## 5 Experimental Results  
The simulation model and the algorithms were implemented in AnyLogic 8.6.0 [57] software, and run in a standard desktop with an Intel(r) Core(tm) i7- 9700K CPU @3.60 GHz and 16 GB RAM. This section firstly describes the main results when running the simulation for different cooperation settings. Secondly, we analyse the general effects of an unexpected increase on demand figures. Figure 8: Simulation dynamics overview. The main results are depicted in Figures 9 and 10. They show the boxplots of average distances driven and lead times (which are defined as the temporal distances between the minimum value of the time window and the time when the customer received his or her order) of the 100 simulation replications, respectively. Tables 3 and 4 display average distance driven (in km) and average lead times (in minutes), respectively, for each supermarket and cooperation settings. They also show the percentage variation in the averages for non- and limited cooperation and limited and full cooperation strategies. Note that the last row in Table 3 shows the total distance driven by all supermarkets during a week, whereas the last row in Table 4 shows the average lead time a customer has to be waiting, independently from the chosen supermarket. As it can be observed, horizontal cooperation significantly improves the logistics performance of the e-grocery distribution. First of all, the total distance driven is reduced by a 20.25% when the limited cooperation mechanism is activated; and by a 42.96% when full cooperation is achieved, on average. Nevertheless, this effect clearly depends on the size of the supermarket (in terms of expected demand). Reductions are greater for large supermarkets (up to 49.27%) and much lower for smaller supermarkets (up to 30.58%). Secondly, service quality, measured as the lead time, is also benefited from the application of horizontal cooperation in a similar way. Actually, average lead time is reduced by a 22.54% and a 46.21%, on average, for limited and full cooperation, respectively. Here, the size of the supermarket also determines the horizontal cooperation impacts amplitude. Finally, we can observe how boxplots ranges and interquartile ranges clearly get reduced for all supermarkets when cooperation is implemented. Therefore, the KPIs, that is, distances and lead times, gain stability while uncertainty is mitigated. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **No Cooperation** & **Limited Cooperation** & \% **Change** & **Full Cooperation** & \% **Change** \\ \hline S1 & 166.69 & 126.74 & \(-\)23.97\% & 80.36 & \(-\)51.79\% \\ S2 & 147.77 & 115.58 & \(-\)21.78\% & 84.97 & \(-\)42.50\% \\ S3 & 134.14 &  
Figure 9: Boxplots for the average distance driven in the 100 replications for non-. Limited, and full cooperation settings for each supermarket. Figure 10: Boxplots for the average lead times in the 100 replications for non-, limited, and full cooperation settings for each supermarket. Furthermore, additional scenarios have been analysed in order to demonstrate the robustness of the presented approach, featuring increases on the demand figures. Our aim is showing that the horizontal cooperation benefits are kept when we depict a wide range of scenarios. We consider three demand scenarios. Firstly, the base scenario, which has been already analysed and whose demand is estimated in Section 3. Secondly, a scenario featuring an increase of a 25% on demand figures. Finally, a scenario in which the number of orders increase a 50%. The fleet size is kept fixed for all the scenarios according to the description made in Section 4.3. Tables 5 and 6 show the KPIs obtained from the results in the mentioned scenarios, that is, distance driven and lead times, respectively. The first row in the tables show the scenarios to be addressed, the second one the cooperative strategy to be employed, the next four rows show the average results for each of the four supermarkets, and the last row the overall average results.