Due to the issue of the sustainability in transportation area, the number of electric vehicles has significantly increased. Most automakers have decided or planned to manufacture the electric vehicles rather than carbon fueled vehicles. However, there are still some problems to figure out for the electric vehicles such as long charging time, driving ranges, supply of charging stations. Since the speed of growing the number of electric vehicles is faster than that of the number of charging stations, there are lack of supplies of charging stations for electric vehicles and imbalances of the location of the charging stations. Thus, the location problem of charging stations is one of important issues for the electric vehicles. Studies have conducted to find the optimal locations for the charging stations. Most studies have formulated the problem with deterministic or hierarchical models. In this paper, we have investigated the fluctuations of locations and the capacity of charging stations. We proposed a mathematical model for the location problem of charging stations with the vehicle routing problem. Numerical examples provide the strategy for the location routing problems of the electric vehicles.

Evaluating the operational efficiency of electric vehicle charging stations (EVCSs) is important to understand charging network evolution and the charging behavior of electric vehicle users. However, aggregation of efficiency performance metrics poses a significant challenge to practitioners and researchers. In general, the operational efficiency of EVCSs can be measured as a complicated function of various factors with multiple criteria. Such a complex aspect of managing EVCSs becomes one of the challenging issues to measure their operational efficiency. Considering the difficulty in the efficiency measurement, this paper suggests a way to measure the operational efficiency of EVCSs based on data envelopment analysis (DEA). The DEA model is formulated as constant returns of output-oriented model with five types of inputs, four of them are the numbers of floating population and nearby charging stations, distance of nearby charging stations and traffic volume as desirable inputs and the other is the traffic speed in congestion as undesirable one. Meanwhile, the output is given by the charging frequency of EVCSs in a day. Using real-world data obtained from reliable sources, we suggest operational efficiencies of EVCSs in Seoul and discuss implications on the development of electric vehicle charging network. The result of efficiency measurement shows that most of EVCSs in Seoul are inefficient, while some districts (Nowon-gu, Dongdaemun-gu, Dongjak-gu, Songpa-gu, Guro-gu) have relatively more efficient EVCSs than the others.