The development of electric vehicles (EVs) has led to an increase in the number of electric vehicle charging stations (EVCSs). However, the lack of proper charging infrastructure can demote the expansion of the electric transportation fleet. In this regard, reducing the impact of EVCS on the distribution networks and choosing optimal charging operations are essential challenges. The optimal placement of an EVCS to minimize the supply cost will encourage the rapid development of the EV transportation system. This paper presents a two-step linear programming (LP) solution for the placement of EVCS with the purpose of optimal operation of an electric vehicle charging station. The charging starting time and charging time interval of each EV are modeled as uncertainty variables. A case study based on a medium-voltage CIGRE distribution network is used to perform simulations and demonstrate the proposed methodology. The numerical analysis is carried out for different charging operation modes based on the standard EV conductive charging systems, IEC 61851.