A fuzzy analytic hierarchy process for risk evaluation of urban rail transit PPP projects

Abstract

The Public-Private Partnership (PPP mode) has been widely used in the field of transportation infrastructure. It can relieve the debt pressure of local governments and improve the efficiency of resource allocation. However, due to the long life cycle of urban rail transit PPP projects and numerous participants, the potential risks arising from the coordination of multi-party relations have become a major obstacle to the development of urban rail transit PPP mode. Based on the perspective of the PPP project company (SPV), this paper adopts the method of fuzzy analytic hierarchy process, takes Shenzhen Metro Line 4 project as the research object and constructs the risk index system from nine dimensions to evaluate the risks of PPP project. Political risk, legal risk and project promotion risk are the most important risk indicators, while relationship risk and force majeure risk take the lowest proportion. According to the above results, the risk management system, risk sharing scheme and countermeasures in key risk areas are proposed. The study not only applies the fuzzy analytic hierarchy process to the research of urban rail transit risks, but also provides a systematic risk assessment basis and prevention and control reference for the smooth implementation of PPP projects.

Keywords

Fuzzy analytic hierarchy process urban rail transit PPP mode risk evaluation

1 Introduction

The 14th Five-Year Plan for economic and social development proposed that China should accelerate the construction of a country with strong transportation network, vigorously develop urban rail transit, accelerate the network of rail transit in urban agglomerations and metropolitan areas, and build a new type of city clusters and urbanization. Urban rail transit, as an intensive and compound mode of transportation, has the advantages of large passenger transport volume, environmental friendliness and convenience [9, 13]. It is of great significance to improve the urban traffic network, strengthen the exchange of economic regions, and promote the process of urbanization.

However, the investment in urban rail transit construction is huge, and the cost in the operation stage can be as high as 2–6 times of the construction investment [36]. The government is faced with the double financial burden of construction investment and operation subsidies and bears huge debt pressure, which provides a feasible soil for the implementation of PPP mode in the field of urban rail transit. Transportation has also become the largest industry of PPP project construction investment, with an accumulated investment of 5.04 trillion yuan, accounting for one third of the total PPP investment.

The PPP mode is a multi-party cooperation mode established by government departments and social capital based on public infrastructure and service projects [12, 25]. By introducing social capital, the government can avoid the establishment of vertically integrated infrastructure construction and operation organization. At the same time, by virtue of the social capital’s advantages in technology and management, it can not only improve the supply efficiency of the project and ensure the reasonable profit of social capital, but also force the government to promote functional transformation, thus achieving a win-win situation of risk sharing, benefit sharing, and mutual benefit [16 , 34]. Since 2013, China’s National Development and Reform Commission and the Ministry of Finance began to issue and improve relevant policies and regulations to guide the development of PPP projects. The PPP mode has entered a new era of rapid development in China. By August 2020, China PPP Comprehensive Information Platform has managed 9746 projects with an investment of 15.1 trillion yuan. As an important starting point of supply side reform, PPP mode has fully played the role of encouraging competition, breaking monopoly, relaxing access, and encouraging all kinds of social capital to actively participate in infrastructure construction. However, in the construction and operation of PPP projects, there are always practical problems such as low landing rate and low participation of private capital.

The PPP projects have many stakeholders and complex relationship between rights and responsibilities, leading to various potential risks in the whole life cycle of the project [43]. Due to the huge investment and long franchise period, urban rail transit PPP project further aggravates the uncertainty of project implementation, which in turn affects the enthusiasm of social capital to participate in PPP projects and the quality of public services provided by the government. Therefore, how to effectively identify, evaluate and control the risks of PPP projects has become the key to promote the sustainable development of PPP mode.

In PPP projects, the government and the social capital jointly establish a PPP project company responsible for the construction and operation of the project, namely special purpose vehicle (SPV). Based on the perspective of PPP project company (SPV), according to the risk characteristics of urban rail transit PPP project, this paper uses the method of fuzzy analytic hierarchy process to construct the whole life cycle risk index system of PPP project, identifies and evaluates the risks in the construction and operation process of the project, and puts forward risk response measures for the important risk areas. The possible research contributions of this paper are as follows: (a) Clarify the subject of PPP project risk assessment, and enrich the research in the field of PPP project risk. Based on the perspective of SPV, this article establishes a risk indicator system for the entire life cycle to evaluate PPP project risks, which helps to comprehensively identify and evaluate potential risks. (b) Taking Shenzhen Metro Line 4 project as research object, the risk index system is applied to practice. According to the risk characteristics and evaluation results, the risk bearers are divided, and the specific coping strategies are proposed, which responds to the practical concerns of the regulatory authorities on the implementation rate of PPP projects and the participation of social capital.

2 Literature review

According to the characteristics of PPP project risks, risk management is a long and complex process, including risk identification, risk assessment, risk sharing and risk response [30].

Risk identification is the basis of PPP project risk management. By collecting a large amount of project data, systematically identify project-related risk factors, analyze the source and characteristics of risks [41]. Through the summary of the literature, risks can be classified in the following ways: according to the source of risk, Li et al. [21] divide the risk into three levels: micro, medium and macro; according to whether the risk is controllable, the risk is divided into system risk and non-system risk [28]; according to the theory of the whole life cycle, the risk can be divided into negotiation period, construction period and operation period Risk [3]; according to the relevance of the risk to the project subject, it can be divided into project risk and general risk [2]; according to risk characteristics, it can be divided into nine categories: technical risk, construction risk, recovery risk and financial risk [5]. Risk evaluation is the analysis and judgment of PPP project risks that have been identified. It is the basis for project risk quantification and effective risk management measures [22]. The existing literature uses questionnaire survey, analytic hierarchy process factor analysis, fuzzy comprehensive evaluation and Monte Carlo simulation to evaluate risks [1 , 38].

