# Remedial Modelling of Steel Bridges through Application of Analytical Hierarchy Process (AHP)
## 1 Introduction  
Steel bridges are subject to continuous degradation and many of them in existence, which were constructed 50-100 years ago, have exceeded, or are approaching the end of their design life [1]. With many now listed on heritage registers, road authorities have extra incentive to rehabilitate these structures to their former glory. Hence, selecting the most beneficial remediation concept is paramount. The service life of a bridge can be subdivided into four phases [2]: Phase A--Design, planning and construction; Phase B--Propagation of damage has not yet begun but initiation processes are in progress; Phase C--Deterioration propagation has just started; and Phase D--Extensive damage is occurring. According to the Law of Fives, one dollar spent in Phase A, is equivalent to five dollars spent in Phase B; twenty-five dollars in Phase C; and one hundred twenty-five dollars in Phase D. Implying this rule is the basis for any asset management decision making. This justifies the importance of employing structured decision support models to assist in improving the bridge network and effective distribution of the allocated budget [3]. Most of the bridge management systems base their decision making process on optimisation of life cycle cost and parameters such as social and environmental impacts are usually ignored. According toAbu [PERSON] and [PERSON] (2008), applying the optimised life cycle methodology may cause difficulties particularly when the available fund is larger or lower than the computed life cycle cost [3]. The benefit to cost (B/C) ratio technique can also be employed at the project level to compare different remediation strategies. This parameter is introduced as the benefit gained by moving from one repair solution to another more expensive option divided by the related extra costs. The benefits include those for both the user and the agency. User benefits are measured in terms of cost reductions or savings to the user as a result of an improvement. Agency benefits are defined based on the present value of future savings because of the expenditures. Over exaggeration of cost as a constraint and subjectivity of benefit evaluation are the negative aspects of this technique. In mathematical optimisation models, an optimal solution can be reached through the manipulation of the trade-off between the objectives and the constraints. [PERSON] (1990) constructed an optimisation model using integer-linear programming for the Indiana Department of Transportation (INDOT) [4]. Three key solutions were considered: bridge replacement, deck replacement and deck rehabilitation. Each option is represented a zero-one variable: \"0\" if the activity is not selected and \"1\" if it is selected. The model subdivides the decision problem into stages; each year is defined as a stage. The Markov chain technique is used to predict the future bridge condition at each stage, and integer-linear programming is employed to maximise the effectiveness of the network. The only criterion considered in this model was the budget and the fact that only one strategy can be undertaken. As the age of bridge increases, the condition rating gradually decreases [5]. The 1991 the FHWA sponsored a bridge management system (BMS) called \"Pontis\". This bridge management software was adopted quickly and is one of the primary systems used for bridge management [6]. The current bridge management systems do not provide detailed information for accurately selecting remediation strategies. Hence, many efforts have focused on enhancing the condition rating and maintenance procedures. The development of a decision support system for bridge remediation will complement these efforts. The research presented in this paper deals with the development of a decision support system for asset management of steel bridges using Multi Criteria Decision Making (MCDM) methods. In infrastructure management, MCDM has emerged as a support to integrate various stakeholder preferences and technical information [7].