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The undertaking of construction projects in metropolitan areas is a risky, competitive, and dynamic proposition requiring a reliable risk assessment model for adequate planning. This study employs a fuzzy multiple criteria decision making (FMCDM) approach to systematically assess risk for a metropolitan construction project. Consistent fuzzy preference relations (CFPR) are used to measure and investigate the relative impact on project performance of twenty identified risk factors included in four risk dimensions. The fuzzy multiple attributes direct rating (FMADR) approach is employed to analyze the probable occurrence of multiple risk factors. Finally, the level of risk for the overall project caused by individual risk factor is evaluated based on synthesized analysis of the relative impacts and probability of occurrence. The implementation of FMCDM makes the proposed risk assessment approach more reliable and practical than the traditional statistical approach. The proposed approach can be employed by project management to evaluate the overall project risk, and the process of determining the risk criteria and perceived level of risk could eliminate much wasted information.
Keywords: construction risk; risk assessment; consistent fuzzy preference relations; fuzzy multiple attribute direct rating
Rapid economic development has increased the demand for the construction of public and private infrastructure and facilities in metropolitan areas worldwide and has resulted in the undertaking of numerous public construction projects. Compared with projects in urban and rural areas, construction projects in metropolitan area not only attract more attention but are also much more risky, competitive, and dynamic since their surrounding environments are complicated in terms of transportation, the number of stakeholders, the removal of any existing facilities, and the existence of pipelines utilities connections. At the present time, construction firms often fail to take a proactive approach in their treatment of the uncertainties of metropolitan construction projects. As a consequence, project delays and budget overruns are commonly encountered when problems arise due to overlooking potential risks. Insufficient information and ineffective management of project risks not only cause project cost overrun, completion delays, and even termination prior to completion, but also negatively impact the project team's reputation. To improve the chance of success and reduce potential risks, in the initial phase, project risks and uncertain factors should be carefully identified, assessed and monitored.
Construction projects are well known for their unique and uncertain characteristics. Three approaches have commonly been applied in construction project risk assessment: probability analysis (Elkjaer, 2000; Titarenko,1997; Ye and Tiong, 2000; Adams, 2008), interval analysis (Mak, and Picken, 2000; Baccarini and Archer, 2001; Chapman, 2001), and fuzzy set analysis (Tah and Carr, 2001; Lu et al., 2001; Rebiasz, 2007; Sadiq et al., 2007). Probability analysis techniques include sensitivity analysis, basic probability analysis, decision-tree analysis, and Monte Carlo simulation techniques. Interval analysis estimates plausible ranges of results based on ranges for the input variables. Recently, fuzzy set theory has been used to solve uncertainty problems, especially when probability information is limited and when the boundaries of variables are not obvious (Chen and Hwang, 1992; Tah and Carr, 2000; Sadiq et al., 2004).
Effective management of project uncertainty can improve performance but detailed information and the experience if past project risk management is required for the risk assessment process. There are several factors that affect construction project risk such as construction type and location, the characteristics of the work site and project team, and the time. To estimate construction project risks in a more precise way, project risk assessment should subjectively address the unique and uncertain characteristics of construction projects. Past studies have discussed some of the problems and shortcomings of methods used to conduct project risk assessment in civil engineering fields (Faber and Stewart, 2003). One of the major problems explored is the lack of practical risk assessment techniques, which are urgently needed to increase the credibility of the results of risk assessment. This study therefore proposes a more systematic and practical approach than the traditional ad-hoc project risk assessment strategy for assessing risk in metropolitan construction projects. The proposed approach employs consistent fuzzy preference relations (CFPRs) to assess related potential negative impact on a metropolitan construction project caused by the occurrence of identified risk factors. In addition, fuzzy multiple attribute direct rating (FMADR) is used to assess the possibility of occurrence of various risk factors. The relative impact and possibility of occurrence are further integrated to determine the causal project risk for each factor of interest. For detailed risk assessment one needs to carefully identify a project's vulnerability factors and evaluate their impact on project performance, a complicated process which frequently impedes the implementation of project risk management. This study proposes an improved and more practical approach to facilitate the project risk assessment for a metropolitan construction project.
