## 5 Results
### Baseline Scenario  
We performed several preliminary tests, we set all the exponents of the Huff formula with values close to 0.0. In this case, no hubs were open in the optimal solution. This implies that hubs would not be able to attract farmers and that the business would not be profitable. We propose a baseline scenario which, based on our validations with the RAP-E- officers, is the most likely to occur. In this scenario, we considered a distance exponent \(\gamma\) of 2.0 and 0% of variation in hubs' costs. Figure 4 shows the hub locations and their links with the farmers in this baseline. The solid lines are links that account for more than two (2) weekly tons of delivered products. Figure 5a shows the geographical location of the 23 open hubs and the total tons supplied in the baseline scenario. We can observe that the larger supplied quantities are concentrated to the west of the central region where more and larger hubs are open. In this part of the central region, most hubs operate at full capacity. This area concentrates the larger portion of total agricultural production (see Figure 1b). Additionally, the population of the cities in this area, indicated in Figure 1a, and of its neighbors make the area attractive for the food hub business. The largest open hubs are located in the provincial capital cities of Villavicencio (east in the Meta department) and Ibague (west in the Tolima department) and in the mid-size city of Duitama (Boyaca, north). The first two hubs would be supplied by the rich agricultural regions of the neighbor lowlands whereas the Duitama hub would be supplied by many small farmers of the Andean northern region. The other larger open \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{3}{c}{**Parameter Values**} \\ \hline \(\gamma\) (distance exponent (farmers to hubs) & 0.1, 0.5, 1.0, 2.0, 3.0 \\ _fixed\_cost\_factor_ & Changes in fixed operation costs: 0.8\(\times\), 1.0\(\times\), 1.2\(\times\) \\ _hub\_capacity\_factor_ & Increase in hub capacity: 1.5\(\times\), 2\(\times\), 3\(\times\)\({}^{*}\) \\ \hline \hline \end{tabular} \({}^{*}\) denotes 3 times the current capacity of all hubs.  
\end{table} 
Table 6: Combination of parameter values. The letter x is referred to the initial value of the parameter to vary. hubs would be located around the high plain areas of Cundinamarca, the valleys of Huila in the south, and the fertile valleys of the Magdalena river in Tolima. The participation of the agricultural chains at each hub is shown in Figure 5b. We observe that these results are consistent with the agriculturalocation of each area of the region: Hot and humid flat areas of the western and eastern part of the central region are ideal for rice and other grains, whereas potato, some fruits, and vegetables are mostly cultivated in the mountainous areas of the central region. We also analyze the quantities delivered to the main cities. Figure 6a shows the quantities from hub-to-demand. As expected, the city that receives the largest quantities is Bogota, the country capital (about 2800 weekly tons). Considering the hubs in the western part of the central region, we can observe that the proximity to Bogota clearly facilitates the business activity. Bogota is by far the largest urban center of the country that also hosts the largest wholesaler (Corabastos) in which, as of today, over 12,000 tons of food are traded daily [1]. Following Bogota, the other two larger demand points are Medellin (northwest of the region in the Antioquia department) and Cali (west of the region in the Valle del Cauca department). These two cities receive around 400 weekly tons. These cities are out of the Central Region, but their size, population, and proximity with several hubs near the borders of the central region, are a reason for their business. The other smaller  
Figure 4: Supply-to-hubs main links. cities (Ibague, Neiva, Villavicencio, Tunja, Cartagena, and Barranquilla) commercialize between 5 and 65 weekly tons.