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Article

A Fuzzy Comprehensive Evaluation Model for Sustainability Risk Evaluation of PPP Projects

1
School of Economics and Management, Chang’an University, Middle Section of South Second Ring Road, Xi’an 710064, China
2
School of Civil Engineering, Chang’an University, Middle Section of South Second Ring Road, Xi’an 710064, China
*
Author to whom correspondence should be addressed.
Sustainability 2017, 9(10), 1890; https://doi.org/10.3390/su9101890
Submission received: 14 September 2017 / Revised: 14 October 2017 / Accepted: 16 October 2017 / Published: 20 October 2017
(This article belongs to the Section Economic and Business Aspects of Sustainability)

Abstract

:
Evaluating the sustainability risk level of public–private partnership (PPP) projects can reduce project risk incidents and achieve the sustainable development of the organization. However, the existing studies about PPP projects risk management mainly focus on exploring the impact of financial and revenue risks but ignore the sustainability risks, causing the concept of “sustainability” to be missing while evaluating the risk level of PPP projects. To evaluate the sustainability risk level and achieve the most important objective of providing a reference for the public and private sectors when making decisions on PPP project management, this paper constructs a factor system of sustainability risk of PPP projects based on an extensive literature review and develops a mathematical model based on the methods of fuzzy comprehensive evaluation model (FCEM) and failure mode, effects and criticality analysis (FMECA) for evaluating the sustainability risk level of PPP projects. In addition, this paper conducts computational experiment based on a questionnaire survey to verify the effectiveness and feasibility of this proposed model. The results suggest that this model is reasonable for evaluating the sustainability risk level of PPP projects. To our knowledge, this paper is the first study to evaluate the sustainability risk of PPP projects, which would not only enrich the theories of project risk management, but also serve as a reference for the public and private sectors for the sustainable planning and development.

1. Introduction

Public–Private Partnership (PPP) has been popular for 15 years, and continues to grow at a fast pace in China. The Chinese government continuously encourages the expansion of PPP applications to boost economic revenues; this emerging management pressure has made the study of PPP project management a research hotspot, and several achievements have been made [1,2,3].
As a new financing model, the relevant theory of PPP is imperfect [4] and the process of PPP holds great uncertainty [5]. Many uncertain factors can affect the implementation process of PPP projects, including environment risk, payment risk, etc. [6], thus many scholars have conducted an in-depth study for this problem. For example, Marques examined how risk is reflected in infrastructure regulatory contracts and got a conclusion that risk is the key issue in contracting with the private sectors [7]. Roehrich et al. applied the logic of bounded rationality and explored the extent to which companies implement responsible supply chain management (RSCM) as a result of their reputational risk exposure, and how bounded rationality impacts on the decision of RSCM [8,9]. Many other scholars have studied the relationship between public and private sectors in PPP projects [10]. Barlow proved that European governments were increasingly partnering with the private sector to underwrite the costs of constructing and operating public hospitals and other health care facilities and delivering services by constrained national budgets [11]. Hoejmose et al. proposed that responsible supply chain management can help protect a firm’s corporate reputation by shielding it from negative media attention and consumer boycotts [12]. However, many studies explored the role of organization and ecosystem in complex PPP projects [13,14,15]. Even though there are so many studies on PPP projects, unfortunately, little attention has been given to sustainability risk of PPP projects. Here, sustainability risk is the combination of likelihood and consequences of events which affect the achievement of organization’s sustainable development. It is related to the concepts of sustainable development and the “triple bottom line” [16], which emphasizes “the development should meet the needs of the present world without compromising the ability of the future generations to meet their own needs” [17]. Sustainability risk has been brought into many areas, and numerous studies have been conducted to discuss its connotations, applications and mechanisms. Among them, Touboulic and Walker [18] investigated theoretical perspectives in sustainable supply chain management and contributed to understanding the current state in the field of PPP and its future development. Cucuzzella [19] presented a series of design projects to illustrate the difference in thinking and outcomes when sustainability is thought of in varying temporal and spatial perspectives. Harclerode et al. [20] developed a foundational framework to define and integrate the sustainability and risk management objectives in the life cycle of complex project towards a more sustainable state. In the area of PPP project management, the common perception of sustainability risk evaluation involves economy, society, resources, and environment aspects, and aims at monitoring changes of PPP projects, adjusting strategies so that a balance among economy, society, resources, and environment can be found. However, there is no recipe for reaching this balance [21,22]. Furthermore, complex arrangements and incomplete contracting in PPP projects have led to increased risks of unsustainability, for both public and private partners [23,24]. Effective sustainability risk evaluation of PPP projects is therefore challenging and demanding.
At the same time, the accuracy of sustainability risk evaluation is crucial for PPP as a whole [25]. Risk evaluation of PPP projects is fundamentally different from that of traditional projects, where traditional projects emphasize the temporary and disposable nature of which risk evaluation is limited to the processes of design and implementation. In PPP projects, investors place special emphasis on the sustainability of projects and are entitled to reducing investments or terminating projects if PPP fails to achieve sustainability standards. Accordingly, one of the most important drivers for value-for-money is sustainability risk evaluation, which means the sustainability risk of a PPP project can be evaluated, prevented, and controlled during the implementation process [26]. As a result, lower-risk and higher-quality PPP projects may be implemented relative to conventional methods.
This work is intended to reduce project risk incidents and achieve the sustainable development of the organization by accurately evaluating the sustainability risk level of PPP projects and achieving the most important objective of providing a reference for the public and private sectors when making decisions on PPP project management. The rest of this paper is organized as follows. Section 2 analyzes the main influencing sustainability risk factors of PPP projects, by classifying these factors into five categories: culture and society, cost and economy, ecology and environment, project and organization, politics and policy, via an extensive literature review, and then this paper builds a factor system of sustainability risk of PPP projects. In Section 3, a fuzzy comprehensive evaluation model for assessing the sustainability risk level of PPP projects, based on FCEM and FMECA, is proposed, which provides a holistic view focused on reflecting the sustainability risk level factors of PPP projects by evaluating the sustainability risk level of each category. Section 4 verifies the effectiveness and feasibility of this model using a computational experiment. Section 5 draws the conclusions.

