## 4 Case Study Development and Results
This means that as the EVCS network becomes denser, the EV user can more easily find a nearby available station to charge at and, therefore, reduce the daily travel distance. However, the number of charging stations should be determined and kept at a certain level, based on the charging demand, the size of the area of interest/service coverage, as well as any budget availability constraints. A number of runs have been made for different values of the w1/w2 ratio of Equation (3) (i.e., the relative weights of the model objective function). For instance, with w1/w2 = 100, the optimal number of stations is 12 (based on repetitive runs). The full picture of this investigation is depicted in Figure 7. At a low value of w1/w2 = 25, the optimal number of stations is 25, while at w1/w2 = 300, a network of 5 stations provides the best solution. The wi's are the input values representing each specific charging station deployment area and provide the appropriate number of stations that better serves the tradeoff between deployment cost and EV travel cost. In terms of computational effort, the multi-objective configuration requires more time (as it solves a more complex problem), which, compared to the single-objective travel distance problem, presents an increased time by an order of 1.3 to 1.5 times in average values. Figure 6: Total distance traveled by EV users as a function of the number and capacity of charging stations. Case Study 4: Station Allocation for \(EV\) Travel Distance (Cost) Minimization for Different Station Deployment Cost Zones  
The previous analyses assume the same cost for deploying all charging stations within a scenario. However, it is known that different land uses and human activity concentrations create different cost zones within a city. To account for such cost variances, the present analysis considers four different cost zones in the form of inner to outer rectangles, with the cost being the highest in the inner zone and decreasing outward. Another parameter that plays a role in the charging station allocation is the cost rate among zones. As part of this study, different zone cost sets have been analyzed, with the expected result of station construction toward the cheaper zones, especially if the cost proportions are high. A representative allocation solution for this case is presented in Figure 8.  
Figure 8: Optimal charging station deployment for 10 stations: (**a**) fixed station cost; (**b**) variable station cost (demand points in blue color, charging stations in orange color, highest cost zone in beige color, lowest cost zone in purple color). Figure 7: Optimal number of charging stations for different w1/w2 ratios. Case Study 5: Station Allocation for EV Travel Distance (Cost) Minimization for Highly Unequal Demand Dispersion  
The demand distribution is quite unequal in certain cases. For example, places of high interest (e.g., downtown premises, shopping malls, sport arenas, etc.) may attract a high charging demand. This may be modeled by a disproportionally increased demand at specific sites. To deal with this case, an example is formulated based on the original input data but considering 10 random locations having 5 or 10 times higher demand than all other spots. Here, 15 charging stations are considered for serving the EV demand. The station allocation results are indicated in Figure 9. The dark blue dots indicate low-demand spots, the light blue ones are high-demand spots, and the orange circles indicate station places. It can be seen that 10 out of 15 stations are placed exactly on or close to high-demand spots, while the other 5 stations are optimally placed to cover the sparse demand. Case Study 6: Station Allocation for EV Travel Distance (Cost) Minimization for Irregular Service Area Shape  
An interesting research question with practical importance is the adjustment of the solutions to the uneven shape of a typical city or neighborhood area.