## 5 Case Study  
The company studied in this work is a highly relevant e-commerce retailer in the industry, covering the entire Latin American region. The sample used in this study consists of data from one day of deliveries in the city of Sao Paulo, Brazil. A total of 1.2 thousand shipments delivered throughout the city of Sao Paulo were analyzed, and specific regions were selected for the evaluation of the heuristic. In the problem, the objective is to minimize travel costs, which include costs per hour of travel and per kilometer traveled. All distance and time information between points were calculated using the OpenStreetMap API, and data for the vehicles used, which consist of electric bicycles, used as parameters for the model, were estimated based on the work of [PERSON] (2016), technical specifications from the manufacturers of the vehicles, company data, and the freight table from the TRC Guide (2016). The data include the capacity of the bicycles, which is 15 packages given the delivery profile in the regions, a cost of 0.35 per kilometer (km) traveled, and a cost of 29.25 per working hour, in Brazilian real, to be used in the second echelon. For the first echelon, a truck with a capacity of 450 packages is used, with a cost of BRL 1.89 per kilometer (km) traveled and a cost of BRL 81.69 per working hour. The evaluated regions were the neighborhoods of Mooca, Pinheiros, Republica, and Tucuruvi, as they are some of the main extremes of the city, with Pinheiros being slightly closer to the distribution center than the others; Tucuruvi, with slightly lower demand than normal; Republica, with one of the highest daily demands; and Mooca, a region with extremely high demand and irregular terrain, with few flat areas. Figure 2 contains images of the four regions, with customers marked with blue drops and satellites in red, green, and brown drops. \begin{table}
\begin{tabular}{l r r r r r r} \hline \hline  & **nS** & **nC** & **BKS** & **T (s)** & **heur. \({}^{*}\)** & **T (s)** & **\%dev2** \\ \hline
**Set 3a** & & & & & & & \\ E-n22:k4=s13-14 & 2 & 21 & 526.15 & 43.00 & 526.15 & 0.03 & 0.0\% \\ E-n22:k4=s13-16 & 2 & 21 & 521.09 & 44.00 & 561.84 & 0.05 & 7.8\% \\ E-n22:k4=s13-17 & 2 & 21 & 496.38 & 49.00 & 496.38 & 0.02 & 0.0\% \\ E-n22:k4=s14-19 & 2 & 21 & 498.80 & 43.00 & 517.80 & 0.02 & 3.8\% \\ E-n22:k4=s17-19 & 2 & 21 & 512.80 & 26.00 & 524.80 & 0.02 & 2.3\% \\ E-n22:k4=s19-21 & 2 & 21 & 520.42 & 34.00 & 545.72 & 0.01 & 4.9\% \\ E-n33:k4=s16-22 & 2 & 32 & 672.17 & 58.00 & 689.83 & 0.15 & 2.6\% \\ E-n33:k4=s16-24 & 2 & 32 & 666.02 & 60.00 & 747.90 & 0.25 & 12.3\% \\ E-n33:k4=s19-26 & 2 & 32 & 680.36 & 60.00 & 689.21 & 0.06 & 1.3\% \\ E-n33:k4=s22-26 & 2 & 32 & 680.36 & 60.00 & 708.27 & 0.16 & 4.1\% \\ E-n33:k4=s24-28 & 2 & 32 & 670.43 & 60.00 & 677.69 & 0.22 & 1.1\% \\ E-n33:k4=s25-28 & 2 & 32 & 650.58 & 60.00 & 722.64 & 0.18 & 11.1\% \\  & & & **Avg.** & **49.75** & & **0.10** & **4\%** \\
**Set3b** & & & & & & & \\ E-n51:k5=s12-18 & 2 & 50 & 690.59 & 60.00 & 694.18 & 0.13 & 0.5\% \\ E-n51:k5=s12-41 & 2 & 50 & 683.05 & 60.00 & 704.66 & 0.24 & 3.2\% \\ E-n51:k5=s12-43 & 2 & 50 & 710.41 & 60.00 & 849.89 & 0.12 & 19.6\% \\ E-n51:k5=s39-41 & 2 & 50 & 728.54 & 60.00 & 788.26 & 0.23 & 8.2\% \\ E-n51:k5=s40-41 & 2 & 50 & 723.75 & 60.00 & 730.11 & 0.18 & 0.9\% \\ E-n51:k5=s40-43 & 2 & 50 & 752.15 & 60.00 & 822.11 & 1.41 & 9.3\% \\  & & & **Avg.** & **60.00** & & **0.38** & **7\%** \\
**Set3c** & & & & & & & \\ E-n51:k5=s13-19 & 2 & 50 & 560.73 & 60.00 & 570.12 & 0.47 & 1.7\% \\ E-n51:k5=s13-42 & 2 & 50 & 564.45 & 60.00 & 618.68 & 1.79 & 9.6\% \\ E-n51:k5=s13-44 & 2 & 50 & 564.45 & 60.00 & 644.85 & 6.52 & 14.2\% \\ E-n51:k5=s40-42 & 2 & 50 & 746.31 & 60.00 & 764.60 & 0.24 & 2.5\% \\ E-n51:k5=s41-42 & 2 & 50 & 771.56 & 60.00 & 857.37 & 0.17 & 11.1\% \\ E-n51:k5=s41-44 & 2 & 50 & 802.91 & 60.00 & 831.81 & 0.09 & 3.6\% \\  & & & & **Avg.** & **60.00** & & **1.55** & **7\%** \\ \hline \hline \end{tabular} \({}^{*}\)heur.: Results of the heuristic.  
\end{table}