairT3285.6Relatively goodFairGoodT338.73ExcellentRelatively goodGoodT3476.5FairGoodFairTable5 shows the data information of the simulation candidate company and uses the model in the previous chapter to select partners.Take this case as a dynamic programming problem and divide the stages according to the links. It is divided into three stages.The first stage is to determine the relative superiority of the quantitative target using formula (2); the relative superiority of the quantitative target matrix of the four companies in the first stage is obtained as follows:(30)R11=0.7750.6321.0000.7250.7921.0000.7000.894.The second stage is to determine the relative superiority of the qualitative target, taking the logistics service level as an example. After binary comparison among the four companies, the following consistent scaling matrix is obtained:(31)E1=T11T12T13T140.511100.500010.510100.5T11T12T13T14∑eij3.50.52.51.5order1423.According to the superiority rankingT11>T13>T14>T12, which means that T11 is better than T13, T13 is better than T14, and T14 is better than T12. According to Table 5, the relative superiority of the logistics service levels of the four companies is(32)r11=T11,T12,T13,T14=1.000,0.429,0.667,0.538.Similarly, the relative superiority of the other two qualitative indicators can be obtained as follows:(33)r21=T11,T12,T13,T14=0.5380.4291.0001.000,r31=T11,T12,T13,T14=0.4290.6671.0000.429,Based on the abovementioned results, the relative superiority matrix of all quantitative and qualitative evaluation targets in the first stage can be obtained as follows:(34)R1=0.7750.6321.0000.7250.8831.0000.7000.7831.0000.4290.6670.5380.5380.4291.0001.0000.4290.6671.0000.429.Take the target weight vectorω1=ω11,ω12,ω13,ω14,ω15,T=0.32,0.24,0.17,0.12,0.15T. Assuming ai=1 and bi=0, through the equation (11), the relative superiority of the four enterprises in the first stage is u11=0.9071, u21=0.9018, u31=0.9780, and u41=0.8440.According to the above steps, the relative superiority matrix of the second and third stages is obtained as follows:(35)ϕ2=0.81240.78560.83030.80120.92140.81020.90120.82780.82830.75980.68190.7391,ϕ3=0.74010.80790.86570.85270.76820.77060.71960.69380.88090.92960.86690.9381.By using equation (14) for recursive calculation, the best optimal combination is (see appendix) as follows:(36)d=T11,T22,T34,f=max∑s=13ujs=2.7676.That is, the first stage selects enterpriseT11, the second stage selects enterprise T22, and the third stage selects enterprise T34 to form the partner combination of the alliance.Through the calculation, it can be concluded that the combination of the optimal candidate enterprises at each stage is not the globally optimal combination: in the first stage,T13 (0.9779); in the second stage, T21 (0,8186); and in the third stage, T32 (0.836 0). The combined superiority of the three stages is fd1=2.7581<f, which is not the optimal combination. Therefore, the choice of the alliance should be based on the whole process rather than the optimal combination of various stages. This will maximize the benefits of the alliance.


## 5.2. Case II

Assuming that the market changes at timet, and the partners in the first link of the alliance operation in case I should be updated. High-speed rail logistics enterprises have collected the resource information of the three enterprises through the client side of the cloud platform. It is known that the resource status of the cooperative enterprises and the proposed external cooperative enterprises in the first link of the alliance are shown in Table 6, among which E1 is the enterprise in the alliance and E2, E3, and E4 are the proposed external cooperative enterprises. To ensure that the resources of the proposed external enterprises that have cooperated are reasonably matched with the needs of the alliance, the profit distance to meet the requirements is set to be 7.Table 6
Resource status of enterprises in the alliance and proposed cooperative enterprises.
EnterpriseThe number of medium truckThe number of large trucksE15050E25050E3120120E4150150The resource utilization rate of the alliance and the proposed cooperative enterprise is shown in Table7.Table 7
Resource utilization rate of the alliance and proposed cooperative enterprises.
EnterprisesMedium truck utilization rateLarge truck utilizationAlliance0.980.98E20.750.79E30.840.87E40.820.88Using the random scoring criteria, the SC and RP of the enterprises in the alliance and external partners are obtained as shown in Table8. At the same time, equation (15) is used to calculate the profit distance between the enterprises in the alliance and the external ones at time t, as shown in Table 9.Table 8
Scores of enterprises’ SC and RP.
EnterprisesComprehensive serviceBusiness conditionsE14327E23519E33926E44627Table 9
Profit distance of each enterprise.
EnterprisesProfit distanceE17.616E218.601E311.705E45.000As shown in Table10, the profit attraction and willingness resistance of E2, E3, and E4 are calculated by the equations (16), (17), and (20).Table 10
Profit attraction and willingness resistance of the proposed cooperative enterprises.
EnterprisesAttraction of profitWill resistanceE26.23034.012E324.90025.504E4141.5874.393Combining the results of Tables9 and 10, according to the equations (21) and(22), the change of the partner at time t can be obtained, if the profit distance of enterprise E1 is greater than the ideal profit distance of 7, E1 will exit from the alliance; if the profit distances of enterprises E2 and E3 are greater than the ideal profit distance of 7, they will not choose to enter into the alliance; if the profit distance of enterprise E4 is less than the ideal profit distance of 7 and its profit attraction is greater than willingness resistance, E4 will choose to enter into the alliance, which will realize the dynamic replacement of partners in the alliance.The dynamic replacement of partners at timet is shown in Figure 2. At time t, the alliance dynamically selects partners; E1 exits the alliance while E4 enters.Figure 2
Dynamic changes of alliance partner at timet (a) before selection and (b) after selection.
(a)(b)


## 6. Conclusion

With the rapid development of e-commerce, the demand for high-value-added products is growing, which makes the development prospect of high-speed railway logistics broad. Based on the perspective of the cloud platform, this paper establishes the target system, confirms the weight through the multiobjective fuzzy optimization method, and then determines the order of each partner in a unified and comparable form through the quantitative calculation of the degree of membership. It uses the dynamic programming method to achieve the second stage of partner optimization, the optimization stage, which selects the overall optimal scheme through comparison. In the face of a rapidly changing market, this paper uses the efficiency profit field model to dynamically update partners, set the critical point for enterprises to enter and exit the alliance, and form a profit field-based dynamic entry and exit mechanism for the alliance partners, so that the high-speed rail alliance becomes more flexible. In the future, it can be further considered to add other evaluation indicators to the model to better provide a scientific decision-making basis for the selection of high-speed railway dynamic logistics alliance partners.



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*Source: 6987845-2023-01-14.xml*