2. Factor System of Sustainability Risk of PPP Project

Risk management exerts a profound influence on PPP project management and its success [26]; especially, sustainability risk evaluations have been found to be highly variable, intuitive, subjective, and unsophisticated [27,28]. Given its critical importance in PPP projects, many studies have been conducted to seek an approach to evaluate the level of sustainability risk evaluation effectively, such as the work of Xu et al. [25], where a fuzzy synthetic evaluation model for assessing the level of a particular critical risk group, and the sustainability risk level associated with PPP projects in China, based on objective evidence rather than subjective judgment, was developed. Effah Ameyaw [29] conducted a risk perception analysis in water supply projects in Ghana to evaluate the risk criticality, risk management capability, and risk factors that could influence the sustainability risk level of water supply projects. Kumaraswamy [26] analyzed the factors of sustainability risk from the perspective of project teams to empower them to focus on developing sustainable infrastructures and, ultimately, overall sustainable development. Jin [24] established an artificial neural network model for modeling risk allocation decision-making processes in PPP projects. Hayford and Partner [30] proposed an optimal sustainability risk model which could enable partners to deal with external changes and events, and explore the behaviors between different partners, even while confronted with opposite objectives in the allocation of risks. However, this work either deems the sustainability risk level as one that is only affected by the status of the PPP project itself [25] or management capability [29], but lacks foundations and empirical evidence to support their claims.
More importantly, sustainability risk evaluation of PPP projects is a complex process, in which all project stakeholders cooperate and compete with each other in accordance with its sustainable development strategic objectives [31]. Running a PPP project at the lowest level of sustainability risk is a challenge for any enterprise, since many unpredictable factors could influence it [26]. This is probably because the studies on PPP project management, including risk management, are mainly concerned with processes and techniques [32,33]. PPP projects have a great impact developing the social economy and building a harmonious society [34]; thus, merely using risk indicators of a PPP project to measure the sustainability risk level is insufficient [35]. Zhang et al. [36] argued that measurements supported by other factors, such as society and the environment, need to be employed. Nonetheless, no further empirical studies have been conducted to support their conclusions.
Recently, Valipour et al. [37], Li and Zou [38] and Chou et al. [39] argued that the sustainability risk factors of PPP projects, if integrated with the aspects of financial, legal, and political risks, can contribute to the evaluation of the sustainability risk level of PPP projects, and allow a more logical and holistic understanding and interpretation of the sustainability risk evaluation process. In addition, although many scholars have already used the determinants of PPP project sustainability risk factors in aspects of economy, society, environment, management ability, and techniques, some of them lacked integrity [40,41].
To evaluate the sustainability risk level of PPP projects and maintain the systematic nature of the factors, the 1st-level sustainability risk factors of PPP projects can be generalized into five categories: culture and society, cost and economy, ecology and environment, project and organization, and politics and policy [24,36,42]. These factors can help evaluate the sustainability risk level of PPP projects and maintain the systematic nature. There are many 2nd-level evaluation factors in each 1st-level sustainability risk factor, so it is important to build a sustainability risk factor system before evaluating the sustainability risk level of a PPP project. Based on existing research and literature, the factor system of the sustainability risk of a PPP project can be built, as shown as Table 1.

