Integrated Optimization of Scheduling and Flexible Charging in Mixed Electric-Diesel Urban Transit Bus Systems

TL;DR

This paper addresses the integrated optimization of scheduling and charging for mixed fleets of BEBs and DBs in urban transit. It introduces a mixed-integer linear program (MILP) that jointly optimizes fleet composition, daily vehicle schedules, and flexible charging across garage and terminal locations, including both slow and fast chargers and partial charging. To tackle computational complexity, a column generation (CG) framework is developed, with a BEB subproblem formulated as a shortest path problem with resource constraints (SPPRC) and stabilized by a tailored pricing and stalling strategy; a two-stage heuristic accelerates pricing for large instances. Numerical experiments on Chicago CTA and Pace data show that mixed BEB/DB fleets can reduce total costs under certain BEB-share levels, while restricting charging to garages increases fleet size and costs, underscoring the value of distributed opportunistic charging. The work provides a scalable methodology for transit agencies contemplating BEB adoption and informs charger placement and operational policies that balance capital and operating expenditures.

Abstract

The transition of transit fleets to alternative powertrains offers a potential pathway to reducing the cost of mobility. However, the limited range and long charging durations of battery electric buses (BEBs) introduce significant operational complexities, necessitating innovative scheduling and charging strategies. This study proposes an integrated mixed-integer linear programming model to optimize vehicle scheduling and charging strategies for mixed fleets of BEBs and diesel buses. Unlike existing models, which often assume a fixed BEB fleet size or restrict charging to a single charger type, our approach simultaneously determines the optimal fleet composition, scheduling, and flexible partial charging strategy incorporating both slow and fast chargers at garages and terminal stations. The model minimizes combined fleet purchase and operational costs. A queuing strategy is introduced, departing from traditional first-come, first-served methods by dynamically allocating waiting and charging times based on operational priorities and resource availability, improving overall scheduling efficiency. To overcome computational complexities arising from numerous variables, a column generation framework is developed, facilitating scalable solutions for large-scale transit networks. Numerical experiments using real-world transit data from the Chicago Transit Authority and the Pace suburban bus systems demonstrate the model's effectiveness. Results indicate that while a full transition to alternative powertrains results in a modest cost increase, optimal mixed-fleet configurations can actually reduce total system costs. Furthermore, sensitivity analyses reveal that restricting charging to garages significantly increases fleet size and operational costs, underscoring the potential of distributed opportunistic charging.

Figures (13)

• Figure 1: Queuing strategies for BEBs at charging stations.
• Figure 2: Comparison of computational time for Exact and CG methods.
• Figure 3: Change in the total system cost relative to the baseline scenario ($A^\nu=0$).
• Figure 4: Fleet decomposition under different BEB penetration rates.
• Figure 5: Average percentage of operational time distributed across different activities.