A Multi-Period Optimization Model for Bus Fleet Allocation: Balancing Operational Costs, Social Discomfort, and Environmental Impact

This paper presents a multi-period mixed-integer linear programming model for optimizing bus fleet allocation and frequency setting in urban transit systems. The model simultaneously minimizes operational costs, passenger discomfort (from overcrowding and waiting), and carbon emissions while adhering to operational constraints. Unlike traditional single-period approaches, our formulation captures temporal demand variations throughout the day, enabling more responsive service planning. Computational experiments using adapted real-world data were used to create 8 different scenarios, which test the sensitivity of the model. Results reveal capacity thresholds beyond which service quality deteriorates, illustrating trade-offs between passenger experience and resource utilization. Furthermore, the model successfully balances service quality during peak hours while maintaining efficiency during off-peak periods. This approach represents an advance in sustainable transit planning by integrating social and environmental considerations with operational metrics, supporting transport authorities in developing more equitable, efficient, and environmentally responsible service strategies.