The rest of this paper is organized as follows. Section 2 explores the hierarchical structure of project risk factors for a metropolitan construction project. Section 3 introduces the concept of FMCDM and proposes a novel approach for quantifying project risks. Next, Section 4 describes a practical example of the proposed approach. Finally, Section 5 concludes the study by presenting the findings and managerial implications of the proposed risk assessment approach, and offering recommendations for further work in project risk assessment.
2. Hierarchical structure of project risk factors
Risk analysis and assessment are critical components of the overall risk management process, since risk management plans are deployed based on the results. Risk analysis identifies sources of risk as they exist and emerge; that is, it identifies potential risk factors or risk items. Risk assessment further computes project risk by evaluating the potential impact on project performance and possibility of occurrence of these potential risk factors (Zhang, 2007). This section describes the proposed risk analysis and assessment process for overall project risk evaluation applied to a metropolitan construction project.
Sources of risk in construction projects have been investigated in several past studies. Frequently identified categories of risk factors for construction projects are listed in Table 1.
Insert Table 1 here
Potential risk factors impacting on metropolitan construction projects were carefully selected and synthesized from the literature review and several expert interviews. Several experts in the field (see the profiles displayed in Table 2) were asked to verify the framework of potential risk factors for a metropolitan construction project. They can be classified into five dimensions: engineering design, construction management, construction safety-related, natural hazards, and social and economic. Figure 1 presents the final hierarchical structure of potential risk factors for metropolitan construction projects. The hierarchy includes twenty risk factors divided into five groups, and detail descriptions list in table 3.
Insert Table 2 here
Insert Table 3 here
Insert Figure 1 here
3 Investigating Project Risk Elements
Project risk assessment usually includes the evaluations of two parameters, the likelihood of risk factors and the impact of risk factors on project performance.
3.1 Relative impact of risk factors
This study measures the relative impact of risk factors by asking participating experts in the field to consider the mean magnitude of pair-wise unintentional events and then evaluate the comparative impact of pair-wise events on project performance. However, it is not realistic to assume that different project risk factors will affect project performance equally. To better manage project risks and increase chances of project success, the relative impact of risk factors on project performance should be carefully evaluated and further used as fundamental information for the control, response and management of project risks. That is, the varying degree of impact of each risk factor on project performance could provide valuable information for the allocation of construction project resources and developing the associated project risk prevention countermeasures to enhance project success.
Approaches that have proven effective for evaluating risk factors include the eigenvector method, weighted least square method, entropy method, and linear programming techniques for multi-dimensional of analysis preference (Hwang and Yoon, 1981; Mon et al., 1994). The analytic hierarchy process (AHP) was developed (Saaty, 1977; 1980) to solve decision making problems and has been employed in the construction industry for many decision making problems (Fong and Choi, 2000; Al-Harbi, 2001; Mahdi et al., 2002; Cheung and Fung, 2002). Some of these studies applied have also AHP to risk assessments (Dikmen and Birgonul, 2006; Sadiq et al., 2007; Lu et al., 2007; Zeng et al., 2007; Zayed et al., 2008; Lu, 2010).
The conventional AHP has been extensively refined, because the process of asking participating experts to evaluate the relative impacts between two criteria has proven difficult and inefficient when a huge number of pair-wise criteria comparisons is required or inconsistencies in the collected data are encountered. To enhance and simplify the operations of the AHP, the consistent fuzzy preference relations (CFPR) approach has been developed. For example, Herrera-Viedma et al. (2004) proposed such an approach to deal with the issue of inconsistency in data collection and reduction of the number of comparisons required for the implementation of AHP. This study employs CFPR to evaluate the relative impact of identified risk factors on project performance in metropolitan construction projects.
The CFPR approach is used to construct decision matrices of pair-wise comparisons based on additive transitivity (Herrera-Viedma et al., 2004). It requires a decision maker to assign values for a set of criteria. The value represents the degree of the preference for a criterion over another criterion. The concept and steps of using the CFPR are described below.
(1) Determining a CFPR sequential pair-wise comparison matrix
Sequential and adjacent pair-wise comparison matrices for CFPR are constructed from among the five identified risk dimensions and all investigated risk factors in each identified project risk dimension. Each participated expert was asked to input their subjective judgment of the relative impact of each pair-wise risk dimension and factors by sequential pair-wise comparison. The diagonal elements of the positive reciprocal matrix are developed using Eq. (1)
where is a fuzzy value indicating the comparative impact of risk factor i over risk factor i+1 on project performance, for m experts participating in the evaluations. The geometric mean approach (Buckley, 1985) formulated as in Eq. (2) can be used to synthesize the evaluations of m experts
where is the fuzzy value of the relative impact of risk factor i over risk factor i+1 on project performance according to the mth evaluator.
