## 3 The e-Grocery Demand Analysis in the City of Pamplona (Spain)  
The interest of analysing the e-grocery demand in a medium sized city is three-fold. Firstly, the e-grocery penetration is lower and customers' characteristics heavily differ from those in large cities [46]. Secondly, the transportation infrastructure is usually poorer than in large cities, which makes transportation activities less efficient [47]. Thirdly, the literature review has revealed a lack of research focused on small and medium cities, being large cities the center of attention in most of the research. Therefore, the geographical scope of our experiment is Pamplona area in Northern Spain, which includes a population of about 250,000 inhabitants. Figure 1 shows the location of the city in Spain and demand and supply points, where purple dots stand for demand locations and hexagon marks stand for the selected supermarkets for the experiments. A survey was distributed in the area for gathering e-grocery demand information in the time period from 1 February 2020 to 31 March 2020. The questionnaire was compounded by three blocks of questions. An introductory section, aimed at collecting socio-economic information such as age, gender, and economic status, among others. This section is particularly interesting because it introduces the topic to analyse and focuses the survey on e-groceries. Therefore, the main objective of that section is to clarify what we refer to the  
Figure 1: Survey geographical scope, customer and supermarket agents, and Pamplona location in Spain. e-grocery demand. The second section is intended to gather the e-grocery information. It contains questions related to the supermarket preference, the type of product, the frequency of shopping online groceries, and the expense made on e-grocery. Finally, the third section is focused on the logistic part of the e-grocery service. Therefore, the questions here referred to the day of the week, as well as the preferred time window for the delivery. The selection procedure was based on simple random sampling using the e-mail. For this purpose, different mail distribution lists, for example, from the Council and the Public University of Navarra, were used for reaching the participants. All in all, we accounted for 182 observations. Analysing carefully the survey, we can highlight the main aspects related to the e-grocery demand patterns in Pamplona. Firstly, there are four main supermarkets for ordering online. They are detailed in Table 1. Thus, we will use these four supermarkets for our simulation model. Secondly, most of the participants do not usually order groceries online. About a 25% of the total order e-groceries at least once a month. The frequency of ordering is provided in Figure 2. Third, delivery preferences are basically during the weekdays at the 19-22 h time window. The detailed delivery preferences are provided in Figure 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Supermarket** & **Nickname** & **Preference** & **Webpage** \\ \hline Eroski & \(S1\) & 17.60\% & [[https://www.eroski.es/](https://www.eroski.es/)]([https://www.eroski.es/](https://www.eroski.es/)) \\ Mercadona & \(S2\) & 9.10\% & [[https://www.mercadona.es/](https://www.mercadona.es/)]([https://www.mercadona.es/](https://www.mercadona.es/)) \\ Carrefour & \(S3\) & 7.50\% & [[https://www.carrefour.es/](https://www.carrefour.es/)]([https://www.carrefour.es/](https://www.carrefour.es/)) \\ Dia & \(S4\) & 4.80\% & [[https://www.dia.es/](https://www.dia.es/)]([https://www.dia.es/](https://www.dia.es/)) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Preference for e-grocery supermarkets. Figure 2: E-groceries frequency ordering. With the information previously obtained, we can estimate the expected demand, that is, number of orders, for the considered supermarkets. These estimations, shown in Table 2, are the main input for our simulation model. In particular, we first computed the expected weekly demand at the last row.