Battery-electric transit vehicle scheduling with optimal number of stationary chargers

Because of zero emissions and other social and economic benefits, electric vehicles (EVs) are currently being introduced in more and more transit agencies around the world. One of the most challenging tasks involves efficiently scheduling a set of EVs considering the limited driving range and charging requirement constraints. This study examines the battery-electric transit vehicle scheduling problem (BET-VSP) with stationary battery chargers installed at transit terminal stations. Two equivalent versions of mathematical formulations of the problem are provided. The first formulation is based on the deficit function theory, and the second formulation is an equivalent bi-objective integer programming model. The first objective of the math-programming optimization is to minimize the total number of EVs required, while the second objective is to minimize the total number of battery chargers required. To solve this bi-objective BET-VSP, two solution methods are developed. First, a lexicographic method-based two-stage construction-and-optimization solution procedure is proposed. Second, an adjusted max-flow solution method is developed. Three numerical examples are used as an expository device to illustrate the solution methods, together with a real-life case study in Singapore. The results demonstrate that the proposed math-programming models and solution methods are effective and have the potential to be applied in solving large-scale real-world BET-VSPs