# Decision Support Model for Allocating Maintenance Budgets for Bridges
## 4 Proposed Model
### Computation Process Workflow  
As shown in Figure 3, the model executes the following steps to find the optimal solution (maintenance plan) of bridges and how the limited budget can be distributed:  
Step 1--Data entry  
The following data were entered to start the model:  
* List of bridges to be maintained from the BMS;
* Data related to the prioritization criteria of these bridges (e.g., age of the bridge, condition assessment of each structural element, etc. );
* Pre-defined weight of each prioritization criterion and each structural element from the conducted AHP survey;
* Pre-defined equations of each utility curve as presented in Figure 2;
* The owner (Bridge Management Authority) enters score for each bridge criteria;  
Figure 3: Computation process workflow. The estimated maintenance cost of each structural element in each bridge;  
The available budget. Step 2--Bridge prioritization at the network level  
Starting from the Bridge Data, such as Bridge Age for the first bridge (which was taken from the BMS), the bridge age is then substituted in the equation of bridge age criteria to determine the corresponding utility value \(U_{b,c}\). \(b\) is the bridge number and c is the criteria number;  
The pre-defined Bridge Age criteria weight \(WC_{n}\) is already entered in the first step;  
The model starts by multiplying the utility value \(U_{b,c}\) of prioritization criterion C1 for bridge \(\text{B}_{a}\) by the weight of C1 which is \(WC_{n}\);  
The model does the same as previous points for all prioritization criterions for one bridge and records the sum of all products \(U_{b,c}\times WC_{n}\), which will be the bridge rank;  
The model repeats the same previous points for all bridges to determine the rank of each bridge;  
The mathematical expression of determining the bridge rank for certain number of prioritization criterion is shown in the following Equation (1):  
\[\text{Bridge Rank for bridge }\text{BR}_{b}=\sum_{c=1}^{c=6}(U_{b,c}\times WC_{n}) \tag{1}\]  
where:  
\(b\) is the number of bridges in the network that needs maintenance this year (\(b=1,2,\ldots,n\)) and n is the last bridge;  
\(c\) is the number of prioritization criteria considered in the model with six criteria;  
\(U_{b,c}\) is the utility score of bridge \(b\) for criteria \(c\);  
\(WC_{n}\) is the weight of criteria (\(n\)). The higher the rank is, the more the bridge is eligible for maintenance. Step 3--Structural element prioritization at the bridge level  
Upon determining the bridge rank, the model will have the following parameters:  
Bridge Rank \(\text{BR}_{b}\), condition assessment of each structural element and the corresponding utility value \(\text{U}_{\text{b,se}}\) b is the bridge number, se is the structural element number (from BMS) and the pre-defined weight of each structural element \(\text{W}_{\text{se}}\);  
The model multiplies the Bridge Rank \(\text{BR}_{b}\) by the pre-defined weight of the structural element \(\text{W}_{\text{se}}\) (see Table 5) by the utility value of the condition assessment of the same structural element \(\text{U}_{\text{b,se}}\) to determine the bridge structure element rank;  
The result obtained from the previous step is then multiplied by the maintenance strategy score to obtain the overall priority of that structural element (optional in case the owner wants to prioritize a certain maintenance strategy according to the condition assessment);  
The higher the score value is, the more eligible the bridge's structural element for maintenance becomes.