(2) Multiplicative preference relations
The matrix , , represents the multiplicative preference relations for a set of X criteria, where represented the ratio of preference intensity of criterion to criterion . The ratio of preference intensity with a scale from 1-9 suggested by Saaty (1980) is employed in this study to measure the relative impacts of risk factors on construction project performance. Herein, indicates equal importance between criteria and , indicates that is absolutely important compared to . Preference relation matrix A is typically assumed to be multiplicative reciprocal as presented as Eq. (3). The reflected fuzzy values of the subject levels used in this study are displayed in Table 4.
Insert Table 4 here
(3) Fuzzy preference relations
The fuzzy preference relation for a set of criteria X is a fuzzy set with a membership function . The preference relation is represented by matrix, where. Herein, is interpreted as the level of preference for criterion over . If , it means that and are equally important (i.e.,~); indicates that is absolutely important/preferred to ; shows that is more important/preferred to , i.e., . In this case, the preference matrix, P, is usually assumed to be additive reciprocal as in Eq. (4)
(4) Consistent fuzzy preference relations
A set of alternatives and are associated with reciprocal multiplicative preference relations for . Then, can be used in Eq. (5) to obtain the corresponding reciprocal fuzzy preference relation for associated with A:
Here, is used to transfer to , becauseis between 1/9 and 9. Additive transitivity, with the relationships as in Eq. (6) and Eq. (7), is one of the suggested properties when the reciprocal fuzzy preference relation is consistent (Herrera-Viedma et al., 2004).
(5) Determining the priority of risk factors
After obtaining the preference intensity ratio of criteria/alternative from the experts' judgments as in Eq. (1), then Eq. (5) can be used to construct a fuzzy preference relation for the set of n-1 values . Then the other preference relation values for decision matrix , will be obtained using Eq. (4), Eq. (6) and Eq. (7). However, when Eq. (6) and Eq. (7) are used to calculate preference relation values all the necessary elements in the decision matrix P may not lie within [0,1]; some may lie within , where . In this case, the transformation function , displayed in Eq. (8), should be employed to develop the consistent reciprocal fuzzy preference relation matrix . This transformation process can remain the decision matrix with reciprocity and additive consistency
This method is utilized to assess the relative impacts on project performance of the risk factors. The obtained assessment decision matrix, , shows the consistent reciprocal relation. Eq. (9) and Eq. (10) can now be applied to determine the multiplicative preference relations matrix associated with the relative impacts of risk factors on project performance
(6) Determining relative impact on project performance
The last step to explore the relative impact of risk dimensions and factors on project performance is to investigate the set of eigenvalues for pair-wise comparison matrix for weighting solutions. The reflected eigenvector W of the maximum eigenvalue shown in Eq. (11) is the set of relative impacts of investigated risk dimensions and factors. The final assessment results can be used to determine the priority of the relative impacts of identified risk dimensions and factors on construction project performance
3.2 Determining the probability of occurrence of risk factors
The FMADR was used to evaluate the probable occurrence of risk factor of interest in metropolitan construction projects. The methodology and procedures for the FMADR theory are described below.
(1) Fuzzy Numbers
A fuzzy number is a fuzzy subset of real numbers, which can be viewed as an extension of a confidence interval. A fuzzy number denoted as is comprised of a fuzzy set, and its membership function, which is denoted as .
(2) Triangular Fuzzy Numbers (TFN)
In many cases, it is difficult for an expert to us an exact numerical value to estimate his/her degree of preference. Another possibility is to use linguistic labels. Such linguistic assessments are merely approximate. Pedrycz (1994) verified that linear triangle membership functions are good enough to capture the vagueness of these linguistic assessments with a fuzzy modeling mechanism. Equation (12) represents the membership function of a triangular fuzzy number (TFN), denoted as , where L, M and U are the lower limit, modal value and upper limit of fuzzy number, respectively. The mathematical computation of two fuzzy numbers has been described in greater detail elsewhere (Hsieh et al., 2004):
(3) Linguistic variables
A linguistic variable may use words or sentences expressed in a natural or artificial language instead of a number to represent a situation. Figure 2 shows the linguistic variables employed in this study to evaluate the occurrence probability of risk factors. The membership function of each fuzzy number is defined by three parameters representing the left point, middle point, and right point of the defined range. Table 5 shows the linguistic variables and fuzzy number scale used for quantification in this study.
