[논문]Prediction Model of Final Project Cost using Multivariate Probabilistic Analysis (MPA) and Bayes' Theorem

Yoo, Wi Sung; Hadipriono, FAbian C.

Prediction Model of Final Project Cost using Multivariate Probabilistic Analysis (MPA) and Bayes' Theorem 원문보기

건설관리 : 한국건설관리학회논문집 = Korean journal of construction engineering and management, v.8 no.5 = no.39, 2007년, pp.191 - 200

Yoo, Wi Sung (Civil & Environmental Engineering & Geodetic Science, The Ohio State University) , Hadipriono, FAbian C. (Civil & Environmental Engineering & Geodetic Science, The Ohio State University)

Abstract ▼ AI-Helper

This paper introduces a tool for predicting potential cost overrun during project execution and for quantifying the uncertainty on the expected project cost, which is occasionally changed by the unknown effects resulted from project's complications and unforeseen environments. The model proposed in this stuff is useful in diagnosing cost performance as a project progresses and in monitoring the changes of the uncertainty as indicators for a warning signal. This model is intended for the use by project managers who forecast the change of the uncertainty and its magnitude. The paper presents a mathematical approach for modifying the costs of incomplete work packages and project cost, and quantifying reduced uncertainties at a consistent confidence level as actual cost information of an ongoing project is obtained. Furthermore, this approach addresses the effects of actual informed data of completed work packages on the re-estimates of incomplete work packages and describes the impacts on the variation of the uncertainty for the expected project cost incorporating Multivariate Probabilistic Analysis (MPA) and Bayes' Theorem. For the illustration purpose, the Introduced model has employed an example construction project. The results are analyzed to demonstrate the use of the model and illustrate its capabilities.

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문제 정의

This study is concerned with the fact that the changes of the estimated costs are often caused by the dependencies of work packages and the unpredictable uncertainties under the complicated environments. If work packages are totally independent, then the changes of uncertainties resulted from the dependency are insignificant.

제안 방법

Hence, the method introduced in this study focuses on projects whose work packages are somewhat or highly correlated among each other (which are usually the case); and so the variations of uncertainty will appear during a project execution. Furthermore, because there exist no perfectly satisfied correlation matrix in reflecting the dependency of cost variates, this study is concerned with two specific patterns of Correlation Function; Gaussian and Exponential Correlation Functions with the characteristics that are described in the next section.
The CF represents the probability density of measuring the dependency of cost variates, and this creates the correlation matrix satisfying all the properties for applying it to the cost estimates. In this paper, two types of the Correlation Functions are employed to test the proposed model: Gaussian Correlation Function (GCF) and Exponential Correlation Function (ECF). The GCF shows the dependency from the preceding to the subsequent work packages that is initially decreasing slowly but subsequently decreasing rather quickly (Figure la).
One of the ultimate objectives in this study is to monitor the reduction of cost uncertainties of incomplete work packages by increasing cost information resulted from completed work packages considering the dependency between these packages. Also, others are to quantify its magnitude at an initially desired confidence level and to address the effects of informed cost data on the modifications of the costs of incomplete work packages and expected project cost in quantitative assessment.
The proposed methodology in this paper contributes to modifying the costs of all work packages to be completed corresponding to reported cost data from completed work packages. Such revisions provide project managers with valuable information for embodying strategic management actions, and quantitatively analyzing project cost performance at the desired confidence level.
This study introduced a cost re-estimating model using the Multivariate Probabilistic Analysis (MPA) and Bayes Theorem to accurately predict construction project cost and contingency. The model has predicted the changes of the costs of incomplete work packages and expected project cost in quantitative assessment, resulted from actual cost data of completed work packages of ongoing project.

성능/효과

From a prior condition of a project, it is possible to compute the required contingency to meet any significant confidence level. In this paper, 10% risk and 90% confidence level are defined as the likelihood that an actual total project cost exceeds any specific project cost. These levels are dependent upon the characteristics, conditions, and uncertainties of the project; and they often depend on experts' judgment.
The uncertainty on each work package cost was determined by the coefficient of variation, which was 30% for every individual work package. The coefficient of variation is the standard deviation divided by the expected value, and can be controlled by a project manager.
However, project managers can manage these values on the basis of their experiences and subjective judgments. When the contingency was set at the 90% confidence level, it represented that there was 10% chance that the cost overruns, and a 90% chance that total cost was not overrun. Standard unit variate for one-sided 90% confidence level is 1.

참고문헌 (9)

CII (1994) 'Pre-Project Planning: Beginning a project the right way' Published by Construction Industry Institute, Texas
Clark, D.E. (2001) 'Monte Carlo Analysis: Ten Year of Experience' Cost Engineering, Vol. 43, No.6, pp. 40-45
Ford, D.N. (2002) 'Achieving multiple project objectives through contingency management' Journal of Construction Engineering and Management, Vol. 128, No.1, pp. 30-39

상세보기
Johnson, R.A. and Wichern, D.W. (2002) 'Applied Multivariate Statistical Analysis' Published by Prentice Hall, New Jersey
Karlsen, J. T. and Lereim, J. (2005) 'Management of project contingency and allowance' Cost Engineering, Vol. 47, No.9, pp. 24-29
Nassar, K. (2005) 'Cost contingency analysis for construction project using spreadsheets' Cost Engineering, Vol. 47, No. 9, pp. 24-29
Pugh, LA and Soden, R. G. (1986) 'Use of risk analysis techniques in assessing the confidence of project cost estimates and schedules' Project Management, Vol. 4, No. 3, August pp. 158-162

상세보기
Touran, A. (2003) 'Probabilistic model for cost contingency' Journal of Construction Engineering and Management, Vol. 129, No. 3, pp. 280-284

상세보기
Zwikael, O., Globerson, S., and Raz, T. (2000) 'Evaluation of models for forecasting the final cost of a project' Project Management Journal, March, pp. 53-57

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