3. Methodologies

3.1. Fuzzy Comprehensive Evaluation

During the process of risk evaluation, many factors that affect the level of sustainability risk are with a strong fuzzy uncertainty and cannot be analyzed quantitatively, therefore, it is difficult to evaluate the sustainability risk level by a single, defined management criterion [55]. To solve this fuzzy uncertainty problem, Zadeh [56] proposed the concept of fuzzy sets in 1965 and laid the foundation for the application of FCEM in the area of risk evaluation.
FCEM is based on the membership degree theory in fuzzy mathematics, which transform the qualitative evaluation into quantitative evaluation [57,58,59]. It has now become an effective multi-factor decision-making tool for comprehensive evaluation. Combining with experts grading method, FCEM can make a full reflection on the evaluation criteria and the influence factors of fuzziness, then produce evaluation results closer to the actual situation [60].
From early 1990s, FCEM has been applied to solve real-word problems, and studies on the adoption of this model has been rapidly expanded to various fields, including, but not limited to regional water resources capacity [61], aircraft flight safety [62,63], health, safety and environment management, teaching performance [64] and international relations [65]. According to these studies, the sensitivity of FCEM is much higher compared with other methods thanks to the predetermined weights and decreased fuzziness by establishing membership functions. Therefore, we choose FCEM as the tool to evaluate the sustainability risk level and the process can be divided into 5 steps [66]:
Step 1: Establish a risk assessment factor set. Elements in set Q are the factors that affect the risk evaluation. An integrated level of risk is reflected by these elements at a given time, the risk assessment factor set Q and the elements in this set shown as Equations (1) and (2):
Q = { Q 1 ,   Q ,   Q i ,   Q ,   Q n }
Q i = { Q i 1 ,   ,   Q i j ,   ,   Q i m }   ( i = 1 ,   2 ,   ,   n ; j = 1 ,   2 ,   ,   m )
where Q is the risk assessment factor set and n is the number of 1st-level sustainability risk factors in set Q ; Q i ( i = 1 ,   2 ,   ,   n ) is the i th 1st-level sustainability risk factors, Q i j is the j th 2nd-level sustainability risk factor of Q i   and m is the number of 2nd-level sustainability risk factor. A fuzzy logic relationship is existing among different factors in set Q , and this relationship can be expressed in the risk assessment comments set P .
Step 2: Establish a risk assessment comment set P . Comment set P is a collection consisted of 5 comments that evaluators make evaluation to the sustainability risk level according to the criterion of FCEM, shown as Equation (3):
P = { p 1 ,   p 2 ,   p 3 ,   p 4 ,   p 5 }
where P is the risk assessment comment set, p 1 ,   p 2 ,   p 3 ,   p 4 and p 5 are the comments representing the sustainability risk level are “Devastating”, “Unacceptable”, “General”, “Acceptable” and “Desirable”, which is represented as the score of comment: 1, 2, 3, 4 and 5, respectively. Thus, the risk assessment comment set can be recorded as P = { p 1 ,   p 2 ,   p 3 ,   p 4 ,   p 5 } = { Devastating ,   Unacceptable ,   General ,   Acceptable ,   Desirable } =   { 1 ,   2 ,   3 ,   4 ,   5 } . According to this criterion, the fuzzy comprehensive evaluation matrix R and R i ( i = 1 ,   2 ,   ,   n ) can be determined, shown as Equation (4):
R i = { r i 11 r i 12 r i 13 r i 14 r i 15 r i 21 r i 22 r i 23 r i 24 r i 25 r i 31 r i 32 r i 33 r i 34 r i 35 r i m 1 r i m 2 r i m 3 r i m 4 r i m 5 }
Here R = { R 1 ,   R ,   R i ,   R ,   R n } and R i ( i = 1 ,   2 ,   ,   n ) are the fuzzy comprehensive evaluation matrix of Q and Q i , r i m k ( k = 1 ,   2 ,   3 ,   4 ,   5 ) is the comment of 2nd-level sustainability risk factor Q i m . Then, the fuzzy comprehensive evaluation matrix of 1st-level sustainability risk factors can be constructed based on the scores of 2nd-level sustainability risk factors.
Step 3: Build a weights vector W and W i . Each element in set Q and Q i makes different contribution to the realization of risk assessment, so the weight of these factors are different. The assessment index weights vector can be determined, shown as Equations (5)–(8):
W = { W 1 ,   W 2 ,   ,   W i ,   ,   W n }   ( i = 1 ,   2 ,   ,   n )
W i = { W i 1 ,   W i 2 ,   ,   W i j ,   ,   W i m }   ( i   =   1 ,   2 ,   ,   n ; 1     j     m )
i = 1 n W n = 1
j = 1 m W i m = 1
where W and W i are the weights vector of 1st-level and the 2nd-level sustainability risk factors, W i and W i m is the weight of Q i and Q i m , respectively. The values of W i and W i m can be calculated by the method of Failure Mode, Effects and Criticality Analysis (FMECA).
Step 4: Establish a fuzzy comprehensive assessment matrix G to reflect the sustainability risk level of the PPP project, shown as Equations (9) and (10):
G = W · B T
B = ( B 1 ,   ,   B i ,   ,   B n )
B i = W i · R i
where G is the fuzzy comprehensive assessment matrix which could reflect the sustainability risk level of PPP project, B i is the fuzzy comprehensive assessment matrix of the 1st-level sustainability risk factor Q i   ( i = 1 ,   2 ,   ,   n ) , B is the fuzzy comprehensive assessment matrix set. According to Equations (9)–(11), the fuzzy comprehensive assessment matrix of different levels assessment factors can be calculated.
Step 5: Calculate the value of sustainability risk level of PPP project, recorded as Z, and the sustainability risk level of 1st-level risk factor, recorded as Z′. Combined with risk assessment comment set P, fuzzy comprehensive assessment matrix G and Bi, the value of sustainability risk level can be calculated by Equations (12)–(14):
Z = P · G
Z = ( Z 1 ,   ,   Z i ,   ,   Z n )
Z i = P · B i
where Z is the sustainability risk level of the project, Z i is the sustainability risk level of the 1st-level risk factor Q i . Z is the set of the 1st-level risk factors’ sustainability risk level. Through Equations (12)–(14), the value of sustainability risk level of the PPP project and the sustainability risk level of 1st-level risk factors can be obtained, which would provide a basis for the sustainability risk management decisions.

3.2. Failure Mode, Effects and Criticality Analysis

According to Step 3 in Section 3.1, the values of weights vector W and W i are very important to determine the sustainability risk level and can be calculated by the method of FMECA.
FMECA is an inductive analytical tool provides a systematic, comprehensive evaluation and analyzes the effects of potential failures in the system design [67]. The process of FMECA includes a review and assessment of failure modes, the impact of those failures on system operation and identifies the effects, if any, on the operational safety of the system [65]. FMECA provides appropriate measures depending on the cause of the problem to prevent the recurrence of the failure after determining the possible system failures and failure probabilities, severity and hazards of each component [68,69]. According to FMECA, the weight of sustainability risk factors can be calculated by Equations (15) and (16):
W i   =   H i   ×   S i   ×   D i C i
W i m   =   H i m   ×   S i m   ×   D i m C i m
where W i is the cross-sectional area of 1st-level sustainability risk factor Q i , W i m is the cross-sectional area of the 2nd-level sustainability risk factor Q i m . H i is the occurrence probability of Q i . S i is the loss and impact after Q i occurs. D i is the perceived degree of Q i , C i is the ability to control and compensate the loss after Q i occurs. The value of H i ,   S i ,   D i and C i can be obtained by experts grading method (EGM) where   H i = [ 1 ,   5 ] ,   S i = [ 1 ,   5 ] ,   D i = [ 1 ,   5 ] ,   C i = [ 1 ,   5 ] . The principle of expert evaluation are shown as Equations (17)–(20):
H i = { 1 L o w e s t   p r o b a b i l i t y   o f   r i s k   5 H i g h e s t   p r o b a b i l i t y   o f   r i s k   h i O t h e r w i s e  
Here 1   <   h i   <   5 , the higher h i , the higher the probability of Q i .
S i = { 1 S l i g h t e s t   5   W o r s t   a f f e c t e d s i   O t h e r w i s e  
Here 1   <   s i   <   5 , the higher s i , the worse impact after Q i occurs.
D i = { 1 M o s t   e a s i l y   t o   b e   p e r c e i v e d   5 M o s t   d i f f i c u l t   t o   b e   p e r c e i v e d   d i   O t h e r w i s e  
Here 1   <   d i   <   5 , the higher d i , the greater the difficulty of being perceived
C i = { 1 M o s t   d i f f i c u l t   t o   c o n t r o l / compensate   the   loss   5 M o s t   e a s i l y   t o   c o n t r o l / compensate   the   loss   c i O t h e r w i s e  
Here 1 < c i < 5 , the higher h i , the easier to control/compensate the loss after Q i occurs.
According to Equations (17)–(19), the values of W i and W i m   can be obtained, W i [ 0.2 ,   125 ] , W i m [ 0.2 ,   125 ] . Then, the weight of different levels of sustainability risk factors W i and W i m would be obtained after normalized the value of W i and W i m , respectively.

