# Optimizing Rural Highway Maintenance Scheme with Mathematical Programming
###### Abstract  
Maintaining rural highways is crucial in ensuring the reliability and efficiency of transportation infrastructure in modern rural areas. Rural highways often suffer heavy traffic from logistics and regular transportation users. The efficient management of these roads is essential to avoid issues like traffic bottlenecks, fuel consumption, and environmental problems. Traditional maintenance approaches focus on cost reduction, which can lead to adverse effects such as network congestion and environmental damage. To address these challenges, this study proposes a bi-level mathematical programming model aiming at optimizing rural highway maintenance. This model balances maintenance costs, network congestion, system fuel consumption, and environmental impacts. By transforming the bi-level model into a single-level mixed-integer linear programming model, the study enhances the computational feasibility, enabling practical implementation using commercial solvers. The model's effectiveness is validated through numerical examples, providing insights for the development of optimal maintenance schedules that minimize externality costs while adhering to financial constraints and operational guidelines, providing a valuable addition to the road engineer's toolbox. r +
Footnote †: journal: Applied  
0000-0001-48253-32222-32222-32222-32  
Concurrently, they also amplify the difficulty of cost estimation and reduce the operational efficiency of roads and may potentially influence the formulation and effectiveness of traffic policies [4; 5; 6]. In light of these issues, highway management agencies increasingly need to adopt advances in operations research and balance multiple decision-making objectives to make wise decisions. This requires consideration of the integrity of the road network and the impact of various types of highway maintenance plans on the overall traffic flow. Figure 1 illustrates a typical form of pavement damage and the pavement management system that detects it. The detection of pavement damage is a mature field, but developing an optimal maintenance scheme that minimizes the delay costs is still a major challenge. Current research focuses on minimizing institutional maintenance costs and maximizing the pavement quality. Multiple optimization goals are involved in road maintenance, and pavement management systems have employed multi-criteria optimization to incorporate various objectives simultaneously [7; 8; 9; 10]. Topics include the utilization of road networks [11]; the road infrastructure quality (e.g., pavement deterioration uncertainty) [12; 13]; budgeting and investment, where the budget is also often linked to sustainability goals [14; 15]; vulnerable transport infrastructure [16]; road traffic control [17]; interconnection limits [18]; sustainable pavement maintenance (e.g., economy, energy, and the environment) [19; 20; 21]; greenhouse gas emissions [22]; interdisciplinary tasks, such as the integration and application of computer technology [23; 24; 25]; separating trucks from private vehicles [26; 27; 28]; and the impacts of the climate and seasons [29; 30]. These are commonly covered in research on highway maintenance. However, the calculation of the comprehensive cost of rural road network maintenance often ignores the user costs [9]. The World Bank defines the benefits of road projects as reducing vehicle operating costs, reducing user time costs, and reducing traffic accidents [31]. Rural transportation networks are systems of transport infrastructure consisting of a series of roads and streets located in rural areas. These networks typically serve rural communities, connecting towns, villages, farmland, and remote areas, and provide essential transport services to local residents, while also supporting agro-logistics, tourism, and other economic activities. As rural areas grow, the complexity and scale of rural transportation networks increase. Many tourists and road users rely on these networks for regular service.