# Remedial Modelling of Steel Bridges through Application of Analytical Hierarchy Process (AHP)
## 6 Decision Analysis Tool  
Multi Criteria Decision Making (MCDM) tools are used in order to deal with various problems that engage criteria and to attain greater transparency and accuracy of the decision making process [2]. MCDMs go deeper along a holistic approach, aggregating all the data including that of a subjective nature. Almost all the MCDM approaches share some common mathematical components: values for decision alternatives are allocated for each criterion, and then multiplied by associated weights to produce a total score [7]. Various decision making tools have been investigated. Simple Multi Attribute Rating Technique (SMART) and Analytical Hierarchy Process (AHP) have been identified as the most applicable techniques. Analytical Hierarchy Process (AHP) is a multi-attribute decision making method that belongs to a broader category of tools known as \"additive weighting methods\". The AHP was proposed by [PERSON] (1991) and employs an objective function to aggregate the different aspects of a problem where the main goal is to choose the option that has the highest value of the objective function. AHP is grouped as compensatory methods, in which constraints with low scores are compensated by higher scores on other factors, but in contrast to the utilitarian techniques, the AHP uses pair wise comparisons of criteria where all individual criteria are paired with all other criteria and at the end results accumulated into a matrix [25]. The advantages of the AHP method are that it offers a systematic approach through a hierarchy and it has objectivity and consistency. On the other hand, the main limitations are that calculation of a pair-wise comparison matrix for each factor is a complex task and as the number of alternatives and/or criteria increases, the number of calculations for comparison matrix rises considerably. Moreover, if a new option/alternative is added, all the calculations have to be restarted [26]. The process of AHP includes three phases: decomposition, comparative judgments, and synthesis of priority. Through the AHP method, decision problems are decomposed into a hierarchy, and both qualitative and quantitative data can be used to derive ratio scales between the decision elements at each \begin{table}
\begin{tabular}{c c c} \hline \hline
**Criteria** & **Risks** & **Client Constraint** \\ \hline \multirow{2}{*}{Safety} & Potential injury/fatality & Minimal damage/Maximum safety of the public \\  & Damage to property & \\ \hline \multirow{3}{*}{Servicability} & Low level of service & Maximum service life \\  & Difficult to access the element & Easy access to element/site \\ \cline{1-1}  & Insufficient level of expertise & Maximum availability of skilled labour \\ \cline{1-1}  & Closure of a strategic/regional route & Minimal traffic disruption \\ \hline \multirow{3}{*}{Sustainability} & Excessive remediation cost & Minimal cost \\ \cline{1-1}  & Excessive work implications & Minimal work implications \\ \cline{1-1}  & Environmental damage & Minimal environmental damage \\ \hline \multirow{2}{*}{Legal/Political} & Major changes in standards & Minimum vulnerability to legal/political pressures \\ \cline{1-1}  & & \\ \end{tabular}
\end{table} 
Table 3: Major Risks and Client Constraints for Bridge Remediation. hierarchical level by means of pairwise comparisons. The top level of hierarchy represents overall goals and the lower levels correspond to criteria, sub-criteria, and alternatives. With comparative judgments, decision makers are requested to set up a matrix at each hierarchy by comparing pairs of criteria or sub-criteria. A scale of values ranging from 1 (indifference) to 9 (extreme preference) is employed to express the preferences. Finally, in the synthesis of priority stage, each comparison matrix is then solved by an eigenvector technique for determining the weight of criteria and alternative performance.