## 3 Methodology
### Bridge Maintenance Strategy and RCPSP  
This section describes the whole idea regarding the bridge maintenance activity with project scheduling. To illustrate the entire concept in detail, basic definitions relevant to the RCPSP are elaborated as follows:  
* Activity: a plan refers to the process of implementing maintenance methods on any bridge parts at any point in time within a period and achieving the maintenance benefits in a given duration. The _ACTIVITY_ in the RCPSP has been referred to as a maintenance plan for this study.
* Duration: when a maintenance plan is selected, the maintenance effects for the targeted bridge will last for a different period in each case. This period corresponds to the activity _DURATION_ defined in the RCPSP.
* Cost: the maintenance cost of each plan can be referred to as the _COST_ of each activity in the RCPSP. This derived maintenance cost will be expressed as an annual value at each time point in this study. In each plan, an equal amount of the maintenance budget must be expended at each time point. Taking \"year\" as the unit in the calculation method also conforms to the style adopted by the government in compiling budgets each year.
* Facility Resource: the subject matter of this study--bridge components--is also regarded as the _FACILITY RESOURCE_ item in the RCPSP. That is, an activity requires resources for execution. When the activity is in the execution status, the facility resource is used. Similarly, when the facility resource is in use, the bridge can still function.  
Based on the above definitions, to explain the scope and limitations of model applicability, some assumptions are made, as follows:  
1. The maintenance plans for each bridge are evaluated in terms of the cost and the functional period after the maintenance is completed.
2. When a maintenance plan is completed, the corresponding bridge is safe and functional within the aforementioned period (i.e., endurance time).
3. Based on experience, unless a bridge suffers from major damage, it is rarely in an unusable condition. Even when maintenance work is being carried out, the bridge will still have a certain degree of usability. Therefore, in this study, the bridge examined is considered to be usable during the maintenance period. The functional period includes the maintenance period and the effect period and corresponds to the duration of the RCPSP.
4. Through intensive expert reviews, we found out that the maintenance information for some bridges was not completely preserved, for example the detailed cost and the maintenance period. Therefore, some parameters used in this study, such as the effect period and year remaining of the effect period, were based on assessments provided by the maintenance unit, and reasonable assumptions were made.
5. The major contribution of this study is to provide a budget allocation and adjustment mechanism for maintenance scheduling problems, from the perspective of life cycle routine maintenance. As the statement of assumption three explains, all facilities still have a certain degree of usability above the minimal acceptable condition. Though major disaster impacts to bridges, such as earthquakes and typhoons, may be the crucial factors for bridge failures, post-disaster emergency repairs and rehabilitation are not considered in this study due to budgeting issues in such emergence repair projects related to special funding, not included in the category of the annual budgeting discussed in this study.  
The relationship between the bridge maintenance budget allocation and RCPSP framework is listed in Table 1.