Risk sharing is based on the principle of matching control power, the lowest cost and the risk-return equivalence to allocate risks to the party who is more suitable to bear [35 , 39]. There are two main ideas: one is the study of quantitative risk sharing mechanism based on game theory [7, 42]; another is qualitative risk sharing based on contract negotiation [8, 21]. Risk response is to prevent foreseeable risks by analyzing the probability of occurrence of risks and the degree of its influence, which includes risk aversion, risk acceptance, risk reduction and risk transfer [40].

Specific to the field of urban rail transit, the PPP projects have the characteristics of a longer franchise period, larger investment, higher technical standards and a more complex construction environment than general engineering projects [13]. As a result, it faces more uncertainties and potential risks in the process of risk identification, evaluation, sharing, and response. Previous studies have analyzed the financing risk, debt risk and economic risk of urban rail transit projects from qualitative and quantitative perspectives respectively, and put forward the mechanism of financing risk transmission and the method of dynamic evaluation, the preventive measures of debt risk and the effective ways to control economic risk [10 , 32].

Although some scholars have used the analytic hierarchy process or fuzzy evaluation method to assess the risks of PPP projects, the existing literature lacks the identification of the whole life cycle risk of urban rail transit PPP project, and there is a problem that the risk assessment subject is not clearly defined in the risk assessment process. The definition of risk assessment subjects is particularly important, which will directly affect the results of risk identification and assessment. Therefore, this article starts from the perspective of SPV Company, systematically identifies and evaluates the risks that exist in the full life cycle of PPP projects. And further proposed the risk sharing and response system of metro PPP projects in the Chinese context.

3 Research methodology

Due to the characteristics of long-term, variability and complexity of PPP projects, the risks are more difficult to control than general projects. Therefore, it is necessary to establish a comprehensive risk management system, which can effectively prevent and control the occurrence of risks, accurately evaluate the risk factors, and provide guarantee for risk management. In this paper, the analytic hierarchy process (AHP) and fuzzy comprehensive evaluation method (FCE) are combined to analyze the risk of PPP projects more accurately.

3.1 Urban rail transit PPP project risk assessment and analysis system

Based on literature and expert interviews, combined with the characteristics of the project, the paper establishes the risk index system of urban rail transit PPP project. It includes 9 level-I risk factor indicators at the national, market and project levels, which are further subdivided into 27 level-II risk factor indicators, as shown in Table 1.

Table 1
Urban rail transit PPP project risk assessment and analysis system

The target level First-level indicators Secondary indicators Explain

National level B1 Political risk C11 Policy risk National macro-policy adjustment affects the implementation of PPP projects

C12 Corruption risk Increased costs or reduced project quality due to corruption

C13 Expropriation and nationalization When the project violates the policy direction, the government forcibly confiscates the project

C14 Political stability The influence of the host country on the project due to political changes such as change of terms

B2 Legal risks C21 Tax system changes An increase in the cost of a change in the tax system

C22 Industry law changes The change of laws and regulations causes the increase of project cost and decrease of revenue

Market level B3 Economic risk C31 Interest rate risk The risk of market interest rate changes, such as the impact of interest rate liberalization

C32 Exchange rate risk Changes in foreign exchange rates affect foreign exchange payments

C33 Inflation risk Prices rise, the purchasing power of money falls, raw materials, equipment, labor costs increase

B4 Environmental risks C41 Natural environmental risks The change of natural environment affects the construction and operation of the project

C42 Social and environmental risks Social environment changes affect the passenger flow and revenue of the project

B5 Market risk C51 Market competition Market competition leads to reduced project demand and revenue

C52 Demand changes Reduced passenger flow due to changes in consumer demand

C53 Price change A reduction in passenger flow and revenue resulting from price changes

Project level B6 Financing risk C61 Financing feasibility The capital market is not active, the financial innovation is insufficient, the financing channel is relatively single, and it is not easy to meet the project fund demand

C62 Excessive financing cost Unreasonable financing structure and high cost increase the project cost

B7 Project promotion risk C71 Design risk Inadequate design leads to claims

C72 Engineering safety quality Project safety and quality are not up to standard, resulting in claims

C73 Construction costs Material prices rose and costs exceeded expectations

C74 Operation and maintenance risk In the course of operation, the maintenance cost increases due to the influence of operating conditions and other factors

C75 Pricing risk The government adjusted the charging standard and charging period, so that the charging price of PPP products and services was too high and too low, and the adjustment of charging was not free, leading to lower operating income than expected

C76 Technology risk The technology is not mature, difficult to meet the predetermined requirements, poor applicability

C77 Handover risk Risks arising from the handover of PPP projects to the government or designated agencies after the expiration of the PPP project cooperation period or the end of the cooperation period in advance

B8 Relationship risk C81 Public-private sector relationship risk The multi-party game between departments of the company causes the delay of the project, the increase of project cost and the decrease of revenue

C82 Improper distribution of responsibilities The contract does not clearly define the rights, responsibilities and risks of the participants; The cost of negotiation is high and the initiative of participants to control risks is reduced

B9 Force majeure risk C91 Natural disaster risk Risks caused by natural disasters such as climate

