Traffic congestion significantly increases fuel/electric consumptions of vehicles in road transportation and causes other environmental and economic costs as well. A road-based delivery company can reduce its operating cost through operational decisions such as efficient vehicle routes and delivery schedules by considering time varying traffic congestion in its service area. In this study, we observe the green fixed tour scheduling problem with electric vehicles (GFTSP-EV) aiming to minimize electric consumptions of electric vehicles in logistics systems through better planning of delivery time and charging time. We define a mixed-integer linear programming (MILP) model which considers nonlinear charging functions, time varying traffic congestion, customer time window constraints and the impact of vehicle loads and velocities on electric consumptions in the GFTSP-EV. The proposed model allows vehicles to wait at nodes of customers and determine charging time, which is shown to reduce electric consumptions compared with the non-waiting assumption on simulated data (small-sized instances) solved by a commercial optimization toolbox, CPLEX, with promising results, and so the efficiency and effectiveness of the approach are confirmed. The study can potentially be implemented by road-based logistics companies that wish to align their businesses with the idea of sustainability. The study can also help individual vehicle drivers make more economical travel schedules and lower their carbon dioxide emissions.