# INTUITIVE AND USABLE RISK-BASED COST CONTINGENCY ESTIMATION MODEL FOR GENERAL CONTRACTING FIRMS

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2 risk analysis steps and the implantation of the proposed contingency estimation model. 2. MODEL DESCRIPTION & IMPLEMENTATION The proposed integrated cost contingency model uses a risk management process as depicted in the figure below (Fig. 1) and Monte Carlo simulation as its engine to model uncertainties. The model implementation has been done using a VBA based on Palisade Excel add-in program. This section describes each step in detail with examples of the model. (1) Contractor Estimate Contracting firms have their own established practice of determining project budget and contingency. They typically have estimating templates in a spreadsheet format, which encapsulate their estimating experience and process. It is important, therefore, to preserve their process in the risk analysis so that they can focus on extracting their experience and expertise, not learning the new system. Thus the proposed model is based on a contracting firm s estimating spreadsheet as a starting point for the series of risk analyses. Fig. 2 shows an example of the estimate template and data of a firm, which provides a deterministic base estimate. Fig. 2 Contracting Firm s Estimate Template and Data Fig. 1 Risk Analysis Steps in the Proposed Model (2) Uncertainty Analysis One of the basic components needed for the risk analysis is the identification of uncertainties affecting the base cost 194

3 estimate, affecting unit prices or quantities in the cost estimate. Internal uncertainty is the uncertainty associated with the items listed in a cost estimate or activity durations; this uncertainty is caused by incompletely defined estimation parameters or incomplete knowledge. External uncertainty arises from risks that are beyond the immediate scope for the project [3]. In the cost risk analysis model, every cost component with a potential for variability is modeled as a random variable. The most common way to model this variability is the use of probability density distributions. A Monte Carlo simulation (MCS) adopted in the model uses the probability distribution functions (PDFs), from which a random sample of values is generated to represent the variability. Several authors claim that the triangular distribution is as good as other distributions and is preferred due to its simplicity [4,5]. The generated random values and the constant cost figures (cost components that are considered to have no variability) are added up and a value for the total cost is computed. This procedure is repeated thousands of times so a cumulative distribution function (CDF) for the project cost can be obtained. Fig. 3 shows a cost item in the contractor s estimate whose variability is specified through the triangular distribution. (3) Correlation Analysis In construction cost estimating the assumption of independence is usually adopted due to the difficulty of modeling dependence. Under the independence assumption, the single figure estimate of the system variable is almost guaranteed to be exceeded if the summation of the estimates is a large number of small subsystem variables[6]. When historical data are not available, subjective judgment is needed for the estimation of correlation coefficients. Dependency can be categorized in: negative strong, negative medium, negative weak, independent, positive weak, positive medium, positive strong with coefficients of -0.85, -0.55, -0.25, 0, 0.25, 0.55, and 0.85 respectively [6]. Touran [7] gives values of 0.15, 0.45, and 0.8 for weak, moderate and strong correlation correspondingly. Fig. 4 shows the correlation between cost items in the model. Fig. 4 Correlation between Cost Items (4) External Event (Risk/ Opportunity) Analysis Fig. 3 Assignment of Triangular Distribution to a Cost Item Internal uncertainty is best characterized by specifying a feasible range of values and probability distributions, while external uncertainty is more appropriately modeled by assessing the likelihood of that risk event happening or not[8]. External risks are relatively uncontrollable while internal factors are more controllable and vary between projects [9]. 195

4 To handle these external risks systematically in the risk analysis, a risk register is created. The general procedure first assesses qualitatively the probability of occurrence of each risk and then its consequences on project performance. In a similar way the consequence of certain risk on project cost can be also evaluated. Once the occurrence probability and consequences of each risk are scored they can be mapped into a matrix where the importance of each one can be evaluated. Fig. 5 provides a way to rank the importance of each risk affecting the project. For example, risks that fall in the upper right area of the matrix are the ones to be considered critical and need to be investigated in order to avoid undesirable results on project performance targets; conversely, risks mapped in the lower left area of the matrix are less critical. The benefits of this methodology are visible for risk prioritization and communication; however, it is limited when assessing and planning for consequences in terms of money. allows management to analyze probabilities of exceeding certain targets. By determining the level of risk acceptance or confidence level, the amount of contingency and tender price can be determined. By comparing the base cost estimate total and the estimate based on a certain confidence level, a contingency can be determined. Fig. 6 Contingency Calculation from the CDF As a rule of thumb, the tornado chart can be used to distribute the determined contingency for the cost items in the estimate. Fig 7 shows the tornado chart example. Fig 5 Project Risk Register (5) Contingency Analysis If risk can be assessed, it can be reflected by the inclusion of a contingency sum. Probabilistic risk analysis directly helps the process of contingency determination and allocation. The use of the results generated by the risk analysis (i.e., CDF of project cost) as shown in Fig. 6 Fig. 7 Tornado Chart for Total Cost Variation 196

5 (6) Mitigation Analysis Since the contingency depends on the variability of the cost items, before finalizing it, one can attempt to reduce the range of the uncertainty by implementing some mitigation strategies. As shown in Fig. 8, a mitigation strategy can be implemented at a certain cost, resulting in lowering the probability of occurrence of an uncertain event and/ or its level of impact. This process can be repeated for other cost items and one more round of Monte Carlo simulation will be performed. Fig. 9 Total Cost Comparison Before and After Mitigation 3. CONCLUSION Fig. 8 Uncertainty Mitigation Strategy (7) Risk Analysis Report After the mitigation strategies implemented in the risk simulation, estimators can make a decision on the contingency by evaluating the contingencies before and after the mitigation. Fig. 9 shows two contingencies where the reduction in the contingency is justified because it is exceeds the mitigation-related expense at the same level of confidence. This paper described an integrated cost contingency estimation model implemented as an add-in to Excel, the most common spreadsheet platform, which can be easily adoptable by contracting firms without special training required. This model used a well-defined project risk management process and Monte Carlo simulation as its engine to model uncertainties and a project risk register. This paper focuses on the model s contribution of separating complex analytical aspects from its input and output processes to emphasize the following reality - contracting firms, after all, need an intuitive and yet flexible contingency estimating model, which should help them focus on extracting their experience and expertise in adequately determining contingency. 197

6 REFERENCES [1] Barraza GA, Bueno RA. Cost Contingency Management. Journal of Management in Enginnering 2007 Jul;23(3): [2] Smith GR, Bohn CM. Small to Medium Contractor Contingency and Assumption of Risk. Journal of Construction Engineering and Management 1999;125(2): [3] Attoh-Okine NO. Probabilistic analysis of factors affecting highway construction costs: a belief network approach. Canadian Journal of Civil Engineering 2002;29(3): [4] Back WE, Boles WW, Fry GT. Defining triangular probability distributions from historical cost data. Journal of Construction Engineering and Management 2000;126(1): [5] Wilson JR, Vaughan DK, Naylor E, Voss RG. Analysis of Space-Shuttle Ground Operations. Simulation 1982;38(6): [6] Chau KW. Monte Carlo simulation of construction costs using subjective data. Construction Management and Economics 1995;13(5): [7] Touran A. Probabilistic Cost Estimating with Subjective Correlations. Journal of Construction Engineering and Management 1993;119(1): [8] Diekmann JE, Featherman WD. Assessing cost uncertainty: Lessons from environmental restoration projects. Journal of Construction Engineering and Management 1998;124(6): [9] Tah JHM, Carr V. Knowledge-based approach to construction project risk management. Journal of Computing in Civil Engineering 2001;15(3):

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