Insert Figure 2 here
Insert Table 5 here
The possibility of occurrence of project risk factor i evaluated by expert k can be denoted by, as in Eq. (13). Here, S represents the set of overall project risk factors
and respectively represent the lower limit, modal value, and upper limit of the occurrence probability of the interesting risk factor i, evaluated by the kth evaluator. in Eq. (14) indicates the average fuzzy value of the occurrence possibility of project risk i evaluated by m experts. Thus
where symbolizes fuzzy multiplication and denotes fuzzy addition. The TFN of the synthesized occurrence possibility matrix for m evaluators is displayed in Eq. (15). The equations for the computation of , , and are adopted from Buckley (1985) and displayed in Eq. (16) below:
, , (16)
A defuzzification method is needed to transform the obtained fuzzy values into their optimal nonfuzzy assessed crisp values, which represent the possibility of occurrence of the risk factors of interest. Defuzzification methods include the mean of maximal (MOM), center of area (COA), and ¡-cut, etc (Zhao and Govind, 1991; Lu et al., 2001). The ¡-cut approach is employed in this study as in Eq. (17). This method was derived from Liou and Wang (1992) and has been applied in the studies of Wu et al. (2008) and Chang et al. (2009). The advantage of this method is that it can explicitly display the preference () and risk perception () of the decision makers. Notably, can be viewed as a stable or fluctuating condition (Wu et al., 2008). When, it means that the range of uncertainty is the greatest; indicates that variance for decision making is most stable; can be viewed as the degree of the decision maker's optimism. When , the decision maker is more pessimistic and when , the decision maker is more optimistic (Liou and Wang, 1992). The number ranges from 0 to 1 are frequently used to represent the mental state of the decision maker. This study assigned a value of 0.5 to both and to indicate moderation by a decision maker.
(5) Determine project risk
The effects and occurrence possibility of risk factors in a metropolitan construction project should be integrated to evaluate the overall project risk. This integrated computation is presented as in Eq. (18)
where , and .
The purpose of this study is to set up an improved and more practical approach to facilitate project risk assessment for a metropolitan construction project. The project risk value is defined as the product of the impact of the factors and the probability of occurrence. The results of the project risk value application are mainly used for comparison, either for preparation of the bid for project selection or initiation or for the allocation of more resources for riskier items. Project managers can adopt the most suitable elements and components to investigate to produce an overall project risk value and further deploy strategies to monitor and manage project risks after initiation or successful acquisition of a project.
4. Case Study
The proposed risk assessment approach is demonstrated using data from a metro system construction project in the city of Taipei. Five experts with more than fifteen years experience in construction project management who are familiar with construction project risks were recruited to participate in this demonstration. The investigated project involved underground construction in a heavy traffic area. The scope of the targeted construction project includes building an underground station for the Taipei Metro system, which requires deep excavation, as well as protective measures for deep excavation, and drainage work.
Some difficulties encountered with the application of CFPR for evaluation of the relative impact of identified risk factors that have been identified in past studies should be corrected. When CFPR is employed to evaluate the relative impact of risk dimensions and risk factors on project performance, high preference relation values between two criteria could increase the chance of measurement bias and inconsistency (Herrera-Viedma, 2007). Therefore, the relative impacts of identified risk dimensions and risk factors on project performance should be initially assessed to roughly determine the ranking sequence. The rough ranking information is used to design the CFPR questionnaire.
This study measures the pair-wise preference relations between two risk dimensions and two risk factors with a close degree of impact on project performance. We first ask the participating experts to rank the relative impact on metropolitan construction project performance of identified risk dimensions and identified risk factors in each risk dimension. Five experts with knowledge of risk assessment were selected from the group to be interviewed to verify the framework of project risk factors. The ranking results were further used to arrange pair-wise comparative questions for evaluation of the relative impact of identified risk dimensions and factors in the CFPR questionnaire. The preliminary preference ranking results, based on Figure 1 and presented in Table 6, were used to rearrange the risk dimensions and risk factors into a hierarchical structure of risk dimensions and risk factors, displayed in Figure 3, to facilitate the design of the CFPR questionnaire.
