Short-term scheduling optimization of battery electric buses in the context of sustainable energy resources under uncertainty

• This study presents a robust optimization model for short-term scheduling of battery electric buses (BEBs), integrating vehicle-to-grid (V2G) and grid-to-vehicle (G2V) services while addressing uncertainty in energy demand and pricing. • A mixed-integer linear programming (MILP) model combined with metaheuristic algorithms efficiently assigns BEBs to charging stations, optimizing operational costs and enhancing sustainability through renewable energy integration. • The model incorporates robust counterpart formulations under box and polyhedral uncertainty sets, demonstrating its effectiveness in managing fluctuating demand, pricing, and capacity to maximize profitability and system reliability. With growing emphasis on sustainability goals, particularly in adopting electric vehicles (EVs) as a public transportation mode, battery electric buses (BEBs) have attained significant market attention. However, a critical obstacle lies in efficiently assigning BEBs to suitable charging stations (CSs) during daily transit operations, which still need enough space to be filled. The primary goal is to allocate BEB to the best CSs while focusing on increasing overall profit by serving the grid and passenger needs effectively. To solve this issue, several factors are considered, including transit hours, sustainable energy resources, state-of-charge (SOC), vehicle-to-grid (V2G) and grid-to-vehicle (G2V) service trading, bus, CS capacity, data-sharing, and route dynamics. A mixed-integer linear programming (MILP) model framework is constructed, utilizing energy network flows and operational-level information to optimize short-term scheduling. Due to the large-scale nature of the problem, metaheuristic algorithms are used to solve the proposed model. The objective seeks to maximize the profit of the transportation company (TC), which owns both CSs and BEBs, by optimally scheduling the CS selection for its in-transit buses. In addition, the model simultaneously considers the peak hours of energy capacities and its transactions. The model is enhanced through a robust counterpart formulation, incorporating a realistic case study that addresses uncertainties in critical parameters such as electricity selling prices and purchasing costs. By dynamically optimizing charging station selection and energy trading strategies, the robust model successfully maintains 90 % of the deterministic profit under independent price fluctuations (box uncertainty) and 78 % under correlated market risks (polyhedral uncertainty). Consequently, the proposed framework effectively balances operational efficiency with resilience against price volatility, supporting reliable scheduling operations while optimizing renewable energy integration and enhancing grid flexibility.