Multi-Criteria Decision Making and Graph Theory-Based Optimization of the Lahore Metro System: A Metric Dimension, VIKOR, and PROMETHEE Approach

Urban transportation networks play a crucial role in modern city planning, requiring efficient design, optimization, and management strategies. This study examines the Lahore Metro Orange Line using a combination of graph theory and multi-criteria decision-making (MCDM) techniques, specifically the metric dimension analysis, VIKOR, and PROMETHEE methods. The research begins with graph-theoretic modeling, where metro stations are treated as nodes and railway tracks as edges, revealing that the system exhibits a metric dimension of 1, indicating that a single reference station is sufficient for uniquely identifying all others. To further enhance decision-making for metro optimization, VIKOR is applied to rank stations based on key performance criteria such as passenger flow, accessibility, centrality, and congestion levels. Additionally, PROMETHEE is used to establish a preference-based ranking system, identifying priority stations for infrastructure improvements and congestion management. The findings highlight that integrating graph theory with MCDM approaches provides data-driven insights for optimizing urban transit systems. The study offers valuable recommendations for metro expansion planning, efficient station management, and smart city integration. The proposed methodologies can be adapted to other metro networks, making them scalable, commuter-friendly, and operationally robust.