Stochastic Optimization in Charging Station Planning and a Robust Methodology with a Statistical Upper Bound Framework

Abstract

Metropolitan areas globally are increasingly adopting electric taxis (ET) to mitigate transportation-related emissions, leading to a significant impact on urban transportation networks (TN) and electricity power distribution networks (PDN). This evolution presents challenges, including higher electricity demand and altered demand profiles, which underscore the critical interdependence between these systems. To address these complexities, we propose a novel two-stage stochastic programming planning model aimed at optimizing both the TN and PDN. This model strives to balance ET drivers' charging preferences, minimize infrastructure deployment and grid expansion costs, and ensure synchronized coordination between the TN and PDN. In transitioning to a more sustainable urban mobility paradigm, we also consider the advantages of incorporating an autonomous ET fleet to boost system efficiency.The application of stochastic optimization in this context, however, is often obstructed by distributional ambiguity - where crucial probability distributions are not well-defined or are unknown. To counteract this, our study introduces an innovative approach that leverages the Average Percentile Upper Bound (APUB) framework. APUB is designed to minimize a statistical upper bound for the expected value of uncertain objectives, thus providing a more robust foundation for decision-making under uncertainty. This method offers a statistically rigorous upper limit for the population mean while serving as a viable risk metric for the sample mean. By integrating APUB into our stochastic optimization model, we address distributional ambiguities inherent in the deployment of electric taxis and their charging stations, thereby enhancing the model's reliability, consistency, and comprehensibility. Our empirical investigations, using two-stage product mix and multi-product newsvendor benchmark problems, demonstrate the effectiveness of the APUB-enhanced optimization framework compared to traditional methods such as sample average approximation and distributionally robust optimization. This combined approach ensures that the transition to electric taxis not only addresses environmental concerns but also proceeds with a robust and economically feasible strategy for infrastructure development.