4. Computational Experiment and Results

PPP model has been widely used to deliver infrastructure projects. Over the past two decades, the Chinese government has been embarking on an ambitious program of large investments on infrastructure development. To facilitate urbanization in China, the funds required for urban infrastructure development during the first twenty years of the 21 century are expected to be around 3500–5000 billion RMB. Funds supported by government is unlikely to be used only to finance such large investments and so, reforms need to be undertaken by Chinese government regarding the investment and financing of infrastructure projects. Therefore, the model of PPP was brought in China to alleviate this problem.
Yu River Wetland Park (YRWP), in Xi’an, is a PPP demonstration project of the Ministry of Finance of the People’s Republic of China, the total area of this park is 5236 acres and the total planned investment is 1.17 billion RMB which will be used in the construction of lake, heap mountain, wetland restoration, landscape greening, sculpture sketch, square construction, as well as other projects. This is a public welfare infrastructure project which focus on the ecological construction, environmental protection and sustainable development of Xi’an and will become the largest wetland park in the Xi’an if built in 2018. Many stakeholders such as Xi’an Municipal Government, GC Investment Group, SBG Construction and Development Co., Ltd. (Shanghai, China) participated in the construction process of this project. Obviously, the construction form of this park is a typical application of PPP model which emphasizes the effective cooperation between government and social capital. Therefore, the YRWP is representable of the wider PPP population. In addition, Xi’an is the ancient historical and cultural capital of China, with many historical sites and many ethnic groups; thus sustainability risk evaluation of this PPP project involves history, economy, culture, and many other aspects. Thus, the YRWP project can be chosen as an example for computational experiments to introduce the application and effectiveness of the sustainability risk evaluation model in this paper.
According to Table 1 and the process of sustainability risk evaluation, described in Section 3.1, the risk evaluation factor set of YRWP, Q, can be established (shown in Table 2).
In Table 2, Q is the risk assessment factor set of YRWP, n is the number of 1st-level sustainability risk factors in set Q , which is n = 5 . Q i   ( i ( 1 ,   n ) ) is the i th 1st-level sustainability risk factor, Q i j is the j th 2nd-level risk factor of Q i , and m   is the number of 2nd-level risk factors. As shown in Table 2, the number of YRWP’s risk factors are m = { 24 ,   i = 1 16 ,   i = 2 10 ,   i = 3 12 ,   i = 4 10 ,   i = 5 .
According to the criterion of FCEM, and Equation (3), the risk assessment comment set of YRWP, P , can be established, where P = { p 1 ,   p 2 ,   p 3 ,   p 4 ,   p 5 } = { 1 ,   2 ,   3 ,   4 ,   5 } . Fuzzy comprehensive evaluation matrix R and R i ( i = 1 ,   2 ,   ,   n ) could also be determined based on the results of the questionnaire survey (the sample of this survey questionnaire is shown in Appendix A).
To collect the risk assessment comments of YRWP, a questionnaire survey was designed (Appendix A). The objective of this questionnaire survey included three categories: Management, implementation, and technical staff, which could ensure the correctness of the survey results. A total of 500 questionnaires were issued and 448 were collected, including nine unfinished and seven identical questionnaires; these 16 questionnaires were considered as invalid according to statistical principles, thus 432 questionnaires were valid. The recovery rate and the valid questionnaire were 89.6% and 86.4%, respectively. Therefore, the results of this survey are considered real and effective, and can be used for further analyses.
Based on the results of the assessment comments of 2nd-level sustainability risk factors, the fuzzy comprehensive evaluation matrix of 1st-level sustainability risk factors, was constructed. This section takes the 1st-level sustainability risk factors, Q 3 ( Q 3   was selected because the number of 2nd-level sustainability risk factors of Q 3 is the minimum), as an example to introduce the calculation process of fuzzy comprehensive evaluation matrix R 3 .
By analyzing the results of the survey questionnaires, the assessment comment of sustainability risk factor Q 3 can be obtained (Table 3).
In Table 3, the level of comment of 2nd-level risk factor Q i m can be calculated by r i m k = F r e q u e n c y ( Q i m p α ) α = 1 5 F r e q u e n c y ( Q i m p α ) ; here, F r e q u e n c y ( Q i m p α ) is the time that the object of this questionnaire survey evaluated the sustainability risk level of Q i m is p α ( α = 1 ,   2 ,   3 ,   4   or   5 ). Then, fuzzy comprehensive evaluation matrix R 3 can be established:
R 3 = [ r 311 r 312 r 315 r 321 r 322 r 325 r 331 r 332 r 335 r 3 m 1 r 3 m 2 r 3 m 5 ] = [ 0.100 0.130 0.317 0.255 0.199 0.109 0.220 0.331 0.190 0.150 0.060 0.174 0.241 0.317 0.208 0.123 0.248 0.329 0.174 0.127 0.116 0.222 0.333 0.185 0.144 0.111 0.227 0.333 0.174 0.155 0.174 0.248 0.303 0.144 0.132 0.090 0.208 0.324 0.211 0.167 0.100 0.208 0.329 0.201 0.162 0.201 0.257 0.243 0.169 0.130 ]
Similarly, the fuzzy comprehensive evaluation matrix of the other 1st-level sustainability risk factors R 1 ,   R 2 ,   R 4 , and R 5 , can be established:
R 1 = [ 0.049 0.225 0.354 0.225 0.148 0.231 0.313 0.280 0.083 0.093 0.118 0.285 0.394 0.086 0.118 0.241 0.313 0.282 0.074 0.090 0.219 0.291 0.323 0.072 0.095 0.058 0.236 0.352 0.215 0.139 0.113 0.275 0.396 0.090 0.125 0.030 0.238 0.368 0.218 0.146 0.046 0.204 0.275 0.280 0.194 0.060 0.229 0.356 0.220 0.134 0.044 0.201 0.280 0.289 0.185 0.074 0.236 0.396 0.148 0.146 0.049 0.231 0.366 0.220 0.134 0.039 0.241 0.368 0.206 0.146 0.037 0.243 0.377 0.188 0.155 0.116 0.273 0.398 0.088 0.125 0.111 0.269 0.400 0.088 0.132 0.037 0.215 0.363 0.236 0.148 0.030 0.238 0.368 0.220 0.144 0.019 0.211 0.280 0.294 0.197 0.030 0.236 0.352 0.238 0.144 0.025 0.241 0.370 0.222 0.141 0.037 0.250 0.359 0.208 0.146 0.171 0.301 0.373 0.053 0.102 ]
