## 4 Methodology  
For analyzing the impacts of horizontal cooperation on the urban e-grocery distribution we have developed an agent-based simulation model. This simulation model accounts for two populations of agents (i.e., the _customers_ and the _supermarket_) who interact in the Pamplona metropolitan physical environment. Additionally, the coalition of supermarkets is also included as an agent. This coalition agent includes the supermarket agents and the different cooperative protocols, including the non cooperative setting in which the supermarkets act independently. Thus, each generated entity, as agent in the simulation model, has its own parameters, variables and rules that describe its behavior in the environment. Actually, we chose an agent-based simulation approach because it allows to easily deal with complexity and interdependencies between _customers_ and _supermarkets_ in cooperative and non cooperative settings [45]. As it is described in forthcoming subsections, the idea behind the simulation model is that _customers_ place orders to their preferred _supermarket_ choosing the time to receive their products inside a _time window_. Afterwards, the _supermarkets_ have to fulfill the orders using the cooperative policies or not, depending on the running settings. This simulation model takes the backbone of the previous work \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Day of the Week** & **Time Window** & **S1** & **S2** & **S3** & **S4** \\ \hline \multirow{8}{*}{Monday} & 7–10 h & 38.88 & 20.10 & 16.57 & 10.60 \\  & 10–13 h & 64.79 & 33.50 & 27.61 & 17.67 \\  & 13–16 h & 64.79 & 33.50 & 27.61 & 17.67 \\  & 16–19 h & 103.67 & 53.60 & 44.18 & 28.27 \\  & 19–22 h & 181.42 & 93.80 & 77.31 & 49.48 \\ \hline \multirow{8}{*}{Tuesday} & 7–10 h & 25.92 & 13.40 & 11.04 & 7.07 \\  & 10–13 h & 38.88 & 20.10 & 16.57 & 10.60 \\  & 13–16 h & 64.79 & 33.50 & 27.61 & 17.67 \\  & 16–19 h & 129.58 & 67.00 & 55.22 & 35.34 \\  & 19–22 h & 155.50 & 80.40 & 66.27 & 42.41 \\ \hline \multirow{8}{*}{Wednesday} & 7–10 h & 25.92 & 13.40 & 11.04 & 7.07 \\  & 10–13 h & 38.88 & 20.10 & 16.57 & 10.60 \\  & 13–16 h & 51.83 & 26.80 & 22.09 & 14.14 \\  & 16–19 h & 103.67 & 53.60 & 44.18 & 28.27 \\  & 19–22 h & 194.38 & 100.50 & 82.83 & 53.01 \\ \hline \multirow{8}{*}{Thursday} & 7–10 h & 51.83 & 26.80 & 22.09 & 14.14 \\  & 10–13 h & 51.83 & 26.80 & 22.09 & 14.14 \\  & 13–16 h & 64.79 & 33.50 & 27.61 & 17.67 \\  & 16–19 h & 77.75 & 40.20 & 33.13 & 21.20 \\  & 19–22 h & 116.63 & 60.30 & 49.70 & 31.81 \\ \hline \multirow{8}{*}{Friday} & 7–10 h & 38.88 & 20.10 & 16.57 & 10.60 \\  & 10–13 h & 38.88 & 20.10 & 16.57 & 10.60 \\  & 13–16 h & 64.79 & 33.50 & 27.61 & 17.67 \\  & 16–19 h & 116.63 & 60.30 & 49.70 & 31.81 \\  & 19–22 h & 129.58 & 67.00 & 55.22 & 35.34 \\ \hline \multirow{8}{*}{Saturday} & 7–10 h & 0.00 & 0.00 & 0.00 & 0.00 \\  & 10–13 h & 77.75 & 40.20 & 33.13 & 21.20 \\ \cline{1-1}  & 13–16 h & 38.88 & 20.10 & 16.57 & 10.60 \\ \cline{1-1}  & 16–19 h & 12.96 & 6.70 & 5.52 & 3.53 \\ \cline{1-1}  & 19–22 h & 38.88 & 20.10 & 16.57 & 10.60 \\ \hline \multirow{8}{*}{Sunday} & 7–10 h & 12.96 & 6.70 & 5.52 & 3.53 \\ \cline{1-1}  & 10–13 h & 25.92 & 13.40 & 11.04 & 7.07 \\ \cline{1-1}  & 13–16 h & 25.92 & 13.40 & 11.04 & 7.07 \\ \cline{1-1}  & 16–19 h & 25.92 & 13.40 & 11.04 & 7.07 \\ \cline{1-1}  & 19–22 h & 38.88 & 20.10 & 16.57 & 10.60 \\ \hline \multicolumn{2}{c}{Expected weekly demand} & 2332.53 & 1206.02 & 993.98 & 636.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Expected demand (number of orders) per time window and day of the week. performed by [PERSON] et al. [49] and [PERSON] et al. [50] and adapts it to our research requirements. Thus, [PERSON] et al. [49] test horizontal cooperation for a number of geographical distribution settings for last-mile urban distribution in the city of Vienna (Austria). Similarly, [PERSON] et al. [50] investigate some trust-related issues when some coalitions between supermarkets chains are created.