C92 Unforeseen risks War, earthquake, flood and other unforeseeable risks

The target level	First-level indicators	Secondary indicators	Explain
National level	B1 Political risk	C11 Policy risk	National macro-policy adjustment affects the implementation of PPP projects
		C12 Corruption risk	Increased costs or reduced project quality due to corruption
		C13 Expropriation and nationalization	When the project violates the policy direction, the government forcibly confiscates the project
		C14 Political stability	The influence of the host country on the project due to political changes such as change of terms
	B2 Legal risks	C21 Tax system changes	An increase in the cost of a change in the tax system
		C22 Industry law changes	The change of laws and regulations causes the increase of project cost and decrease of revenue
Market level	B3 Economic risk	C31 Interest rate risk	The risk of market interest rate changes, such as the impact of interest rate liberalization
		C32 Exchange rate risk	Changes in foreign exchange rates affect foreign exchange payments
		C33 Inflation risk	Prices rise, the purchasing power of money falls, raw materials, equipment, labor costs increase
	B4 Environmental risks	C41 Natural environmental risks	The change of natural environment affects the construction and operation of the project
		C42 Social and environmental risks	Social environment changes affect the passenger flow and revenue of the project
	B5 Market risk	C51 Market competition	Market competition leads to reduced project demand and revenue
		C52 Demand changes	Reduced passenger flow due to changes in consumer demand
		C53 Price change	A reduction in passenger flow and revenue resulting from price changes
Project level	B6 Financing risk	C61 Financing feasibility	The capital market is not active, the financial innovation is insufficient, the financing channel is relatively single, and it is not easy to meet the project fund demand
		C62 Excessive financing cost	Unreasonable financing structure and high cost increase the project cost
	B7 Project promotion risk	C71 Design risk	Inadequate design leads to claims
		C72 Engineering safety quality	Project safety and quality are not up to standard, resulting in claims
		C73 Construction costs	Material prices rose and costs exceeded expectations
		C74 Operation and maintenance risk	In the course of operation, the maintenance cost increases due to the influence of operating conditions and other factors
		C75 Pricing risk	The government adjusted the charging standard and charging period, so that the charging price of PPP products and services was too high and too low, and the adjustment of charging was not free, leading to lower operating income than expected
		C76 Technology risk	The technology is not mature, difficult to meet the predetermined requirements, poor applicability
		C77 Handover risk	Risks arising from the handover of PPP projects to the government or designated agencies after the expiration of the PPP project cooperation period or the end of the cooperation period in advance
	B8 Relationship risk	C81 Public-private sector relationship risk	The multi-party game between departments of the company causes the delay of the project, the increase of project cost and the decrease of revenue
		C82 Improper distribution of responsibilities	The contract does not clearly define the rights, responsibilities and risks of the participants; The cost of negotiation is high and the initiative of participants to control risks is reduced
	B9 Force majeure risk	C91 Natural disaster risk	Risks caused by natural disasters such as climate
		C92 Unforeseen risks	War, earthquake, flood and other unforeseeable risks

3.2 Fuzzy analytic hierarchy process

Fuzzy analytic hierarchy process (FAHP) is composed of analytic hierarchy process and fuzzy comprehensive evaluation [17, 26]. Among them, fuzzy comprehensive evaluation is carried out on the basis of analytic hierarchy process. The combination of the two improves the reliability and effectiveness of the evaluation [14 , 26]. The specific steps are as follows:

–Step 1: Establish a hierarchical structure

According to the attribute characteristics of PPP risk, the risk is divided into the highest objective level reflecting the overall objective, the middle level reflecting the specific criteria and the bottom level of the planned implementation scheme [33]. The hierarchy is shown in Fig. 1.

Fig. 1

The hierarchical sub-graph.

–Step 2: Construct the judgment matrix

The construction of judgment matrix is to compare the risk elements of the same level in the established risk index system, by using Saaty’s 1 ∼ 9 scale method (as shown in Table 2) to judge the importance proportion of each risk element in the target evaluation [27]. In the overall evaluation system, different risk indicators account for different proportions.

Table 2

The meaning of size scale of a_ij value

Scale	Meaning
1	Two factors are of equal importance
3	The former is slightly more important than the latter
5	The former is obviously more important than the latter
7	The former is strongly important than the latter
9	The former is extremely important than the latter
2,4,6,8	Represents the intermediate value of the above adjacent judgment
reciprocal	If the ratio of the importance of factor I to that of factor J is a_ij, then the ratio of the importance of factor J to that of factor I is a_ji = 1/a_ij

The judgment matrix A satisfies: (a) a_ij>0 (b) a_ij = 1/a_ij (i, j = 1,2,...n)

–Step 3: Consistency check

There are subjective factors in the scoring of experts. In order to reduce the influence of subjective factors on the judgment matrix, a consistency test is used to ensure that the weights of indicators at all levels are reasonable and logical. The steps to check the consistency of the judgment matrix are as follows:

(a) Calculate the consistency index (CI) $CI = \frac{λ_{max} - n}{n - 1}$ (1)

Among them: n is the number of rows or columns of the judgment matrix. If CI = 0, the judgment matrix has complete consistency, otherwise it needs to be judged according to the consistency ratio CR.

(b) Find the corresponding average random consistency index RI. The RI values for n = 1, 2 ... ... 9 are shown in Table 3.

Table 3

The value of the RI

n	1	2	3	4	5	6	7	8	9
RI	0	0	0.58	0.9	1.12	1.24	1.32	1.41	1.45

When CR < 0.10, it is considered that the consistency of judgment matrix is acceptable, otherwise the judgment matrix should be modified appropriately.

–Step 4: Determine the evaluation factor set U = {U1, U2...Un}. U = U1, U2...Un is the evaluation factor, n is the number of single factors at the same level, and this set constitutes the evaluation framework.