R 2 = [ 0.058 0.225 0.345 0.275 0.097 0.088 0.243 0.368 0.236 0.065 0.090 0.285 0.391 0.167 0.067 0.079 0.231 0.350 0.257 0.083 0.039 0.199 0.313 0.287 0.162 0.037 0.236 0.343 0.269 0.116 0.058 0.231 0.356 0.271 0.083 0.065 0.245 0.366 0.262 0.063 0.060 0.236 0.340 0.280 0.083 0.081 0.273 0.370 0.234 0.042 0.243 0.315 0.280 0.123 0.039 0.250 0.301 0.273 0.132 0.044 0.171 0.229 0.347 0.167 0.086 0.174 0.287 0.289 0.181 0.069 0.183 0.236 0.285 0.199 0.097 0.213 0.241 0.363 0.104 0.079 ]
R 4 = [ 0.060 0.231 0.361 0.271 0.076 0.039 0.201 0.313 0.287 0.160 0.069 0.234 0.350 0.264 0.083 0.141 0.324 0.296 0.174 0.065 0.065 0.243 0.366 0.262 0.065 0.063 0.238 0.336 0.280 0.083 0.032 0.213 0.370 0.282 0.102 0.035 0.225 0.343 0.280 0.118 0.014 0.192 0.273 0.331 0.190 0.079 0.280 0.347 0.213 0.081 0.049 0.197 0.289 0.292 0.174 0.211 0.231 0.366 0.113 0.079 ]
R 5 = [ 0.056 0.236 0.354 0.273 0.081 0.148 0.262 0.361 0.167 0.063 0.063 0.234 0.338 0.282 0.083 0.042 0.174 0.382 0.331 0.072 0.141 0.294 0.282 0.222 0.060 0.030 0.238 0.354 0.292 0.086 0.079 0.213 0.326 0.257 0.125 0.030 0.227 0.350 0.280 0.113 0.060 0.248 0.361 0.167 0.164 0.250 0.234 0.301 0.141 0.074 ]
Weight vectors W and W i are very important to determine the level of sustainability risk and can be calculated using FMECA according to Section 3.2. To obtain the weights of sustainability risk factors, five experts of PPP risk management were invited to score the values of H i ,   S i ,   D i and C i with the principle shown as Equations (15)–(20) (the scoring table is shown in Appendix B), and the scoring results of the 1st-level sustainability risk factors are shown in Table 4. Taking the average as the final score, the weight of 1st-level sustainability risk factors, W i , can be obtained after normalization:
W = { W 1 ,   W 2 ,   W 3 ,   W 4 ,   W 5 } = { 0.102 ,   0.183 ,   0.232 ,   0.362 ,   0.121 }
Similarly, the weight of 2nd-level sustainability risk factors W i can be obtained:
W 1 = [ W 11   ,   ,   W 112   , W 113   ,   ,   W 124 ] = [   0.059 ,   0.025 ,   0.043 ,   0.015 ,   0.026 ,   0.013 ,   0.046 ,   0.039 ,   0.063 ,   0.053 ,   0.103 ,   0.024 , 0.034 ,   0.053 ,   0.032 ,   0.043 ,   0.041 ,   0.043 ,   0.046 ,   0.082 ,   0.042 ,   0.017 ,   0.027 ,   0.031 ]
W 2 = [ W 21   ,   ,   W 28   ,   W 29   ,   ,   W 216 ]   = [   0.031 ,   0.038 ,   0.036 ,   0.064 ,   0.108 ,   0.088     0.044 ,   0.048 , 0.100 ,   0.058 ,   0.066 ,   0.048 ,   0.096 ,   0.049 ,   0.040 ,   0.086 ]
W 3 = [   W 31   ,   ,   W 310   ]          = [ 0.090 ,   0.155 ,   0.098 ,   0.110 ,   0.061 ,   0.139 ,   0.048 ,   0.103 ,   0.083 ,   0.114 ]  
W 4 = [   W 41   ,   ,   W 412   ] = [ 0.076 ,   0.058 ,   0.043 ,   0.137 ,   0.111 ,   0.102 ,   0.08 ,   0.068 ,   0.100 ,   0.062 ,   0.107 ,   0.056 ]
W 5 = [   W 51   ,   ,   W 510   ]          = [ 0.045 ,   0.106 ,   0.193 ,   0.097 ,   0.089 ,   0.093 ,   0.095 ,   0.133 ,   0.079 ,   0.07 ]
According to Equation (11), the fuzzy comprehensive assessment matrix of 1st-level risk factors can be calculated:
B 1   =   | 0.070   0.241   0.345   0.197   0.148 |
B 2   =   | 0.116   0.246   0.336   0.217   0.085 |
B 3   =   | 0.116   0.215   0.309   0.218   0.158 |
B 4   =   | 0.071   0.238   0.329   0.255   0.106 |
B 5   =   | 0.083   0.235   0.342   0.248   0.092 |
According to Equations (9) and (10), fuzzy comprehensive assessment matrix G , which reflects the sustainability risk level of YRWP, can be established:
   G =   W · B T =   W · | B 1 B 2 B 3 B 4 B 5 | =   | 0.102   0.183   0.232   0.362   0.121 |   ·   | 0.070 0.241 0.345 0.197 0.148 0.116 0.246 0.336 0.217 0.085 0.116 0.215 0.309 0.218 0.158 0.071 0.238 0.329 0.255 0.106 0.083 0.235 0.342 0.248 0.092 | = | 0.091   0.234   0.329   0.233   0.117 |
According to Equations (12)–(14), the value of YRWP’s sustainability risk assessment, Z ,   and the sustainability risk level of 1st-level risk factors, Z i , can be calculated:
Z = P · G = | 1 2 3 4 5 | · | 0.091 0.234 0.329 0.233 0.117 | = 3.061
Z 1 = P · B 1 = | 1 2 3 4 5 | · | 0.070 0.241 0.345 0.197 0.148 | = 3.113
Z 2   =   2.909 ,   Z 3   =   3.133 ,   Z 4   =   3.088 ,   Z 5   =   3.030 .
In addition, Figure 1 shows the sustainability risk level of 1st-level risk factors.
Z = 3.061 means that the value of YRWP’s sustainability risk level is 3.061, which is higher than the average value of risk comments, 2.5, which indicates that the YRWP’s sustainability risk level is relatively higher and needed for scientific management in process of project implementation.
In Figure 1, the value of YRWP’s sustainability risk assessment is in accordance with the order, from highest to lowest: cost and economy ( Q 3 ), society and culture ( Q 1 ), project and organization ( Q 4 ), politics and policy ( Q 5 ), and ecology and environment ( Q 2 ). Cost and economy ( Q 3 ), and society and culture ( Q 1 ) are the highest sustainability risk level factors Therefore, if managers want to control the sustainability risk of YRWP effectively, Q 3 and Q 1 are the key factors to be addressed first.
According to Figure 1, the 1st-level sustainability risk factor of cost and economy in YRWP is the highest, which is because the YRWP project is a social welfare project focused on ecological construction, environmental protection, and sustainable development of Xi’an, although the relationship between public and private sectors is not very clear causing the investment plan and expense being relatively unclear, which would keep the risks of cost and economy at a higher level. Compared to different PPP projects, it is not difficult to find that the sustainability risk level of the same factors, such as ecology and environment, society, and culture, in different projects are different due to the particularity of each project; it reflects that the sustainability risk level of different factor is relative, which requires managers to take the actual situation into account when making decision on sustainability risk management for different PPP projects.

