The beta distribution is seen as a suitable model in risk analysis because it provides a wide variety of distributional shapes over a finite interval. Unfortunately, the beta distribution is not easily understood and its parameters are not easily estimated. This paper explores the possibility of using the more intuitively obvious triangular distribution as a proxy for the beta distribution. It is shown that the differences between the two distribution functions are seldom significant and a procedure is proposed for estimating the parameters of a triangular distribution on the basis of two extreme percentiles and the median.

The triangular distribution as a proxy for the beta distribution in risk analysis

A classified bibliography of recent research relating to project risk management

The operations research literature provides little guidance about how data should be generated for the computational testing of algorithms or heuristic procedures. We discuss several widely used data generation schemes, and demonstrate that they may introduce biases into computational results. Moreover, such schemes are often not representative of the way data arises in practical situations. We address these deficiencies by describing several principles for data generation and several properties that are desirable in a generation scheme. This enables us to provide specific proposals for the generation of a variety of machine scheduling problems. We present a generation scheme for precedence constraints that achieves a target density which is uniform in the precedence constraint graph. We also present a generation scheme that explicitly considers the correlation of routings in a job shop. We identify several related issues that may influence the design of a data generation scheme. Finally, two case studies illustrate, for specific scheduling problems, how our proposals can be implemented to design a data generation scheme.

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Generating Experimental Data for Computational Testing with Machine Scheduling Applications

This study demonstrates a quantitative approach to construction risk management through analytic hierarchy process and decision tree analysis. All the risk factors are identified, their effects are quantified by determining probability and severity, and various alternative responses are generated with cost implication for mitigating the quantified risks. The expected monetary values are then derived for each alternative in a decision tree framework and subsequent probability analysis aids the decision process in managing risks. The entire methodology is explained through a case application of a cross‐country petroleum pipeline project in India and its effectiveness in project management is demonstrated.

Decision support system for risk management: a case study

Time, cost and quality achievements on large-scale construction projects are uncertain because of technological constraints, involvement of many stakeholders, long durations, large capital requirements and improper scope definitions. Projects that are exposed to such an uncertain environment can effectively be managed with the application of risk management throughout the project life cycle. Risk is by nature subjective. However, managing risk subjectively poses the danger of non-achievement of project goals. Moreover, risk analysis of the overall project also poses the danger of developing inappropriate responses. This article demonstrates a quantitative approach to construction risk management through an analytic hierarchy process (AHP) and decision tree analysis. The entire project is classified to form a few work packages. With the involvement of project stakeholders, risky work packages are identified. As all the risk factors are identified, their effects are quantified by determining probability (using AHP) and severity (guess estimate). Various alternative responses are generated, listing the cost implications of mitigating the quantified risks. The expected monetary values are derived for each alternative in a decision tree framework and subsequent probability analysis helps to make the right decision in managing risks. In this article, the entire methodology is explained by using a case application of a cross-country petroleum pipeline project in India. The case study demonstrates the project management effectiveness of using AHP and DTA.

Project risk management: a combined analytic hierarchy process and decision tree approach

The traditional method of estimating mean activity-time in PERT analysis, as a weighted average of the pessimistic, most likely and optimistic activity-times, is examined. Based on properties of the beta distribution, it is shown that there are theoretical grounds for using this estimate for a specified range of modal activity times. Finally, a simple refinement of the estimate is suggested when the modal value lies outside this range.

https://link.springer.com/content/pdf/10.1057%2Fjors.1987.45.pdf

Laverne W. Stanton

Papers

Some Results Concerning the Estimation of Beta Distribution Parameters in PERT