–Step 5: Determine the evaluation grade area V, V = {V1, V2... Vm}

In this paper, the risk index system evaluation is divided into five levels: V = {extreme high, high, general, low, extreme low}.

–Step 6: Single-level fuzzy comprehensive evaluation.

A single index evaluation is carried out for each evaluation index in the evaluation factor set, and the evaluation indexes of each index layer are established for various evaluation membership degrees r_ij of evaluation set V, and the fuzzy relation matrix R is obtained. $R = (\begin{matrix} r_{11} & r_{12} & \dots & r_{1 m} \\ r_{21} & r_{22} & \dots & r_{2 m} \\ \dots & \dots & \dots & \dots \\ r_{n 1} & r_{n 2} & r_{n 3} & r_{nm} \end{matrix}), 0 ⩽ r_{ij} ⩽ 1$ (3)

–Step 7: Fuzzy comprehensive evaluation.

The above-mentioned index weights W obtained through the analysis of the analytic hierarchy process are combined with the fuzzy relationship matrix R of the evaluated object, and then the overall evaluation vector of the index is obtained.

$\begin{matrix} B = W \times R = (w_{1}, w_{2}, \dots, w_{n}) \\ \times (\begin{matrix} r_{11} & r_{12} & \dots & r_{1 m} \\ r_{21} & r_{22} & \dots & r_{2 m} \\ \dots & \dots & \dots & \dots \\ r_{n 1} & r_{n 2} & r_{n 3} & r_{nm} \end{matrix}) \end{matrix}$ (4)

4 Case application

4.1 Case introduction

Shenzhen Metro Line 4 in China adopts BOT mode. SPV Company was jointly funded by Shenzhen Municipal Government and MTR Corporation, which is specially responsible for the investment, construction, financing and operation of Shenzhen Metro Line 4 [15]. According to the contract, the MTR Corporation will operate for 30 years after the completion of the project, and will transfer the ownership of Shenzhen Metro Line 4 to the Shenzhen Municipal Government in 2040. The BOT mode of Shenzhen Metro Line 4 is shown in Fig. 2. The BOT mode can effectively reduce the risks of government agencies, mainly because of the signing of concession agreements. Because of the signing of franchise agreement, BOT mode can effectively reduce the risk of government agencies. The project company can carry out the financing, design, construction and supervision of the second phase of Shenzhen Metro Line 4 in accordance with the agreement, and the government departments can supervise and manage it. Its income mode adopts the comprehensive development model of “metro + property”, and carries out commercial development on the land around the metro. By taking advantage of the positive externalities brought by the metro, it obtains income by making the commercial real estate appreciate or collecting rent.

Fig. 2

Shenzhen Metro Line 4 BOT mode.

4.2 Risk assessment system of urban rail transit PPP project

This paper uses the Delphi Method to evaluate the risk elements of PPP projects [6], conducts online and offline surveys of government department personnel, SPV company personnel, and university scientific research personnel. 100 questionnaires are issued and 81 questionnaires are returned, of which 75 are valid questionnaires. Using YAAHP software to filter and calculate the expert data, obtain the weight of each layer of risk indicators, as shown in Table 4, and the weights of primary and all secondary indicators are as follows.

Table 4
Weights of risk assessment analysis system for urban rail transit PPP projects