5. Discussions and Conclusions

Nowadays, many studies on PPP project management have been carried out to study the problems of risk assessment [6,7,8,9], relationship recognition between public and private sectors [10], and analysis of the roles for different organizations [13,14,15]. Besides, many other scholars have researched the area of sustainability risk and presented the connotations, applications and mechanisms from different fields, including, but not limited to, organization’s sustainable development [16], sustainable chain management [18], and project design selection [19]. These studies greatly contribute to promote the application of PPP model in infrastructure construction projects and provide a theoretical support for sustainable risk management. However, even though there are many studies about PPP projects and sustainability risk, little attention has been given to sustainability risk of PPP projects, especially the area of sustainability risk evaluation of PPP projects, and the method used to evaluate the sustainability risk level of PPP is also missed which causes the sustainability risk of a PPP project cannot be evaluated, prevented, and controlled during the implementation process. This emerging management pressure has made the study of sustainability risk evaluation of PPP projects important.
To solve this problem, this paper brings the concept of “sustainability” into the risk evaluation of PPP projects and constructs a factor system of sustainability risk of PPP projects covering five 1st-level factors and 72 2nd-level factors via an extensive literature review. In addition, this paper adapts a comprehensive approach to establish a fuzzy evaluation model for sustainability risk evaluation based on the methods of FCEM and FMECA for evaluating the sustainability risk level of PPP projects, the effectiveness and feasibility of which is verified by a computational experiment. According to the results of this computational experiment, we can see that the approach proposed in this paper is reasonable for evaluating the sustainability risk levels of PPP projects and could achieve the most important objective of providing a reference for stakeholders when making decisions on sustainability risk management of PPP projects. In addition, this evaluation model has also laid a useful foundation for future case analyses; the stakeholders of PPP, i.e., not only public sectors such as government departments, but also private sectors including enterprises and government agents, may adopt this model to assess the sustainability risk level of each PPP project and review the strengths and weaknesses of their current sustainability risk management, so that better risk management plans can be conceived toward the implementation of PPP projects.
This paper, to our knowledge, is the first study to research the sustainability risk in the field of PPP project management, which not only bridges the research areas of sustainability risk and PPP project management, filling the gap between traditional risk management and organization’s sustainable development, but also provides a reference for the public and private sectors for the sustainable planning and development. However, there are two shortcomings in this study: (1) the systematic deficiencies of the factors are induced by the negative synergistic relationship between factors having not been taken into account, and might affect the scientific nature of the evaluation results; and (2) the effectiveness and feasibility of this proposed model was verified using a computational experiment, however, the selected project to be implemented was only consistent for the problem of sustainability risk evaluation, thus, the results of the computational experiment should initially be generalized. These limitations should be studied in the future.

Acknowledgments

This work was supported by the National Social Science Foundation of China (Grant No. 16CJY028), Ministry of Education Humanities and Social Sciences Fund (Nos. 17XJC630001 and 15YJC790015), Soft Science Foundation of Shaanxi Province (2017KRM123) and Social Science Planning Fund of Xi’an (No. 17J173).

Author Contributions

Libiao Bai designed the approach and conceived the experiments; Yi Li and Qiang Du wrote most of the manuscript. Yadan Xu designed the survey questionnaire and analyzed the data.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A. A Sample of Survey Questionnaire

Appendix A.1. Basic Information

  • Gender: □ male □ female
  • Age: □ 20–29 □ 30–39 □ 40–49 □ 50 or more
  • Length of service: □ Within 1 year □ 1–5 years □ 6–10 years
                □ 11–20 years □ 20 years or more
  • Your duties:
  • Department:
  • Nature of your department: □ management □ implementation □ technology □ other

