Pune Bus Optimization: An Intelligent Scheduling System Driven by Mixed Integer Programming and Machine Learning

This article explores how the PMPML bus network in Pune, India, achieves optimal headway allocation through mixed integer programming, machine learning demand forecasting, and decision-focused learning, aiming to improve public transport efficiency and solve the problem of supply-demand mismatch.

Pune is the second-largest city in Maharashtra, India, and an educational and industrial hub. With population growth, the PMPML bus network faces issues such as unreasonable headways, long passenger waiting times, and high operational costs. Traditional scheduling relies on experience, making it difficult to match dynamic demand—overcrowding during peak hours and empty runs during off-peak periods—leading to poor passenger experience and inefficient resource utilization.

This project develops an optimal headway allocation system for PMPML, integrating three technical pillars: operations research optimization, machine learning forecasting, and end-to-end decision learning. The core goal is to minimize operational costs and maximize service quality while meeting passenger demand, considering factors such as line passenger flow, vehicle capacity, operational costs, and passenger waiting time.

Mixed Integer Programming is the mathematical foundation of the system, handling complex decision problems involving continuous and integer variables (headways are in integer minutes). The constructed MIP model includes decision variables (headways for each line, number of vehicles allocated), objective function (minimizing the sum of total operational costs and passenger waiting time costs), and constraints (total vehicle limit, line coverage requirements, maximum waiting time threshold). The globally optimal headway configuration is obtained through solving the model.

Static optimization requires accurate input data, so a machine learning module is introduced to predict passenger demand across different time periods and lines. The model considers time features (hour, day of week, month, holidays), historical passenger flow, external factors (weather, special events, school cycles), and spatial features (line area type). By training on historical data, it predicts passenger flow distribution in advance, providing precise input for the optimization module to proactively adapt to demand changes.

Traditional machine learning optimizes prediction accuracy independently, which may amplify errors. Decision-Focused Learning uses end-to-end training directly targeting decision quality: during training, it considers prediction errors and the decision cost after inputting into the optimizer. Through gradient propagation, the prediction model generates predictions that are "useful" for decision-making, improving the robustness of scheduling plans and breaking the two-stage separation paradigm of "prediction-optimization".

The project provides a replicable framework for developing cities: for operators, it reduces empty run rates, fuel consumption, and wear and tear, allowing them to serve more passengers with the same budget; for passengers, it shortens waiting times and reduces overcrowding, enhancing the attractiveness of public transport; for planners, it provides data support to assist with network adjustments and investment decisions; technically, it demonstrates the potential of integrating operations research and machine learning, pointing the way for intelligent transportation.

The Pune bus optimization project successfully applies Decision-Focused Learning to real-world transportation problems, proving the transformative power of data science. With the popularization of IoT and 5G, real-time data collection becomes more convenient, and intelligent optimization systems are expected to achieve more granular dynamic adjustments. The project provides an open-source implementation, offering valuable references for researchers and engineers.