Main target First-level weights Eigenvalues and CI Secondary weight Total weight

CI = 0.0143 CR = 0.0262 B1 0.2542 λ = 4.0710 CI = 0.0237 CR = 0.0263 C11 0.4168 0.1060

C12 0.1928 0.0490

C13 0.2695 0.0685

C14 0.1209 0.0307

B2 0.1953 λ= 2.00 CI = 0.00 CR = 0.00 C21 0.3333 0.0651

C22 0.6667 0.1302

B3 0.1206 λ=3.0387 CI = 0.0194 CR = 0.0334 C31 0.2605 0.0314

C32 0.1062 0.0128

C33 0.6333 0.0764

B4 0.0517 λ= 2.00 CI = 0.00 CR = 0.00 C41 0.2000 0.0103

C42 0.8000 0.0414

B5 0.0926 λ= 3.0092 CI = 0.0046 CR = 0.0079 C51 0.1638 0.0152

C52 0.5389 0.0499

C53 0.2973 0.0275

B6 0.068 λ= 2.00 CI = 0.00 CR = 0.00 C61 0.2500 0.0170

C62 0.7500 0.0510

B7 0.1469 λ= 7.2245 CI = 0.0374 CR = 0.0283 C71 0.3054 0.0449

C72 0.0563 0.0083

C73 0.0774 0.0114

C74 0.2419 0.0355

C75 0.0369 0.0054

C76 0.1720 0.0253

C77 0.1101 0.0162

B8 0.0404 λ= 2.00 CI = 0.00 CR = 0.00 C81 0.6667 0.0269

C82 0.3333 0.0135

B9 0.0303 λ= 2.00 CI = 0.00 CR = 0.00 C91 0.1667 0.0051

C92 0.8333 0.0252

Main target	First-level weights	Eigenvalues and CI	Secondary weight	Total weight
CI = 0.0143 CR = 0.0262	B1 0.2542	λ = 4.0710 CI = 0.0237 CR = 0.0263	C11 0.4168	0.1060
			C12 0.1928	0.0490
			C13 0.2695	0.0685
			C14 0.1209	0.0307
	B2 0.1953	λ= 2.00 CI = 0.00 CR = 0.00	C21 0.3333	0.0651
			C22 0.6667	0.1302
	B3 0.1206	λ=3.0387 CI = 0.0194 CR = 0.0334	C31 0.2605	0.0314
			C32 0.1062	0.0128
			C33 0.6333	0.0764
	B4 0.0517	λ= 2.00 CI = 0.00 CR = 0.00	C41 0.2000	0.0103
			C42 0.8000	0.0414
	B5 0.0926	λ= 3.0092 CI = 0.0046 CR = 0.0079	C51 0.1638	0.0152
			C52 0.5389	0.0499
			C53 0.2973	0.0275
	B6 0.068	λ= 2.00 CI = 0.00 CR = 0.00	C61 0.2500	0.0170
			C62 0.7500	0.0510
	B7 0.1469	λ= 7.2245 CI = 0.0374 CR = 0.0283	C71 0.3054	0.0449
			C72 0.0563	0.0083
			C73 0.0774	0.0114
			C74 0.2419	0.0355
			C75 0.0369	0.0054
			C76 0.1720	0.0253
			C77 0.1101	0.0162
	B8 0.0404	λ= 2.00 CI = 0.00 CR = 0.00	C81 0.6667	0.0269
			C82 0.3333	0.0135
	B9 0.0303	λ= 2.00 CI = 0.00 CR = 0.00	C91 0.1667	0.0051
			C92 0.8333	0.0252

W = [0.2542, 0.1206, 0.1953, 0.0517, 0.0926, 0.0680, 0.1469, 0.0404, 0.0303]

W₁ = [0.4168, 0.1928, 0.2695, 0.1209]

W₂ = [0.3333, 0.6667]

W₃ = [0.2605, 0.1062, 0.6333]

W₄ = [0.2000, 0.8000]

W₅ = [0.1638, 0.5389, 0.2973]

W₆ = [0.2500, 0.7500]

W₇ = [0.3054, 0.0563, 0.0774, 0.2419, 0.0369, 0.1720, 0.1101]

W₈ = [0.6667, 0.3333]

W₉ = [0.1667, 0.8333]

Political risk, legal risk and project promotion risk account for the largest proportion in the risk index system. Because PPP project is based on the national strategy of promoting rail transit to lead urban development, the government plays a key role in promoting and developing PPP projects. The change of tax system related laws will directly affect the amount of project income, and the laws and regulations related to transportation and PPP are very important to the project risk. The risk of project promotion includes all risks in the whole process of implementing PPP project. PPP mode makes the project adopt the mode of modular and professional operation, and the risk of project promotion takes up a high proportion in the overall index.

4.3 Fuzzy evaluation results of risks of shenzhen metro PPP project

According to the secondary indicators of the evaluation index system, the evaluation set is selected as “extreme high, high, general, low, extreme low". The corresponding grade value is assigned as E = [90, 70, 50, 30, 10]. In view of the risk of Shenzhen Metro PPP project, experts were invited to conduct a questionnaire survey. A total of 220 questionnaires were distributed online and offline. 207 questionnaires could be recovered, including 200 valid questionnaires. According to the results of the questionnaire, the risk of PPP project is evaluated. The proportion of five evaluation levels in each secondary index forms a fuzzy judgment matrix R. $R_{1} = [\begin{matrix} 0.05 & 0.11 & 0.1 & 0.25 & 0.49 \\ 0.04 & 0.16 & 0.15 & 0.2 & 0.45 \\ 0.09 & 0.14 & 0.13 & 0.3 & 0.34 \\ 0 & 0.08 & 0.2 & 0.16 & 0.56 \end{matrix}]$ $R_{2} = [\begin{matrix} 0.20 & 0.24 & 0.38 & 0.12 & 0.06 \\ 0.20 & 0.29 & 0.32 & 0.14 & 0.05 \end{matrix}]$ $R_{3} = [\begin{matrix} 0.06 & 0.21 & 0.25 & 0.33 & 0.15 \\ 0.08 & 0.16 & 0.36 & 0.35 & 0.05 \\ 0.02 & 0.21 & 0.14 & 0.33 & 0.3 \end{matrix}]$ $R_{4} = [\begin{matrix} 0.08 & 0.10 & 0.42 & 0.21 & 0.19 \\ 0.06 & 0.05 & 0.35 & 0.34 & 0.20 \end{matrix}]$ $R_{5} = [\begin{matrix} 0.14 & 0.41 & 0.23 & 0.15 & 0.07 \\ 0.12 & 0.38 & 0.35 & 0.10 & 0.05 \\ 0.10 & 0.30 & 0.38 & 0.15 & 0.07 \end{matrix}]$ $R_{6} = [\begin{matrix} 0.07 & 0.15 & 0.36 & 0.34 & 0.08 \\ 0.03 & 0.10 & 0.32 & 0.37 & 0.18 \end{matrix}]$ $R_{7} = [\begin{matrix} 0.21 & 0.36 & 0.34 & 0.08 & 0.01 \\ 0.07 & 0.16 & 0.35 & 0.27 & 0.15 \\ 0.24 & 0.35 & 0.29 & 0.11 & 0.01 \\ 0.23 & 0.53 & 0.19 & 0.03 & 0.02 \\ 0.18 & 0.39 & 0.29 & 0.08 & 0.06 \\ 0.25 & 0.43 & 0.22 & 0.08 & 0.02 \\ 0.39 & 0.40 & 0.14 & 0.07 & 0 \end{matrix}]$ $R_{8} = [\begin{matrix} 0.10 & 0.15 & 0.35 & 0.39 & 0.01 \\ 0.12 & 0.10 & 0.36 & 0.34 & 0.08 \end{matrix}]$ $R_{9} = [\begin{matrix} 0 & 0.03 & 0.31 & 0.36 & 0.30 \\ 0 & 0.09 & 0.30 & 0.31 & 0.30 \end{matrix}]$

Use Matlab7.0 programming to calculate the comprehensive evaluation result B of the first-level index.