Appendix A.2

Table A1. Assessment comments of YRWP’s sustainability risk factors.
Table A1. Assessment comments of YRWP’s sustainability risk factors.
Assessment CommentsLevel of Sustainability Risk Factor
Factors 12345
Culture and Society Q1Local cultural inheritance Q11
Cultural heritage protection Q12
Respect for local cultural customs Q13
Cultural diversity protection Q14
Spread of advanced culture Q15
Public participation Q16
Public awareness Q17
Public satisfaction Q18
Public happiness Q19
Public credit Q110
Related organization participation Q111
Degree of project on behalf of the public Q112
Safety of employees Q113
Safety of users Q114
Safety of local community Q115
Safety of construction Q116
Safety technology training Q117
Impact on the safety of other projects Q118
Absorb local employment Q119
Social service Q120
Harmony between project and society Q121
Local employment skills Q122
Sustainable construction consciousness Q123
Local social environment Q124
Ecology and Environmental Q2Natural landscape protection Q21
Fauna and flora protection Q22
Rate of change of green coverage in built-up area Q23
Project barrier effect Q24
Rate of green coverage in built-up area Q25
Harmony between project and ecosystem Q26
Land governance Q27
Industrial sulfur dioxide emissions Q28
Industrial waste water discharge Q29
Industrial soot emissions Q210
Municipal wastewater treatment rate Q211
Domestic garbage harmless treatment rate Q212
Industrial dust removal Q213
Industrial sulfur dioxide removal Q214
Pollution control capital investment Q215
Industrial solid waste comprehensive utilization Q216
Cost and Economy Q3Cost of resettlement Q31
Cost of ecological compensation Q32
Cost of labor Q33
Cost of the user Q34
Cost of land Q35
Interest rate Q36
Foreign currency exchange Q37
Market demand Q38
Project uniqueness Q39
Inflation Q310
Project and Organization Q4Project design Q41
Project financing Q42
Project Technology Q43
Project construction Q44
Daily maintenance Q45
Synergy with other projects Q46
Renovation Q47
Project management maturity Q48
Shared resource allocation capabilities Q49
Stakeholder coordination Capabilities Q410
Project portfolio capabilities Q411
Multi-objective optimization capabilities Q412
Politics and Laws Q5Government decision-making mistakes Q51
Policy updates Q52
Political opposition Q53
Political instability Q54
Government dishonesty Q55
Project publication Q56
Government decision-making process lengthy Q57
Laws and regulations Q58
Project contract Q59
Third party default Q510

Appendix B. A Sample of Expert Scoring Table

Table A2. Expert scoring table.
Table A2. Expert scoring table.
ScoringOccurrence Probability (H)Loss and Impact (S)Perceived Degree (D)Ability to Control and Compensate (C)
Factors 12345123451234512345
Culture and Society Q1
 Local cultural inheritance Q11
 Cultural heritage protection Q12
 Respect for local cultural customs Q13
 Cultural diversity protection Q14
 Spread of advanced culture Q15
 Public participation Q16
 Public awareness Q17
 Public satisfaction Q18
 Public happiness Q19
 Public credit Q110
 Related organization participation Q111
 Degree of project on behalf of the public Q112
 Safety of employees Q113
 Safety of users Q114
 Safety of local community Q115
 Safety of construction Q116
 Safety technology training Q117
 Impact on the safety of other projects Q118
 Absorb local employment Q119
 Social service Q120
 Harmony between project and society Q121
 Local employment skills Q122
 Sustainable construction consciousness Q123
 Local social environment Q124
Ecology and Environmental Q2
 Natural landscape protection Q21
 Fauna and flora protection Q22
 Rate of change of green coverage in built-up area Q23
 Project barrier effect Q24
 Rate of green coverage in built-up area Q25
 Harmony between project and ecosystem Q26
 Land governance Q27
 Industrial sulfur dioxide emissions Q28
 Industrial waste water discharge Q29
 Industrial soot emissions Q210
 Municipal wastewater treatment rate Q211
 Domestic garbage harmless treatment rate Q212
 Industrial dust removal Q213
 Industrial sulfur dioxide removal Q214
 Pollution control capital investment Q215
 Industrial solid waste comprehensive utilization Q216
Cost and Economy Q3
 Cost of resettlement Q31
 Cost of ecological compensation Q32
 Cost of labor Q33
 Cost of the user Q34
 Cost of land Q35
 Interest rate Q36
 Foreign currency exchange Q37
 Market demand Q38
 Project uniqueness Q39
 Inflation Q310
Project and Organization Q4
 Project design Q41
 Project financing Q42
 Project Technology Q43
 Project construction Q44
 Daily maintenance Q45
 Synergy with other projects Q46
 Renovation Q47
 Project management maturity Q48
 Shared resource allocation capabilities Q49
 Stakeholder coordination Capabilities Q410
 Project portfolio capabilities Q411
 Multi-objective optimization capabilities Q412
Politics and Laws Q5
 Government decision-making mistakes Q51
 Policy updates Q52
 Political opposition Q53
 Political instability Q54
 Government dishonesty Q55
 Project publication Q56
 Government decision-making process lengthy Q57
 Laws and regulations Q58
 Project contract Q59
 Third party default Q510

