A Lagrangian relaxation approach for the electric bus charging scheduling optimisation problem

The planning and operational decision-making problems of electric transit systems have received significant attention recently in the process of transport electrification. Given an electrified electric transit system with constructed charging facilities, a coordinated bus charging scheduling strategy can improve the system's operating efficiency by fully utilising available charging resources. This paper proposes a novel optimisation approach for the electric bus charging scheduling problem. To tackle the nonlinear relationship between the amount of energy and the time spent charging, this paper discretizes the decision variables for the charging schedule into time intervals. A linear integer program is formulated with the objective of minimising the system's total charging time. A Lagrangian relaxation-based solution approach is proposed to decompose the model into subproblems with respect to individual vehicles. The results provide a number of insights that can help transit operators design cost-effective electric transit operational plans.