Fuzzy Model for Risk Evaluation in Construction Projects
AMAURY A. CABALLERO AND KANG K. YEN
Department of Electrical and Computer Engineering
Florida International University, Miami, Florida
USA
Abstract: - When dealing with activities that are uncertain and variable, associated risks are often permanent and complex. Traditionally, many risk analysis models are based on quantitative techniques, which require numerical data. In industrial projects, the consequences of not taking the different risk factors into account are related to failure in the form of unusual delays in project completion, with cost surpassing the budgeted cost and sometimes even failing to meet quality standards and operational requirements. Thus, effective analysis and management of industry-associated risks remain a big challenge to the industry practitioners. The purpose of this work is to establish a simple method of evaluating the risk and uncertain factors that are present in a construction project. The research uses as a basis a questionnaire survey and in-depth interviews conducted in the State of Florida. From this information, a risk management fuzzy logic model for the construction sub-contractors is proposed.
Key Words: Construction, Risk management, Risk allocation, Project management, Fuzzy logic models.
1 Introduction
Different parties in a construction project face a variety of uncertain factors. These factors can be compiled under the category of risk. Making decisions on the basis of assumptions, expectations, estimates and forecasts of future events involves taking risks. Risk and uncertainty characterize situations where the actual outcome for a particular event or activity is likely to deviate from the estimate or forecast value [1].
The process of taking a project from initial investment appraisal to completion, then into use, is complex, generally bespoke, and entails time-consuming design and production processes. It requires a multitude of people with different skills and expertise and the coordination of a wide range of disparate, yet interrelated activities. Such complexity, moreover, is compounded by many external, uncontrollable factors [2].
In the context of project management, risk management is defined as: "A formal orderly process for systematically identifying, analyzing, and responding to risk events throughout the life of a project to obtain the optimum or acceptable degree of risk elimination or control" [3]. In practice, a risk management system must be practical, realistic and must be efficient on cost and schedule control. In any industrial project, an effective risk management system depends very much on the characteristics and conditions of the project and the attitude of the individuals of the decision-making group.
The risk management, which embraces risk analysis and risk response, is a matter of increasing significance. The effect of not delivering a project according to its predetermined requirements can be disastrous to all parties concerned. In analyzing the causes of project failures, it is clear that little or no attention has been paid to the problems that can materialize in most projects.
2 Identification of Critical Risks
As shown in Figure 1, risk identification process is the first step in risk management modeling. It is the process of systematically and continuously identifying, classifying, and assessing the risks associated with a project. In this research, the critical risks were identified in three stages as follows:
Fig. 1. Steps Adopted for Building a Risk Management Model
· Identification of all possible risks, which may be encountered by a risk analyzer through detailed literature and Internet search.
· Identification of critical risks that may apply to the particular case under analysis. These risks are identified from a list generated through a questionnaire to practitioners in the field.
· Verification of critical risks via interviews with professionals.
There are two factors that are always present when analyzing risk: the probability or chance of occurrence of the different possible events, and the maximum potential loss, expressed as a percent of the total cost lost due to each event. These two factors will be used as inputs in the fuzzy logic model.
3 Development of the Risk Management Fuzzy Logic Model
The risk management model for any application has to be developed based on a systematic methodology of risk identification, risk classification, risk allocation and risk response. This risk management information, can be used by the risk manager to accurately classify the identified risk element, estimate their chance of occurrence to decide whether to avoid the risk completely, retain it and try to reduce its impact by taking preventive steps, or finally, transfer it to a party better able to handle it. From the obtained information, a mathematical model can be developed. This model gives the manager a quantified evaluation of the risk that can be used as an element to compare different projects.
Fuzzy logic appears like an attractive tool for solving this task. As indicated by Zadeh [4], it is very difficult for conventional quantification to express reasonably those situations that are complex or hard to define. From this, the notion of a linguistic variable is necessary. A linguistic variable is a variable whose values are words or sentences. Here these expressions are used to compare two uncertainty factors.
Let’s define the vector C, as the chance of occurrence of the different possible events. This vector can be represented through:
C = [C1, C2, … , CN ], (1)
where CN is the chance of occurrence of event (type of risk) number N, which will vary in general from one project to another.
The vector M will represent the Maximum Potential Loss, expressed as a percent of the total cost lost due to each event. Where,
M = [M1, M2, ……., MN ], (2)
which is defined in a similar way to the previously defined C.
These two vectors have been found in different surveys as the most important factors affecting the risk. Both vectors can be taken as fuzzy inputs in a fuzzy model, where the risk vector R will be the output. This risk vector will be represented through:
R = [R1, R2, ………RN], (3)
where RN is the risk incurred due to the event N.
There are two ways of assessing the risk depending on the type of combination process [5]. In the first one, each expert system or fuzzy policy is executed as a stand-alone component. The result of the policy is used by the risk assessment manager to derive a final value on a scale between zero and one hundred. The other approach (used in this work) combines expert intelligence inside the model. The result of this aggregation, a final outcome fuzzy set, is then defuzzified using the center of gravity technique to produce a risk assessment measure.
As indicated in [6] and [7], fuzzy measure F(X), is a set function defined on the power set R(X) of X, and satisfies the following properties:
a) F(0) = 0 and F(X) = 1; (boundary conditions)
b) if A,B Î R(X) and A £ B then
F(A) £ F(B); (monotonicity)
c) if Fk Î R(X) for 1 £ k £ ¥ and a sequence {Rk} is monotone, then
lim k®¥ F(Rk) = F(lim k®¥ Rk); (sense of inclusion).