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Figure 1. Sustainability risk level of 1st-level risk factors.
Figure 1. Sustainability risk level of 1st-level risk factors.
Sustainability 09 01890 g001
Table 1. Factor system of sustainability risk of PPP project.
Table 1. Factor system of sustainability risk of PPP project.
1st-Level Factors2nd-Level Factors and ContentsReferences
1. Culture and Society1.1. CultureLocal cultural inheritance[31,35,36,42,43,44,45,46]
Cultural heritage protection
Respect for local cultural customs
Cultural diversity protection
Spread of advanced culture
1.2. PublicPublic participation
Public awareness
Public satisfaction
Public happiness
Public credit
Related organization participation
Degree of project on behalf of the public
1.3. SafetySafety of employees
Safety of users
Safety of local Community
Safety of Construction
Safety technology training
Impact on the safety of other projects
1.4. SocialAbsorb local employment
Social service
Harmony between project and society
Local employment skills
Sustainable construction consciousness
Local social environment
2. Cost and Economy2.1. CostCost of resettlement[24,25,45,46,47,48,49]
Cost of ecological compensation
Cost of labor
Cost of the user
Cost of land
2.2. EconomicInterest rate
Foreign currency exchange
Market demand
Project uniqueness
Inflation
3. Ecology and Environmental3.1. EcosystemNatural landscape protection[42,43,44,50,51]
Fauna and flora protection
Rate of change of green coverage in built-up area
Project barrier effect
Rate of green coverage in built-up area
Harmony between project and ecosystem
Land governance
3.2. Environmental Pollution and GovernanceIndustrial sulfur dioxide emissions
Industrial waste water discharge
Industrial soot emissions
Municipal wastewater treatment rate
Domestic garbage harmless treatment rate
Industrial dust removal
Industrial sulfur dioxide removal
Pollution control capital investment
Industrial solid waste comprehensive utilization
4. Project and Organization4.1. ProjectProject design[35,36,42,44,45,46,47,52]
Project financing
Project Technology
Project construction
Daily maintenance
Synergy with other projects
Renovation
4.2. OrganizationProject management maturity
Shared resource allocation capabilities
Stakeholder coordination Capabilities
Project portfolio capabilities
Multi-objective optimization capabilities
5. Politics and Laws5.1. PoliticsGovernment decision-making mistakes[25,53,54,55,56,57]
Policy updates
Political opposition
Political instability
Government dishonesty
Project publicization
Government decision-making process lengthy
5.2. LawsLaws and regulations
Project contract
Third party default
Table 2. Risk assessment factor set of YRWP, Q .
Table 2. Risk assessment factor set of YRWP, Q .
1st-Level Sustainability Risk Factors Q i 2nd-Level Sustainability Risk Factors Q i j
Culture and Society Q 1 Local cultural inheritance Q 11
Cultural heritage protection Q 12
Respect for local cultural customs Q 13
Cultural diversity protection Q 14
Spread of advanced culture Q 15
Public participation Q 16
Public awareness Q 17
Public satisfaction Q 18
Public happiness Q 19
Public credit Q 110
Related organization participation Q 111
Degree of project on behalf of the public Q 112
Safety of employees Q 113
Safety of users Q 114
Safety of local Community Q 115
Safety of Construction Q 116
Safety technology training Q 117
Impact on the safety of other projects Q 118
Absorb local employment Q 119
Social service Q 120
Harmony between project and society Q 121
Local employment skills Q 122
Sustainable construction consciousness Q 123
Local social environment Q 124
Ecology and Environmental Q 2 Natural landscape protection Q 21
Fauna and flora protection Q 22
Rate of change of green coverage in built-up area Q 23
Project barrier effect Q 24
Rate of green coverage in built-up area Q 25
Harmony between project and ecosystem Q 26
Land governance Q 27
Industrial sulfur dioxide emissions Q 28
Industrial waste water discharge Q 29
Industrial soot emissions Q 210
Municipal wastewater treatment rate Q 211
Domestic garbage harmless treatment rate Q 212
Industrial dust removal Q 213
Industrial sulfur dioxide removal Q 214
Pollution control capital investment Q 215
Industrial solid waste comprehensive utilization Q 216
Cost and Economy Q 3 Cost of resettlement Q 31
Cost of ecological compensation Q 32
Cost of labor Q 33
Cost of the user Q 34
Cost of land Q 35
Interest rate Q 36
Foreign currency exchange Q 37
Market demand Q 38
Project uniqueness Q 39
Inflation Q 310
Project and Organization Q 4 Project design Q 41
Project financing Q 42
Project Technology Q 43
Project construction Q 44
Daily maintenance   Q 45
Synergy with other projects Q 46
Renovation Q 47
Project management maturity Q 48
Shared resource allocation capabilities Q 49
Stakeholder coordination Capabilities Q 410
Project portfolio capabilities Q 411
Multi-objective optimization capabilities Q 412
Politics and Laws Q 5 Government decision-making mistakes Q 51
Policy updates Q 52
Political opposition Q 53
Political instability Q 54
Government dishonesty Q 54
Project publicization Q 56
Government decision-making process lengthy Q 57
Laws and regulations Q 58
Project contract Q 59
Third party default Q 510
Table 3. Assessment comment of sustainability risk factor Q 3 .
Table 3. Assessment comment of sustainability risk factor Q 3 .
Comment P 1 P 2 P 3 P 4 P 5
Frequency
Risk Evaluation Indicators
Cost and Economy Q 3 Cost of resettlement Q 31 435613711086
Cost of ecological compensation Q 32 47951438265
Cost of labor Q 33 267510413790
Cost of the user Q 34 531071427555
Cost of land Q 35 50961448062
Interest rate Q 36 48981447555
Foreign currency exchange Q 37 751071316257
Market demand Q 38 39901409172
Project uniqueness Q 39 43901428770
Inflation Q 310 431111057356
Table 4. Values of H i ,   S i ,   D i and C i scored by five experts.
Table 4. Values of H i ,   S i ,   D i and C i scored by five experts.
Q Evaluation of 1st ExpertEvaluation of 2nd ExpertEvaluation of 3rd ExpertEvaluation of 4th ExpertEvaluation of 5th ExpertAverage
1234512345123451234512345
Q 1 H 6.6
S
D
C
W 1 7.531084.5
Q 2 H 11.8
S
D
C
W 2 312121220
Q 3 H 15
S
D
C
W 3 24158244
Q 4 H 23.34
S
D
C
W 4 1020481226.7
Q 5 H 7.8
S
D
C
W 5 10106.748.3

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MDPI and ACS Style

Bai, L.; Li, Y.; Du, Q.; Xu, Y. A Fuzzy Comprehensive Evaluation Model for Sustainability Risk Evaluation of PPP Projects. Sustainability 2017, 9, 1890. https://doi.org/10.3390/su9101890

AMA Style

Bai L, Li Y, Du Q, Xu Y. A Fuzzy Comprehensive Evaluation Model for Sustainability Risk Evaluation of PPP Projects. Sustainability. 2017; 9(10):1890. https://doi.org/10.3390/su9101890

Chicago/Turabian Style

Bai, Libiao, Yi Li, Qiang Du, and Yadan Xu. 2017. "A Fuzzy Comprehensive Evaluation Model for Sustainability Risk Evaluation of PPP Projects" Sustainability 9, no. 10: 1890. https://doi.org/10.3390/su9101890

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