Optimization of Bus Dispatching in Public Transportation Through a Heuristic Approach Based on Passenger Demand Forecasting

Accurate and adaptive bus dispatching is vital for medium-sized urban centers, where static schedules often fail to accommodate fluctuating passenger demand. In this work, we propose a dynamic heuristic that integrates machine learning-based demand forecasts into a discrete-time planning horizon, thereby enabling real-time adjustments to dispatch decisions. Additionally, we introduce a tailored mathematical model—grounded in mixed-integer linear programming and space-time flows—that serves as a benchmark to evaluate our heuristic’s performance under the operational constraints typical of traditional public transportation systems in Colombian mid-sized cities. A key contribution of this research lies in combining predictive modeling (using Prophet for passenger demand) with operational optimization, ensuring that dispatch frequencies adapt promptly to varying ridership levels. We validated our approach using a real-world case study in Montería (Colombia), covering eight representative routes over a full day (5:00–21:00). Numerical experiments show that: 1. Our heuristic matches or surpasses 95% of the optimal solution’s operational utility on most routes, with an average gap of 4.7%, relative to the benchmark mathematical model. 2. It maintains high service levels—above 90% demand coverage on demanding corridors—and robust bus utilization, without incurring excessive operating costs. 3. It reduces computation times by up to 98% compared to the optimization model, making it practically viable for daily scheduling where solving large-scale models exactly can be prohibitively time-consuming. Overall, these results underscore the heuristic’s practical effectiveness in boosting profitability, optimizing resource use, and rapidly adapting to demand fluctuations. The proposed framework thus serves as a scalable and implementable tool for transportation operators seeking data-driven dispatch solutions that balance operational efficiency and service quality.