# MILP-Based Approach for High-Altitude Region Pavement Maintenance Decision Optimization
## 1 Introduction
### The Focus of This Study
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Literature** & **Object Characteristic** & **Optimization Objective** & **Model Type** & **Solution Approach** \\ \hline [PERSON] et al. [6] & Project-level; considering greenhouse gas emissions and budget constraints; meeting pavement condition requirements & Greenhouse gas emissions, maintenance costs, pavement condition & Multi-objective nonlinear optimization & Genetic algorithm \\ \hline [PERSON] et al. [11] & Project-level; constrained budget; meeting pavement condition requirements & Pavement condition & Flowchart & Heuristic algorithm \\ \hline [PERSON] et al. [12] & Project-level; meeting pavement condition requirements & Maintenance costs, pavement condition & Multi-objective nonlinear optimization & Improved particle swarm algorithm \\ \hline [PERSON] and [PERSON] [1] & Network-level; different decision-makers & Benefits for different decision-makers & Mixed-integer programming & Lingo \\ \hline [PERSON] et al. [13] & Network-level; different decision-makers; Pareto optimal solution & Maintenance costs, pavement condition, environmental impact & Mixed-integer linear programming & Cplex \\ \hline [PERSON] and [PERSON] [14] & Network-level; multiple pavement condition indicators & Maintenance costs, carbon emissions, and energy consumption & Multi-objective optimization & Generalized differential evolution algorithm \\ \hline [PERSON] and [PERSON] [15] & Network-level; single or multiple budget constraints & Greenhouse gas emission & Single-objective optimization & Lagrangian relaxation \\ \hline [PERSON] et al. [16] & Network-level; Pareto optimal solution & Maintenance costs, pavement condition & Markov-chain, multi-objective optimization & Genetic algorithm-based procedure \\ \hline [PERSON] et al. [17] & Network-level; considering the uncertainty of pavement deterioration and budget & Pavement condition & Multi-stage stochastic mixed-integer programming & GAMS \\ \hline [PERSON] et al. [18] & Network-level; constrained greenhouse gas emissions & Maintenance costs & Single-objective nonlinear & Two-stage algorithm \\ \hline [PERSON] et al. [19] & Network-level; considering dynamic traffic distribution & Maintenance costs, user costs, pavement residual asset value & Multi-stage dynamic programming & Heuristic iterative algorithm \\ \hline [PERSON] and [PERSON] [21] & Network-level; budget uncertainty & Maintenance effectiveness & Stochastic linear programming & Scenario tree-based heuristic algorithm \\ \hline \multirow{2}{*}{This paper} & Network-level; high-altitude region pavement maintenance; monthly maintenance plans; robust solution & Maintenance costs, affected traffic volume, carbon emissions, comfort level, maintenance effectiveness & Mixed-integer linear programming & Gurobi \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of the literature studies on pavement maintenance. 1. For the pavement maintenance decision problem in high-altitude regions, this paper proposes an optimization method for pavement maintenance plans. The initial optimization model constructed considers the typical characteristics of pavement maintenance in high-altitude regions (see Section 2) intending to obtain monthly maintenance plans. By combining the proposed linearization method, the initial nonlinear model is reconstructed into a mixed-integer linear programming (MILP) problem. The composition of the model under five types of decision strategies is discussed (see Section 4.2), responding to the decision- makers' preferences. 2. To address the uncertainty of unit maintenance costs, this paper proposes a robust maintenance plan calculation method using a robust optimization method based on the acceptable objective variation range (AOVR). By setting the unit maintenance cost as an interval number, the corresponding optimistic sub-model and pessimistic sub-model are analyzed, and the construction process of the robust optimization model and the process of obtaining robust maintenance plans are discussed. 3.