# Payment Maintenance Decision Making Based on Optimization Models
## 2 Problem Formulation  
Pavement maintenance usually involves decision making at the macro level for selecting roads to be maintained under objective constraints and decision makers' priorities. In China, pavement maintenance is usually subject to territorial management within each administrative region. For example, each district and county has its own department responsible for decision making during pavement maintenance at the macro level. Typical decision-making tasks involved in pavement maintenance include the formulation of an annual pavement maintenance scheme, budget application, and quality control. When making pavement maintenance decisions in real scenarios, the degree of deterioration of the road network in a certain region is first evaluated based on daily patrol data. Pavement deterioration can be quantified as the pavement condition index (PCI), which is a numerical rating of pavement condition based on the type and severity of distresses observed on the pavement surface. PCI is represented by a numerical value between 0-100, where 0 is the worst condition and 100 is the best.  
Subsequently, under the premise of considering the total maintenance cost and time, the annual maintenance scheme is formulated to improve the condition of roads with low PCIs. Thus, the maintenance of regional road networks must take multiple objectives into account, such as minimum maintenance cost and optimum maintenance quality. Therefore, determining a suitable approach to formulating an efficient maintenance scheme is a decision-making challenge.  
The multiobjective maintenance problem of a road network in a specific region can be described mathematically as follows. Given the number of roads (\(N\)), the area of each road (\(A\)) that requires maintenance, the _PCI_ of each road, and the total budget available for pavement maintenance (\(C\)) in a certain region, \(m\) roads (\(m\leq N\)) are prioritized for maintenance among the total \(N\) roads, such that (1) the total maintenance cost is less than or equal to \(C\), (2) the total maintenance cost is minimized, and (3) the maintenance quality is maximized. Selecting the appropriate roads based on human experience results in \(2^{N}\) combination schemes, because the decision variable is a Boolean representing whether a road is included in the maintenance schedule. Therefore, N cannot be excessively large, for when N is large, it is infeasible to select the final roads manually. This problem is NP-hard. To resolve it, heuristic algorithms were researched and developed aiming at an approximate optimal solution that could be a particularly sensible choice. In this study, a decision-making optimization model for pavement maintenance was solved by using NSGA-II. Optimum maintenance schemes were obtained that could ensure the maximal maintenance quality with minimal maintenance cost.  
Figure 1 shows the overall procedure of decision-making optimization for pavement maintenance. The foundation is to evaluate road condition by pavement condition index, and the key is to establish optimization models of road maintenance. The models can be applied to provide optimal schemes for multiobjective decision making in regional road network maintenance. Many optimization models have been widely used, as found from engineering management and research literature, but these models of optimizing pavement maintenance have not been fully examined. In this paper, we examined how these models could be extended for our research goals and demonstrated how they could be used in pavement maintenance for an application area.