Question

You are the manager of a construction company and you are about to authorize a project for the construction of a bridge. Before you give the authorization, you would like to assess the risk of this project. Your management consultant advises you to use AHP for this purpose. The factors you decide to include in the analysis are F1: Financial and economic risks; F2: Political risks; F3: Force Majeure items. The sub-factors are F11: Subcontractors failure; F12: Unavailability of funds; F13: Inflation; F21: Embargoes/Expropriation; F22: Changes in local laws; F31: Earthquakes; F32: Water damage and floods; F33: Soil subsistence and collapse. The risks are divided into three categories: High risk; medium risk; low risk. (a) Draw the decision hierarchy chart. (b) Calculate the relative importance of F1, F2, F3 with respect to the overall goal. $$ \begin{array}{l|l|l|l} \hline & \text { F1 } & \text { F2 } & \text { F3 } \\ \hline \text { F1 } & 1 & 3 & 6 \\ \hline \text { F2 } & 1 / 3 & 1 & 5 \\ \hline \text { F3 } & 1 / 6 & 1 / 5 & 1 \\ \hline \end{array} $$ Calculate $\lambda_{\max }$; consistency index CI; consistency ratio CR. Take RI as 0.58 . (c) How would you phrase the questions for determining the judgment matrices at the lowest level of the hierarchy? (d) Apply AHP to determine the level of risk for the project. In addition to the judgment matrix in part (a), the following judgment matrices are given, where L, M, H stand for low risk, medium risk and high risk, respectively. $$ \begin{aligned} &\text { Under F1 }\\ &\begin{array}{c|c|c|c} \hline & \text { F11 } & \text { F12 } & \text { F13 } \\ \hline \text { F11 } & 1 & 3 & 1 / 3 \\ \hline \text { F12 } & 1 / 3 & 1 & 1 / 6 \\ \hline \text { F13 } & 3 & 6 & 1 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\begin{array}{c|c|c} \hline {\text { Under F2 }} \\ \hline & \text { F21 } & \text { F22 } \\ \hline \text { F21 } & 1 & 5 \\ \hline \text { F22 } & 1 / 5 & 1 \\ \hline \end{array}\\ &\begin{array}{c|c|c|c} \hline {\text { Under F3 }} \\ \hline & \text { F31 } & \text { F32 } & \text { F33 } \\ \hline \text { F31 } & 1 & 1 / 7 & 1 / 9 \\ \hline \text { F32 } & 7 & 1 & 3 \\ \hline \text { F33 } & 9 & 1 / 3 & 1 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\begin{array}{l|c|c|c} \hline {\text { Under F11 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{C} \\ \hline \mathrm{L} & 1 & 3 & 1 / 3 \\ \hline \mathrm{M} & 1 / 3 & 1 & 1 / 6 \\ \hline \mathrm{C} & 3 & 6 & 1 \\ \hline \end{array}\\ &\begin{array}{l|c|c|c} \hline {\text { Under F12 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 5 & 6 \\ \hline \mathrm{M} & 1 / 5 & 1 & 3 \\ \hline \mathrm{H} & 1 / 6 & 1 / 3 & 1 \\ \hline \end{array}\\ &\begin{array}{l|c|c|c} {\text { Under F13 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 1 / 6 & 1 / 4 \\ \hline \mathrm{M} & 6 & 1 & 5 \\ \hline \mathrm{H} & 4 & 1 / 5 & 1 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\begin{array}{l|c|c|c} \hline {\text { Under F21 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 6 & 1 / 3 \\ \hline \mathrm{M} & 1 / 6 & 1 & 1 / 6 \\ \hline \mathrm{H} & 3 & 6 & 1 \\ \hline \end{array}\\ &\begin{array}{l|c|c|c} \hline {\text { Under F22 }} \\ \hline & \text { L } & \text { M } & \text { H } \\ \hline \mathrm{L} & 1 & 4 & 6 \\ \hline \mathrm{M} & 1 / 4 & 1 & 3 \\ \hline \mathrm{H} & 1 / 6 & 1 / 3 & 1 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\begin{array}{l|c|c|c} \hline {\text { Under F31 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 6 & 1 / 4 \\ \hline \mathrm{M} & 1 / 6 & 1 & 5 \\ \hline \mathrm{H} & 4 & 1 / 5 & 1 \\ \hline \end{array}\\ &\begin{array}{l|c|c|c} \hline {\text { Under F32 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 4 & 7 \\ \hline \mathrm{M} & 1 / 4 & 1 & 3 \\ \hline \mathrm{H} & 1 / 7 & 1 / 3 & 1 \\ \hline \end{array}\\ &\begin{array}{l|c|c|c} \hline {\text { Under F33 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 1 / 3 & 1 / 2 \\ \hline \mathrm{M} & 3 & 1 & 2 \\ \hline \mathrm{H} & 2 & 1 / 2 & 1 \\ \hline \end{array} \end{aligned} $$ 

   You are the manager of a construction company and you are about to authorize a project for the construction of a bridge. Before you give the authorization, you would like to assess the risk of this project. Your management consultant advises you to use AHP for this purpose. The factors you decide to include in the analysis are F1: Financial and economic risks; F2: Political risks; F3: Force Majeure items. The sub-factors are F11: Subcontractors failure; F12: Unavailability of funds; F13: Inflation; F21: Embargoes/Expropriation; F22: Changes in local laws; F31: Earthquakes; F32: Water damage and floods; F33: Soil subsistence and collapse. The risks are divided into three categories: High risk; medium risk; low risk.
(a) Draw the decision hierarchy chart.
(b) Calculate the relative importance of F1, F2, F3 with respect to the overall goal.
$$
\begin{array}{l|l|l|l}
\hline & \text { F1 } & \text { F2 } & \text { F3 } \\
\hline \text { F1 } & 1 & 3 & 6 \\
\hline \text { F2 } & 1 / 3 & 1 & 5 \\
\hline \text { F3 } & 1 / 6 & 1 / 5 & 1 \\
\hline
\end{array}
$$
Calculate $\lambda_{\max }$; consistency index CI; consistency ratio CR. Take RI as 0.58 .
(c) How would you phrase the questions for determining the judgment matrices at the lowest level of the hierarchy?
(d) Apply AHP to determine the level of risk for the project. In addition to the judgment matrix in part (a), the following judgment matrices are given, where L, M, H stand for low risk, medium risk and high risk, respectively.
$$
\begin{aligned}
&\text { Under F1 }\\
&\begin{array}{c|c|c|c}
\hline & \text { F11 } & \text { F12 } & \text { F13 } \\
\hline \text { F11 } & 1 & 3 & 1 / 3 \\
\hline \text { F12 } & 1 / 3 & 1 & 1 / 6 \\
\hline \text { F13 } & 3 & 6 & 1 \\
\hline
\end{array}
\end{aligned}
$$
$$
\begin{aligned}
&\begin{array}{c|c|c}
\hline {\text { Under F2 }} \\
\hline & \text { F21 } & \text { F22 } \\
\hline \text { F21 } & 1 & 5 \\
\hline \text { F22 } & 1 / 5 & 1 \\
\hline
\end{array}\\
&\begin{array}{c|c|c|c}
\hline {\text { Under F3 }} \\
\hline & \text { F31 } & \text { F32 } & \text { F33 } \\
\hline \text { F31 } & 1 & 1 / 7 & 1 / 9 \\
\hline \text { F32 } & 7 & 1 & 3 \\
\hline \text { F33 } & 9 & 1 / 3 & 1 \\
\hline
\end{array}
\end{aligned}
$$
$$
\begin{aligned}
&\begin{array}{l|c|c|c}
\hline {\text { Under F11 }} \\
\hline & \mathrm{L} & \mathrm{M} & \mathrm{C} \\
\hline \mathrm{L} & 1 & 3 & 1 / 3 \\
\hline \mathrm{M} & 1 / 3 & 1 & 1 / 6 \\