A l-fuzzy measure Fl is a fuzzy measure with the following characteristic:
" A,B Î R(X), A Ç B =Æ,
then for l = 0,
Fl (AÈB) = Fl(A) + Fl(B) (4)
Implying that A and B have additive effect. This means that the evaluation of the set {A,B} equals the sum of evaluations for sets {A} and {B}. In other words, it is possible to add the results for each fuzzy output for obtaining a fuzzy general output, assuming that each of them is independent from the other. This result can be extended for obtaining an average value of the different fuzzy sets outputs.
The universe of discourse of the Chance of Occurrence has been defined between 0 and 6. The center of gravity of each membership function has been located as follows: very low (VL)—1; low (L)—2; medium (M)—3; high (H)—4; very high (VH)—5. The Maximum Potential Loss membership functions have been evenly distributed between 0 and 50%. The output Risk is represented as fuzzy functions varying from 0 to 100%, where 0 is no risk at all and 100% is the certainty of occurrence of a non-desired situation. For applying fuzzy logic to each event, the rule set can be selected for each particular case. The rules structure is of the type “if X and Y, then Z”. This rule set may be changed in dependence of the real conditions under which the project is developed.
4 Illustrative Example
Construction is a highly risk-prone industry with not a very good track in dealing with risks. A questionnaire was distributed to construction subcontractors involved in different specialty trades such as concrete, earthwork, HVAC, piping, etc.in the state of Florida, USA.
In this questionnaire different parameters related to the risk involved in the activity were considered. These parameters were: Acts of God, Construction Related, Design related, financial, Physical, and Socio-Political. For each parameter a response was solicited, related to the chance of occurrence and the maximal potential loss. The response was given for each parameter as: Very low (VL), Low (L), Medium (M), High (H), or Very High (VH).
The responses for each parameter, from the different subcontractors, were averaged to obtain a final value for each parameter. As indicated by Kostko [8], “for combining q experts or fuzzy systems
Fk: Rn Rp (5)
The q systems can be viewed as q experts or knowledge sources. Then the combined output F(x) answers a question: What do we conclude from the answers of q experts when we ask them question x?” The proposed way is to use a weighted average.
A fully weighted average normalizes the sum with the sum of credibility weights and has the form of a minimum-variance average:
(6)
where Fk(x) is the expert evaluation of a concrete situation and wk Î [0, 1] are the experts’ credibility weights.
In the composition, the assigned number to each response was the same used for the center of gravity of the correspondent membership function. The Risk is presented on a scale from 0 to 100%. In this application, only the factors with high incidence in this particular place have been taken into account. The results are given by the used fuzzy logic software [9].
Figure 2 shows the surface representation for the risk as per the selected ranges of the input variables and the established fuzzy rules. The figure gives a general idea of the risk variation as a function of the Chance of Occurrence and the Maximal Potential Loss.
The obtained values for each risk category provide management knowledge on the risk and uncertainty inherent in a project and lead to better decision outcomes. It could be desirable to represent the average risk as some number expressed in percent. The task here is to combine the results for each risk parameter after the defuzzification process, in other words, reducing the amount of available information in the model to a single scalar. This calculation will give a number that could help in getting an idea of the average risk, but the particularities of the process being modeled will be hidden (part of the information will be lost), as expressed by Cox [5]: “this single point in the fuzzy hyperspace carries only two dimensions of information: the expected domain value (the horizontal displacement in the fuzzy set), and the value’s degree of membership in the output fuzzy set (the vertical displacement in the fuzzy set). Repeated combinations of fuzzy models at this level tend to increase the overall information entropy associated with the entire system.” The result is a loss of information that increases as the results of many independent fuzzy models are averaged.
The simplest way of getting the average is assuming statistical independence among all the events, as per equation (4), and giving them the same weight, the obtained risk average for the presented situation can be calculated from
N
Rav = 1/N[ S Ri (7)
i = 1
where N is the number of events (type of risk).
Figure 2. Risk Surface Representation (X: Occurrence; Y: Loss; Z: risk)
5 Conclusions
1. In this study, the critical risks were identified in three stages as follows:
· Identification of all possible risks, which may be encountered in a construction project by a sub-contractor through detailed literature and Internet search.
· Identification of critical risks in the Florida construction industry. These risks were identified from the list generated in the first step through the questionnaire.
· Verification of critical risks in the Florida construction industry via interviews with professionals
2. The concept of risk management is relatively new to the Florida construction industry. The responses to the questionnaire reveal that most sub-contractors are not carrying out formal risk management. In fact, some responses were received stating that they were not aware of a discipline called risk management. It appears that Florida sub-contractors are still not aware of the great benefits that risk management provides or can provide to the construction industry. It is found that the Florida construction industry prefers to eliminate and transfer risks instead of finding a systematic procedure to deal with them through such techniques as risk retention or risk reduction.
3. The fuzzy logic model gives the sub-contractor a quantified evaluation of the risk that can be used as an element to compare different projects. There exist several advantages when implementing decision-making models based on fuzzy logic:
· Experts related to the problem area can present their evaluation of the different parameters with concepts such as “worse”, “better”, etc., without having to numerically quantify their opinions from the beginning of the evaluation process.
· The calculus using fuzzy logic is simple and close to the representation of knowledge.
· There is a wide array of software available for solving problems utilizing fuzzy logic.
References
[1] Raftery, J. Risk Analysis in Project Management, E & FN Spon, London SE1 8HN, UK. 1994.
[2] Flanagan, R., and Norman G. Risk Management and Construction. Blackwell Scientific Publications, Oxford, London, 1993.