Insert Table 6 here
Insert Figure 3 here
The experts were asked use a linguistic variable rather than a crisp value to identify the level of the relative impact of the pair-wise risk dimensions and pair-wise risk factors. The results are displayed in Table 7. The relative impacts were then further synthesized using Eq. (2) to obtain Table 8. Furthermore, the preference intensity ratio matrix was transferred to the CFPR matrix by applying Eq. (5). The other preference relation values for the CFPR matrix were calculated using Equations (4), (6) and (7). The CFPR matrix was transformed using Eq. (8) when there are preference relations values outside of [0,1] so as to retain reciprocity and additive consistency in the decision matrix. Finally, Eq. (9) was employed to obtain the complete preference intensity ratio matrix as in Eq. (10). The eigenvector approach described in Eq. (11) was further employed to compute the relative impact on project performance of each risk dimension and interesting risk factor. Table 9 shows the results of the relative impact of risk dimensions and risk factors on metropolitan construction project performance.
Insert Table 7 here
Insert Table 8 here
Insert Table 9 here
Another objective of this study was to determine the possibility of the occurrence of each identified risk factor. The occurrence possibility data, presented in Table 10, collected from five participated experts, were synthesized based on Equations (14)-(16) and then defuzzified using Eq. (17). The relative impact and occurrence probability were further integrated using Eq. (18) to estimate the level of risk induced by the identified risk factors. Table 11 presents the estimated level of risk for the investigated risk factors.
Insert Table 10 here
Insert Table 11 here
4.1 Relative impacts of project risk dimensions
The relative impacts of five risk dimensions on project performance as indicated by the five experts were synthesized and analyzed. CFPR was employed to evaluate the relative impacts of the five identified risk dimensions and their associated risk factors. The results are presented in Table 8. It can be seen that it is engineering design and natural hazard risks that have the greatest negative impact on project performance among the five risk dimensions. Although natural hazard risks, having the second highest relative impact, could cause extensive damage to construction projects, advanced prediction technologies and compulsory insurance have improved the risks. Compared to natural hazard risks, engineering design risks do not cause extensive damage but are frequently encountered and have a considerable effects to the project performance in a complicated construction project. Other than enhanced management to reduce risk, no effective methods of risk transfer and risk reduction have been developed for alleviation of engineering design risks. Among the five risk dimensions, construction management risks have the lowest impact on construction project performance for metropolitan construction projects.
4.2 Relative impacts of identified risk factors
Among the twenty identified risk factors in the five risk dimensions, ground water seepage, typhoons, conflicting interfaces between work items, design drawing errors, and heavy rainfall are the five risk factors with the highest relative impacts on construction project performance. Underestimation of ground water seepage can lead to substantial damage at underground construction sites because it affects the soil structure in the excavation areas. When construction work is carried out based on design drawings with errors, time and money are wasted and other construction processes may be delayed in order to apply changes and corrections. Conflicting interfaces between work items can lead to serious project delays especially for metropolitan construction projects which usually have a limited area and space for multiple crews to work simultaneously. Typhoons and heavy rainfall are other risk factors that have a significant influence on construction project performance.
4.3 Risks of identified risk factors
The risks associated with the twenty identified risk factors on metropolitan construction project performance were further evaluated and discussed. Ground water seepage is the factor with the highest percentage of overall risk based on the synthesized analysis of relative impact and occurrence possibility of investigated risk factors. Underestimation of ground water seepage can cause serious damage to underground construction sites due to the lack of prediction, protection and response measures for ground water seepage. Among the twenty investigated risk factors, heavy rainfall and typhoons had the second and fifth highest percentage of the overall risk value. Global climate change has increased the frequency of heavy rainfall and strong typhoons. Conflicting interfaces between work items and design drawing errors have the third and fourth highest percentage of the overall risk value among the twenty investigated risk factors. The complexity and the limited site area and space available for metropolitan construction projects drive the frequency of occurrence of these two factors.
