An integrated AHP–DEA methodology for bridge risk assessment

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Abstract

The traditional analytic hierarchy process (AHP) method can only compare a very limited number of decision alternatives, which is usually not more than 15. When there are hundreds or thousands of alternatives to be compared, the pairwise comparison manner provided by the traditional AHP is obviously infeasible. In this paper we propose an integrated AHP–DEA methodology to evaluate bridge risks of hundreds or thousands of bridge structures, based on which the maintenance priorities of the bridge structures can be decided. The proposed AHP–DEA methodology uses the AHP to determine the weights of criteria, linguistic terms such as High, Medium, Low and None to assess bridge risks under each criterion, the data envelopment analysis (DEA) method to determine the values of the linguistic terms, and the simple additive weighting (SAW) method to aggregate bridge risks under different criteria into an overall risk score for each bridge structure. The integrated AHP–DEA methodology is applicable to any number of decision alternatives and is illustrated with a numerical example.

Introduction

Bridge risk assessment is often conducted to determine the priority of bridge structures for maintenance. For example, Adey, Hajdin, and Brühwiler (2003) presented a risk-based approach to determining the optimal intervention for a bridge subject to multiple hazards. Johnson and Niezgoda (2004) presented a risk-based method for ranking, comparing and choosing the most appropriate bridge scour countermeasures using the risk priority numbers (PRNs) in failure modes and effects analysis (FMEA). Stein, Young, Trent, and Pearson (1999) developed a risk-based method for assessing the risk associated with scour threat to bridge foundations. The risk of scour failure was defined as the product of the probability of scour failure or heavy damage and the cost associated with failure, adjusted by a risk adjustment factor based on foundation type and type of span. Shetty, Chubb, Knowles, and Halden (1996) proposed a risk-based framework for assessment and prioritization of bridges in need of remedial work, which involves risk evaluation, rankings of bridges in terms of risk, design of remedial action for each bridge, and optimal allocation of resources for remedial work on different bridges. Risk is quantified as the product of probability of failure and consequences of failure. Lounis (2004) presented a risk-based approach for bridge maintenance optimization that takes into account several and possibly conflicting criteria, with emphasis on the risk of failure as a governing criterion. The optimal maintenance strategy was defined as the solution that achieved the best compromise between the three selected relevant and conflicting criteria: minimization of risk of failure, minimization of maintenance costs, and minimization of traffic disruption. Compromise programming was used to determine the optimal ranking of the maintenance strategies in terms of their effectiveness in risk reduction, cost minimization, and traffic control. A multi-criteria optimality index was proposed as a measure of the effectiveness of the optimal maintenance strategy in achieving a satisfactory trade-off between the relevant and competing maintenance criteria.

Bridge risk assessment is essentially a multiple criteria decision making (MCDM) problem, which involves multiple assessment criteria such as safety, functionality, sustainability and so on. Therefore, MCDM approaches can be used for bridge risk assessment. Of the MCDM approaches, the analytic hierarchy process (AHP) method (Saaty, 1980) is particularly suitable for modeling qualitative criteria and has found extensive applications in a wide variety of areas such as selection, evaluation, planning and development, decision making, forecasting, and so on (Vaidya & Kumar, 2006). However, due to the fact that there are hundreds or thousands of bridge structures to be evaluated and prioritized, while the AHP method can only compare a very limited number of decision alternatives, the pairwise comparison manner is obviously infeasible in this situation. To overcome this difficulty, we combine the AHP with the data envelopment analysis (DEA) (Charnes, Cooper, & Rhodes, 1978) and propose an integrated AHP–DEA methodology in this paper.

The paper is organized as follows. In Section 2, we give a brief description of the AHP to provide a ground for the later development of methodology. In Section 3, we first present a literature review on the combination of the AHP and DEA, and then develop an integrated AHP–DEA methodology for the MCDM problems with a large number of decision alternatives. Section 4 compares the proposed AHP–DEA methodology with the method of absolute priorities used in the AHP for handling large number of alternatives. Section 5 presents an application of the proposed AHP–DEA methodology to bridge risk assessment, where 20 bridge structures are to be prioritized in terms of their overall risk scores. Conclusions are offered in Section 6.

Section snippets

The AHP methodology

The AHP is a method developed by Saaty (1980) to support multi-criteria decision making. It involves decomposing a complex MCDM problem into a hierarchy, assessing the relative importance of decision criteria, comparing decision alternatives with respect to each criterion, and determining an overall priority for each decision alternative and an overall ranking for the decision alternatives. The hierarchy is constructed in such a way that the overall decision goal is at the top level, decision

Literature review

The idea of combining the AHP and DEA is not new. There have been several attempts to integrate them in real applications. For example, Bowen (1990) compared the AHP and DEA methods for a site selection problem and discussed their similarities in both structure and results. They suggested a two step process of integrating them in site selection. The first step is to apply the DEA to exclude numerically inefficient sites and the second step is to apply the AHP for DEA-efficient sites. They

Comparison with the method of absolute priorities

It is argued that the method of absolute priorities (Saaty, 1990) used in the AHP can also be used for handling large number of decision alternatives. When the method of absolute priorities is used for handling the generic MCDM problem shown in Fig. 1, the DM first categorizes the n alternatives with respect to each criterion into their linguistic grades and then compares the linguistic grades to construct a pairwise comparison matrix for them. Once the priorities of the linguistic grades under

An application to bridge risk assessment

It is estimated that there are about 160,000 bridges in the UK, of which 140,000 are the responsibility of Local Authorities. The annual budget of repair and maintenance, for the 12,000 highway bridges governed by the Department of Transport (DfT) and the Highways Agency (HA) in England alone, is in the range of £150 million. Allocating funds and other resources for maintenance projects has been identified as a growing problem due to several constraints such as time, budget, manpower,

Conclusions

In this paper, we have proposed a new integrated AHP–DEA methodology to evaluate the risks of hundreds or thousands of bridge structures. To avoid making a large number of pairwise comparisons, the proposed AHP–DEA methodology uses only the AHP to determine the weights of criteria, linguistic terms such as High, Medium, Low and None to assess bridge risks under each criterion, DEA model with common weights to determine the values of the linguistic terms, and the simple additive weighting method

Acknowledgements

The authors appreciate two anonymous reviewers for their constructive comments and suggestions, which are very helpful to the improvement of the paper.

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    This research was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) under the Grant No. GR/S66770/01 and also supported by the National Natural Science Foundation of China (NSFC) under the Grant No. 70771027.

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