B₁ = W₁*R₁ = [0.0528, 0.1241, 0.1298, 0.2430, 0.4503]

B₂ = W₂*R₂ = [0.2000, 0.2733, 0.3400, 0.1333, 0.0533]

B₃ = W₃*R₃ = [0.0368, 0.2047, 0.1920, 0.3321, 0.2344]

B₄ = W₄*R₄ = [0.0640, 0.0600, 0.3640, 0.3140, 0.1980]

B₅ = W₅*R₅ = [0.1173, 0.3611, 0.3393, 0.1231, 0.0592]

B₆ = W₆*R₆ = [0.0400, 0.1125, 0.3300, 0.3625, 0.1550]

B₇ = W₇*R₇ = [0.2349, 0.4066, 0.2559, 0.0798, 0.0228]

B₈ = W₈*R₈ = [0.1067, 0.1333, 0.3533, 0.3733, 0.0333]

B₉ = W₉*R₉ = [0.0000, 0.0800, 0.3017, 0.3183, 0.3000]

The fuzzy evaluation matrix of the target layer is R. $R = [\begin{matrix} B 1 \\ B 2 \\ ⋮ \\ B 9 \end{matrix}]$

Therefore, the comprehensive evaluation results and assignments of the Shenzhen Metro PPP project are as follows: $\begin{matrix} A = W * R = & [0.1126, 0.2214, \\ 0.2562, 0.2166, 0.1932] \end{matrix}$ $F = A * E = 46.8725$

According to the calculation, the risk score of Shenzhen Metro Line 4 is 46.8725, which belongs to the general risk level. According to the principle of maximum degree of membership, the risk assessment results of each first-level indicator and project general evaluation are shown in Table 5. Among them, market risk and project promotion risk belong to high-risk areas.

Table 5
Risk assessment results of Shenzhen Metro Line 4

Risk indicator Risk assessment level

Political risk Extreme low

Legal risks Low

Economic risk General

Environmental risk General

Market risk High

Financing risk Low

Project promotion risk High

Relationship risk Low

Force majeure risk General

General comment General

Risk indicator	Risk assessment level
Political risk	Extreme low
Legal risks	Low
Economic risk	General
Environmental risk	General
Market risk	High
Financing risk	Low
Project promotion risk	High
Relationship risk	Low
Force majeure risk	General
General comment	General

According to the annual report data of MTR Corporation, the passenger volume growth rate of Shenzhen Metro Line 4 from 2015 to 2019 was 12%, 5%, 5.4%, 11% and 3%, respectively. Due to the continuous development of other competitive public transportation vehicles in Shenzhen, the passenger growth rate of Metro Line 4 showed a fluctuating decline. Although the Shenzhen municipal government is implementing the ticket adjustment mechanism, the project has not benefited from the shadow fare compensation mechanism since its operation in 2010. And its subway fares have never been raised, which will affect the financial sustainability of the Shenzhen Metro Line 4 project. Since Shenzhen Metro Line 4 adopts BOT mode, the project will be handed over to the Shenzhen Municipal Government after the operation period, which will lead to a high possibility of handover risk. December 31, 2019 and June 12, 2020, Shenzhen Metro Line 4 experienced multiple failures and outages, which reflected the high operational risks of the project.

4.4 Risk control of urban rail transit PPP project

Based on the results of the risk assessment, a centralized risk control plan is proposed. First, a comprehensive risk management system is established, and the risks are analyzed layer by layer to propose corresponding solutions. Second, distinguish the risk-bearers. Different risks should have the main bearer or be shared by both parties. Finally, design key risk control measures for the important risk areas.

4.4.1 Risk management system

When conducting risk management of PPP projects, a comprehensive risk management system is established based on the identification and evaluation of risk elements. First, the type and degree of risk must be analyzed and determined. Second, choose effective risk management measures. Furthermore, negotiate on the sharing of related risks and improve contract terms. Fourth, determine a reasonable risk-sharing contract. Finally, the corresponding risk response plan was adopted to implement the PPP project. The risk management system is shown in Fig. 3.

Fig. 3

Risk Management System Diagram.

4.4.2 Risk sharing

The sharing of risk factors at different levels has a certain tendency. Among them, most national-level risks tend to be borne by the government, while market-level and project-level risks tend to be borne by social capital. According to the principle of risk control ability, the text further divides the risk sharing methods into five categories: government only sharing, government sharing mainly, joint sharing, social capital only sharing, and social capital sharing mainly, as shown in Table 6.