It is difficult to demonstrate the effectiveness of risk management by assessing project performance unless the long term processing data are well tracked and documented and logical inferences are well implemented. It takes a long span of time and large cost to demonstrate the effectiveness of project performances. This is a major obstacle to implementing risk management for a project or a company. However, risk management is treated as a requirement for project success and the whole process is implemented in research and development (R&D) projects in many sectors such as electronics, automobile, air transportation and railway transportation to assure the quality of the products in these fields. The effectiveness of risk management necessitates a serious review of the risk management process which includes identifying, assessing and managing risks.
This study proposes an improved procedure to conduct risk assessments for construction projects. We propose a framework to facilitate the process of risk identification for construction projects. We review the literature published in the past few years related to construction risks and double check the risk items with experts. The FMCDM approach is also employed to assist the process of evaluating and assessing identified risks. The consistent fuzzy preference relations (CFPR) proposed by Herrera-Viedma et al. (2004) and fuzzy linguistic algorithm methods are employed to enhance the risk management process. Both tools are based upon robust fundamental theory. The enhanced process assists experts to evaluate the perceived risks to construction projects through a clear definition of identified construction risks and the utilization of fuzzy linguistic algorithms. The application of CFPR eliminates the frequent problem of inconsistency in collected data when the traditional AHP is adopted.
To further validate the proposed process, 18 project managers with more than 10 years experience in metropolitan construction projects are interviewed to confirm the validity of the proposed process for "facilitation of operating the proposed risk assessment steps", "applicability of the proposed risk assessment process for metropolitan construction projects", "completeness of the investigated risk factors for general metropolitan construction projects", and "being valuable to the strategic planning of metropolitan construction projects". After understanding the theory and operations of the proposed process almost 90% of project managers interviewed,, gave positive results to the four interview questions.
The application of fuzzy concepts to collecting pair-wise comparison data on occurrence probability and information of the impact on project performance obtained from engineers confirms that the proposed process facilitates the data collection process. This could increase the willingness of participating engineers to give their perceptions of risk information for the targeted projects. In this study, the "average" approach is adopted for synthesizing expert opinions on risk evaluation. This approach is considered compromised when there is a significant discrepancy in the opinions of experts. In future, group decision making could be adopted to reduce the discrepancy in opinions and increase the effectiveness of the proposed approach.
Effective risk management of construction projects requires a reliable risk assessment and risk treatment plan. Traditional risk assessments were usually performed using statistical analysis, which requires substantial data associated with construction risks. In reality though, risk perception and knowledge related to metropolitan construction projects are usually only available from very few experts participating in the planning, design and construction phases. This study proposes a reliable approach for assessing risk in metropolitan construction projects based on direct and subjective expert judgments. The proposed risk assessment approach is more practical and reliable than the traditional statistical methods since it utilizes the experts' perceptions of project risk and uses a small sample size which maintains data quality. In the past, AHP was frequently employed to measure the relative weight of factors for decision making and inconsistent information was frequently collected which reduced the credibility of the results. This study uses Consistent Fuzzy Preference Relations to facilitate the operations of collecting pair-wise comparative impact information for risk dimensions and risk factors. In addition, CFPR also eliminates inconsistencies in the collected information. However, there are a few concerns in the implementation of CFPR. After pair-wise comparative impacts are collected, the ranking order should be roughly determined in advance of pair-wise comparison evaluation to enhance the measurements based on the experts' subjective judgments of comparative preference value.
The proposed approach not only assesses overall project risk, its concept and process can also be used to evaluate the risk of a work item or a series of work items such as excavation, structural work, concrete work, and electrical work when a detailed hierarchical structure of risk factors for the work of interested is established. The high risk factors should then be carefully monitored, controlled and managed to improve the chance of project success and work success.
In this study, risks of individual risk factors on project performance were evaluated by multiplying the relative impact and occurrence possibility. The overall risk value of a project was calculated based on the assumption of the additive characteristic of the risk values for associated risk factors without concern for realistic multiplicative impacts simultaneously caused by multiple risk factors. The efficacy of the aggregate risk values for varied risk factors is therefore suspect and arguable. An improved approach could be applied in future studies, such as the inclusion of fuzzy integrals, to investigate overall project risk with the considerations of multiplicative impacts of risk factors to enhance the proposed approach.