Chance-constrained battery management strategies for the electric bus scheduling problem
Léa Ricard, Guy Desaulniers, Andrea Lodi, Louis-Martin Rousseau
TL;DR
This work tackles electric bus scheduling under uncertainty in energy consumption and battery degradation by formulating a chance-constrained electric vehicle scheduling problem (E-VSP) on a time-expanded, connection-based network that supports partial en-route charging and nonlinear CC-CV charging. A tailored branch-and-price algorithm with stochastic pricing problems and a labeling framework computes schedules while enforcing a chance constraint that keeps SoC within a safe range $[\sigma^{low}, \sigma^{up}]$ with probability at least $1-\epsilon$, without relying on a specific capacity fading model. Key contributions include the probability-based decomposition via $P_s$, a stochastic dominance rule for labels, and heuristic branching with constraint perturbation, all demonstrated on realistic instances where small increases in $\epsilon$ yield notable operational savings and reduced battery wear. The results provide actionable guidance for fleet operators to balance cost efficiency and battery longevity, including how to choose $\epsilon$ and how the safe SoC range interacts with degradation under Monte Carlo-based fading assessments. Overall, the framework enables more flexible and durable EB scheduling by explicitly accounting for uncertainty and battery health in a scalable optimization approach.
Abstract
The global transition to battery electric buses (EBs) presents an opportunity to reduce air and noise pollution in urban areas. However, the adoption of EBs introduces challenges related to limited driving range, extended charging times, and battery degradation. This study addresses these challenges by proposing a novel chance-constrained model for the electric vehicle scheduling problem (E-VSP) that accounts for stochastic energy consumption and battery degradation. The model ensures compliance with recommended state-of-charge (SoC) ranges while optimizing operational costs. A tailored branch-and-price heuristic with stochastic pricing problems is developed. Computational experiments on realistic instances demonstrate that the stochastic approach can provide win-win solutions compared to deterministic baselines in terms of operational costs and battery wear. By limiting the probability of operating EBs outside the recommended SoC range, the proposed framework supports fleet management practices that align with battery leasing company and manufacturer guidelines for battery health and longevity.