Modeling and optimizing mileage homogeneity in public transportation using Gini index

Fleets of city buses experience uneven allocation of miles, which causes uneven wear, elevated maintenance expenditures, and inefficiencies when providing service. This research proposes the application of the Gini index as a base-objective function for attaining a higher level of homogeneity of miles traveled by fleets. Using 756 days of operating data from 160 articulated public buses serving Makkah, Saudi Arabia, the research initially assesses the scope of each day's mileage inequalities using descriptives and Lorenz curve interpretation. The results suggest unevenness during the early operations significantly, whereby the Gini attains a maximum of 0.38, diminishing as allocation tactics by heuristics were undertaken. To further reduce the level of unevenness, an integer model employing the Gurobi optimizer was formulated for Python. Used for a subset of 25 buses, the model reduced the Gini from a level of 0.1648 (mean) down to a level of 0.0462, exhibiting a significant improvement regarding fairness of work. Beyond the numeric contribution, the research results call attention further to operational merits, such as level maintenance scheduling, expanded lifetimes for vehicles, and increased sustainability. While the analysis focuses on a single large-scale urban bus network, the proposed framework can be extended to multi-route and multi-modal systems, incorporating demand variability and additional equity dimensions in future research. By integrating the Gini index as a transport planning objective into the vehicle assignment problem naturally, the research connects transport justice with the efficiency of operations, providing transport agencies with a functional model for sustainable and equitable bus operations.