Cost minimizing decisions on equipment and charging schedule for electric buses in a single depot

Combined decisions on equipment and charging schedule for electric buses (e-buses) are studied in this paper. The most representative day is considered, in which each e-bus fulfills a transfer task composed of a series of passenger transportation trips. Each trip starts and terminates at given times in the same single depot where e-buses re-charge their batteries. The problem is to determine battery variants for the e-buses, number of chargers of different types and daily cyclic charging schedule of e-buses such that a linear combination of (a) the total daily cost of the charging equipment, batteries wear and consumed energy, and (b) the total number of e-bus charging interruptions (switchings) is minimized. The constraints include an upper bound on the supplied electric power, restoration of the initial battery energy state before the next day transfer task for each e-bus and an upper bound on the maximal number of switchings for each e-bus in each depot visit over all e-buses and visits. A bi-level decomposition approach is proposed, in which decisions and constraints related to the detailed charging schedule and the number of switchings are moved to the lower-level problem. The lower level problem is formulated as Mixed Integer Linear Programming (MILP) problem. The upper-level problem is reduced to a MILP problem using linearization techniques. An exact decomposition scheme is developed for the upper-level MILP problem. A case study and comprehensive computer experiments are provided.