Table 6
Division of risk sharing subjects

Level Risk factor Risk bearer

B1 C11 Policy risk Mainly shared by the government

C12 Corruption risk Mainly shared by the government

C13 Expropriation and nationalization The only share of the government

C14 Political stability The only share of the government

B2 C21 Tax system changes Mainly shared by the government

C22 Industry law changes Mainly shared by the government

B3 C31 Interest rate risk Shared by both parties

C32 Exchange rate risk Shared by both parties

C33 Inflation risk Shared by both parties

B4 C41 Natural environmental risks Mainly shared by social capital

C42 Social and environmental risks Mainly shared by the government

B5 C51 Market competition Shared by both parties

C52 Demand changes Mainly shared by social capital

C53 Price change Shared by both parties

B6 C61 Financing feasibility Mainly shared by social capital

C62 Excessive financing cost Mainly shared by social capital

B7 C71 Design risk The only share of social capital

C72 Engineering safety quality The only share of social capital

C73 Construction costs The only share of social capital

C74 Operation and maintenance risk The only share of social capital

C75 Pricing risk The only share of social capital

C76 Technology risk The only share of social capital

C77 Handover risk Shared by both parties

B8 C81 Public-private sector relationship risk Shared by both parties

C82 Improper distribution of responsibilities Shared by both parties

B9 C91 Natural disaster risk Shared by both parties

C92 Unforeseen risks Shared by both parties

Level	Risk factor	Risk bearer
B1	C11 Policy risk	Mainly shared by the government
	C12 Corruption risk	Mainly shared by the government
	C13 Expropriation and nationalization	The only share of the government
	C14 Political stability	The only share of the government
B2	C21 Tax system changes	Mainly shared by the government
	C22 Industry law changes	Mainly shared by the government
B3	C31 Interest rate risk	Shared by both parties
	C32 Exchange rate risk	Shared by both parties
	C33 Inflation risk	Shared by both parties
B4	C41 Natural environmental risks	Mainly shared by social capital
	C42 Social and environmental risks	Mainly shared by the government
B5	C51 Market competition	Shared by both parties
	C52 Demand changes	Mainly shared by social capital
	C53 Price change	Shared by both parties
B6	C61 Financing feasibility	Mainly shared by social capital
	C62 Excessive financing cost	Mainly shared by social capital
B7	C71 Design risk	The only share of social capital
	C72 Engineering safety quality	The only share of social capital
	C73 Construction costs	The only share of social capital
	C74 Operation and maintenance risk	The only share of social capital
	C75 Pricing risk	The only share of social capital
	C76 Technology risk	The only share of social capital
	C77 Handover risk	Shared by both parties
B8	C81 Public-private sector relationship risk	Shared by both parties
	C82 Improper distribution of responsibilities	Shared by both parties
B9	C91 Natural disaster risk	Shared by both parties
	C92 Unforeseen risks	Shared by both parties

4.4.3 Risk response

According to the characteristics of the risk and the difference of the sharing subjects, corresponding risk response measures should be taken. This article analyzes the key risk areas: political risk, economic risk, market risk and project promotion risk, and proposes corresponding risk response behaviors and residual risks. The specific risk response process is shown in Figs. 4 –7.

Fig. 4

Political risk response path.

Fig. 5

Economic risk response path.

Fig. 6

Market risk response path.

Fig. 7

Project promotion risk response path.

5 Conclusion and future directions

From the perspective of SPV Company, based on the existing theoretical research results, combined with the risk characteristics of metro PPP project, this paper uses the method of fuzzy hierarchical analysis to construct the metro PPP project risk assessment framework system from nine dimensions. Political risk, legal risk and project promotion risk are the most important three risk indicators, while environmental risk, relationship risk and force majeure risk take the lowest proportion. Based on the case study of Shenzhen Metro Line 4 project, the risk sharing scheme and countermeasures in key risk areas are put forward. The aim is to provide systematic risk assessment basis for stakeholders of PPP projects, provide theoretical path guidance for regulatory authorities to improve the implementation rate of PPP projects, promote the steady development of urban rail transit PPP projects, and realize the PPP concept of risk sharing and benefit sharing.

For further research, methods such as TOPSIS, Monte Carlo simulation, BP neural network or game theory model can be used to compare results [18, 29], or a combination of qualitative data and quantitative indicators can be used in the model to effectively avoid the influence of subjective factors on the results.

Footnotes

Acknowledgments

The authors thank Fundamental Research Funds for the Central Universities (2020YJS047). The research was also supported by the National Natural Science Foundation of China (71973009, 71902004).

References

Songer

A.D.

, Diekmann

and Pecsko

R.S.

, Risk analysis for revenue dependent infrastructure projects, Construction Management and Economics15 (1997), 377–382.

and Loosemore

, Risk allocation in the private provision of public infrastructure, International Journal of Project Management25 (2007), 66–76.

Thomas

A.V.

, Kalidindi

S.N.

and Ganesh

L.S.

, Modelling and assessment of critical risks in bot road projects, Construction Management & Economics24 (2006), 407–424.

Chung

and Hensher

D.A.

, Modelling risk perceptions of stakeholders in Public–Private Partnership toll road contracts, Journal of Accounting, Finance and Business Studies51 (2015), 437–483.

Grimsey

and Lewis

M.K.

, Evaluating the Risks of Public Private Partnerships for Infrastructure Projects, International Journal of Project Management20 (2002), 107–118.

Helmer

D.O.

, An experimental application of the delphi method to the use of experts, Management Science9 (1963), 458–467.

Medda

F.A.

, Game theory approach for the allocation of risks in transport public-private partnerships, International Journal of Project Management25 (2007), 213–218.

Ahwireng-Obeng

and Mokgohlwa

J.P.

, Entrepreneurial risk allocation in public-private infrastructure provision in South Africa, South Africa Journal of Business Management33 (2002), 29–39.

Liu

F.Z.

, Li

, Fan

B.S.

and Wang

, Risk assessment of the safe operation status of urban transportation systems: Taking Beijing rail transit as an example, Management Review7 (2020), 217–225.

10.

Ren

, Research on Risk Evaluation of Urban Rail Transit Debt, Journal of Humanities11 (2013), 40–45.

11.

Chen

G.T.

, Huang

X.L.

and Zhang

, The Evaluation Model and Application of Internal Control Based on Enterprise Risk Management Framework, Audit Research6 (2013), 93–101.

12.

Mona

, Francois

R.J.

and Etienne B

, Determinants of Public-Private Partnerships in Infrastructure, Social Science Electronic Publishing6 (2011), 1–37.