\hline \mathrm{C} & 3 & 6 & 1 \\
\hline
\end{array}\\
&\begin{array}{l|c|c|c}
\hline {\text { Under F12 }} \\
\hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\
\hline \mathrm{L} & 1 & 5 & 6 \\
\hline \mathrm{M} & 1 / 5 & 1 & 3 \\
\hline \mathrm{H} & 1 / 6 & 1 / 3 & 1 \\
\hline
\end{array}\\
&\begin{array}{l|c|c|c}
 {\text { Under F13 }} \\
\hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\
\hline \mathrm{L} & 1 & 1 / 6 & 1 / 4 \\
\hline \mathrm{M} & 6 & 1 & 5 \\
\hline \mathrm{H} & 4 & 1 / 5 & 1 \\
\hline
\end{array}
\end{aligned}
$$
$$
\begin{aligned}
&\begin{array}{l|c|c|c}
\hline {\text { Under F21 }} \\
\hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\
\hline \mathrm{L} & 1 & 6 & 1 / 3 \\
\hline \mathrm{M} & 1 / 6 & 1 & 1 / 6 \\
\hline \mathrm{H} & 3 & 6 & 1 \\
\hline
\end{array}\\
&\begin{array}{l|c|c|c}
\hline {\text { Under F22 }} \\
\hline & \text { L } & \text { M } & \text { H } \\
\hline \mathrm{L} & 1 & 4 & 6 \\
\hline \mathrm{M} & 1 / 4 & 1 & 3 \\
\hline \mathrm{H} & 1 / 6 & 1 / 3 & 1 \\
\hline
\end{array}
\end{aligned}
$$
$$
\begin{aligned}
&\begin{array}{l|c|c|c}
\hline {\text { Under F31 }} \\
\hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\
\hline \mathrm{L} & 1 & 6 & 1 / 4 \\
\hline \mathrm{M} & 1 / 6 & 1 & 5 \\
\hline \mathrm{H} & 4 & 1 / 5 & 1 \\
\hline
\end{array}\\
&\begin{array}{l|c|c|c}
\hline {\text { Under F32 }} \\
\hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\
\hline \mathrm{L} & 1 & 4 & 7 \\
\hline \mathrm{M} & 1 / 4 & 1 & 3 \\
\hline \mathrm{H} & 1 / 7 & 1 / 3 & 1 \\
\hline
\end{array}\\
&\begin{array}{l|c|c|c}
\hline {\text { Under F33 }} \\
\hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\
\hline \mathrm{L} & 1 & 1 / 3 & 1 / 2 \\
\hline \mathrm{M} & 3 & 1 & 2 \\
\hline \mathrm{H} & 2 & 1 / 2 & 1 \\
\hline
\end{array}
\end{aligned}
$$
Show more…
An Introduction to Project Modeling and Planning
An Introduction to Project Modeling and Planning
Gündüz Ulusoy, Öncü… 1st Edition
Chapter 14, Problem 4 ↓

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Step 1

We can do this by calculating the eigenvector corresponding to the largest eigenvalue of the pairwise comparison matrix. The pairwise comparison matrix is given as: $$ \begin{array}{l|l|l|l} \hline & \text { F1 } & \text { F2 } & \text { F3 } \\ \hline \text {  Show more…

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You are the manager of a construction company and you are about to authorize a project for the construction of a bridge. Before you give the authorization, you would like to assess the risk of this project. Your management consultant advises you to use AHP for this purpose. The factors you decide to include in the analysis are F1: Financial and economic risks; F2: Political risks; F3: Force Majeure items. The sub-factors are F11: Subcontractors failure; F12: Unavailability of funds; F13: Inflation; F21: Embargoes/Expropriation; F22: Changes in local laws; F31: Earthquakes; F32: Water damage and floods; F33: Soil subsistence and collapse. The risks are divided into three categories: High risk; medium risk; low risk. (a) Draw the decision hierarchy chart. (b) Calculate the relative importance of F1, F2, F3 with respect to the overall goal. $$ \begin{array}{l|l|l|l} \hline & \text { F1 } & \text { F2 } & \text { F3 } \\ \hline \text { F1 } & 1 & 3 & 6 \\ \hline \text { F2 } & 1 / 3 & 1 & 5 \\ \hline \text { F3 } & 1 / 6 & 1 / 5 & 1 \\ \hline \end{array} $$ Calculate $\lambda_{\max }$; consistency index CI; consistency ratio CR. Take RI as 0.58 . (c) How would you phrase the questions for determining the judgment matrices at the lowest level of the hierarchy? (d) Apply AHP to determine the level of risk for the project. In addition to the judgment matrix in part (a), the following judgment matrices are given, where L, M, H stand for low risk, medium risk and high risk, respectively. $$ \begin{aligned} &\text { Under F1 }\\ &\begin{array}{c|c|c|c} \hline & \text { F11 } & \text { F12 } & \text { F13 } \\ \hline \text { F11 } & 1 & 3 & 1 / 3 \\ \hline \text { F12 } & 1 / 3 & 1 & 1 / 6 \\ \hline \text { F13 } & 3 & 6 & 1 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\begin{array}{c|c|c} \hline {\text { Under F2 }} \\ \hline & \text { F21 } & \text { F22 } \\ \hline \text { F21 } & 1 & 5 \\ \hline \text { F22 } & 1 / 5 & 1 \\ \hline \end{array}\\ &\begin{array}{c|c|c|c} \hline {\text { Under F3 }} \\ \hline & \text { F31 } & \text { F32 } & \text { F33 } \\ \hline \text { F31 } & 1 & 1 / 7 & 1 / 9 \\ \hline \text { F32 } & 7 & 1 & 3 \\ \hline \text { F33 } & 9 & 1 / 3 & 1 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\begin{array}{l|c|c|c} \hline {\text { Under F11 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{C} \\ \hline \mathrm{L} & 1 & 3 & 1 / 3 \\ \hline \mathrm{M} & 1 / 3 & 1 & 1 / 6 \\ \hline \mathrm{C} & 3 & 6 & 1 \\ \hline \end{array}\\ &\begin{array}{l|c|c|c} \hline {\text { Under F12 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 5 & 6 \\ \hline \mathrm{M} & 1 / 5 & 1 & 3 \\ \hline \mathrm{H} & 1 / 6 & 1 / 3 & 1 \\ \hline \end{array}\\ &\begin{array}{l|c|c|c} {\text { Under F13 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 1 / 6 & 1 / 4 \\ \hline \mathrm{M} & 6 & 1 & 5 \\ \hline \mathrm{H} & 4 & 1 / 5 & 1 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\begin{array}{l|c|c|c} \hline {\text { Under F21 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 6 & 1 / 3 \\ \hline \mathrm{M} & 1 / 6 & 1 & 1 / 6 \\ \hline \mathrm{H} & 3 & 6 & 1 \\ \hline \end{array}\\ &\begin{array}{l|c|c|c} \hline {\text { Under F22 }} \\ \hline & \text { L } & \text { M } & \text { H } \\ \hline \mathrm{L} & 1 & 4 & 6 \\ \hline \mathrm{M} & 1 / 4 & 1 & 3 \\ \hline \mathrm{H} & 1 / 6 & 1 / 3 & 1 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\begin{array}{l|c|c|c} \hline {\text { Under F31 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 6 & 1 / 4 \\ \hline \mathrm{M} & 1 / 6 & 1 & 5 \\ \hline \mathrm{H} & 4 & 1 / 5 & 1 \\ \hline \end{array}\\ &\begin{array}{l|c|c|c} \hline {\text { Under F32 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 4 & 7 \\ \hline \mathrm{M} & 1 / 4 & 1 & 3 \\ \hline \mathrm{H} & 1 / 7 & 1 / 3 & 1 \\ \hline \end{array}\\ &\begin{array}{l|c|c|c} \hline {\text { Under F33 }} \\ \hline & \mathrm{L} & \mathrm{M} & \mathrm{H} \\ \hline \mathrm{L} & 1 & 1 / 3 & 1 / 2 \\ \hline \mathrm{M} & 3 & 1 & 2 \\ \hline \mathrm{H} & 2 & 1 / 2 & 1 \\ \hline \end{array} \end{aligned} $$
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