13.

Yan

H.Y.

, He

Z.C.

, Li

J.J.

and Zhou

C.M.

, Risk assessment of the main body behavior of urban rail transit PPP projects, Scientific Decision4 (2019), 1–22.

14.

Peko

, Gjeldum

and Bilic

, Application of AHP, Fuzzy AHP and PROMETHEE Method in Solving Additive Manufacturing Process Selection Problem, Tehnicki vjesnik-Technical Gazette25 (2018), 453–461.

15.

Zheng

J.F.

, Research on the relationship between urban rail transit and surrounding real estate value, Ph.D. Dissertation, Tsinghua University, (2004).

16.

Guo

, Research on Traffic Volume Risk Sharing Strategy of Highway Infrastructure PPP Project, Management Review7 (2013), 11–19+37.

17.

Jin

J.L.

, Wei

Y.M.

and Ding

, Fuzzy comprehensive evaluation model based on improved analytic hierarchy process, Journal of Hydraulic Engineering2 (2004), 144–147.

18.

Janekova

, Fabianova

and Fabian

, Assessment of Economic Efficiency and Risk of the Project Using Simulation, Journal of Simulation Modelling18 (2019), 242–253.

19.

Jia

and Sun

, The concept, origin, characteristics and function of public-private partnership (PPP), Financial Research10 (2009), 2–10.

20.

Ocampo

L.A.

, Himang

C.M.

, Kumar

and Brezocnik

, A novel multiple criteria decision-making approach based on fuzzy DEMATEL, fuzzy ANP and fuzzy AHP for mapping collection and distribution centers in reverse logistics, Advances in Production Engineering & Management14 (2019), 297–322.

21.

Bing

, Akintoye

, Edwards

P.J.

and Hardcastle

, The allocation of risk in PPP/PFI construction projects in the UK, International Journal of Project Management23 (2005), 25–35.

22.

Li and Zhao

, The construction of PPP project risk evaluation system under the background of new urbanization: Taking Shanghai Xinzhuang CCHP project as an example, Economic System Reform5 (2015), 17–23.

23.

Xiao

, On the economic risk control of urban rail transit in my country-based on the experience of London Underground, Learning and Practice8 (2012), 57–64.

24.

Safayet

M.A.

, Islam

M.H.

and Ahmed

, A Case Study on Risk Management in Existing Construction Project in Bangladesh, Journal of Logistics, Informatics and Service Science5 (2018), 1–16.

25.

Alam

M.M.

and Faisal

, Public-Private Partnership (PPP) Projection Bangladesh: Current Status and Challenges, Journal of System and Management Sciences8 (2018), 38–56.

26.

Saaty and Thomas

, Decision making with the analytic hierarchy process, International Journal of Services Sciences1 (2008), 83–98.

27.

Saaty

T.L.

and Kearns

K.P.

, The analytic hierarchy process, Analytical Planning (1985).

28.

Sun

, Research on Risk Management under the BOT Model, Business Research18 (2004), 100–104.

29.

Zemlickienė

, Using TOPSIS Method for Assessing the Commercial Potential of Biotechnologies, Journal of System and Management Sciences9 (2019), 117–140.

30.

Liu

, Theoretical explanation of PPP model and its practical examples, The Reform1 (2015), 78–89.

31.

Liu

W.Q.

, Zhang

and Xu

Z.F.

, Research on Risk Transmission of Urban Rail Transit Project Financing, Statistics and Decision19 (2016), 58–60.

32.

Liu

W.Q.

, Deng

S.B.

and Xu

Z.F.

, Dynamic evaluation of financing risk of urban rail transit projects, System Engineering12 (2016), 153–158.

33.

X.F.

and Fu

, A review of multi-index comprehensive evaluation methods, Statistics and Decision11 (2004), 119–121.

34.

Zhou

X.F.

and Yan

X.M.

, The Local Good Governance Effect of PPP Risk Sharing Contracts: Theoretical Construction and Policy Recommendations, Financial Research9 (2017), 79–87.

35.

Jin

X.H.

and Doloi

, Interpreting risk allocation mechanism in public-private partnership projects: an empirical study in a transaction cost economics perspective, Construction Management and Economics26 (2008), 707–721.

36.

X.L.

, Analyze the issues that need to be paid attention to during the construction stage of urban rail transit from the perspective of operation, Urban Rail Transit Research7 (2012), 12–15.

37.

Deng

X.P.

, Li

Q.M.

and Wang

W.X.

, Summary and application of risk sharing principles of PPP model, Construction Economy9 (2008), 32–35.

38.

Deng

X.P.

, Li

Q.M.

, Xiong

and Yuan

J.F.

, Study on the key risks of urban infrastructure construction PPP projects, Modern Management Science12 (2009), 55–56+59.

39.

Liu

X.P.

and Wang

S.Q.

, On the risk distribution principles and framework of PPP projects, Construction Economy2 (2006), 59–63.

40.

Wang

X.Q.

, Yu

and Bing

X.G.

, Research on PPP project financing model risk sharing, Soft Science6 (2007), 39–42.

41.

Qia

, Ke

Y.J.

and Wang

S.Q.

, Case-based analysis of the main risk factors of PPP projects in China, China Soft Science5 (2009), 107–113.

42.

Zhou

, Game Analysis of PPP Project Financing Risk Sharing, Cooperative Economy and Technology14 (2009), 78–79.

43.

Zhang

Z.L.

and Hao

J.H.

, Research on PPP Project Risk Sharing Methods, Price Theory and Practice1 (2017), 137–140.