## 5 Results  
### Description of Computer Tests  
This section presents the experimental results of our tests. We coded our model in GAMSTM and ran the experiments using the CPLEX TM solver on a computer with an Intel(r) Core TM i7-6500U chipset, 8 Mb RAM memory, and 2.5 GHz microprocessor. Due to the huge size of the model (98 hub locations, 54 products, 342 farming locations, 5 chains, and 3 truck types), the model could not run in a reasonable time (after 5 h, no feasible solution was provided). Therefore, we implemented the classical \"add\" and \"drop\" heuristics for facility location [25], and according to the results, we short-listed the number of potential candidate hubs to 30 locations. First, we dropped those facilities that were not suitable for fresh food trading (e.g., slaughtering houses, or very small facilities). Next, we ran 24 instances with combinations of values of \(\delta\), \(\gamma\) and fixed costs and filtered out those locations that were never open or that handled minimum quantities. We also kept those facilities that were always present in the solution open. The selected market cities were (i) those with over 500,000 inhabitants for cities outside the central region, and (ii) the provincial capitals of the central region regardless of their population. A similar approach to handle real-life models was proposed in [9]. Figure 3 shows the location of the selected market cities. Still, the number of possible combinations was large, but could be handled in a reasonable time. We set a time limit of 3600 s for each run. The parameter calibration consisted of determining the values of the exponents of the gravity model. The RAP-E-officers estimated that 65% of the total fresh agricultural food supply is commercialized outside the central region. With this in mind, we ran the model in the situation of no open hubs, with all production traded through middlemen located at the production sites. As a result, we set the values of \(\delta\) (population exponent) and \(\hat{\gamma}\) (exponent of distance from hubs to cities) to 1.25 and 0.1, respectively. Preliminary tests showed that the factor that affected most of the decisions and, hence the profitability of the model, was the ability to capture \"market share\" from farmers. Since, at the present pandemic time, it was not possible to conduct surveys to farmers to have accurate information about their choices, we varied the exponent \(\gamma\) in the Huff formula of Equation (3). We did some preliminary validations with officers of RAP-E- in which essentially, they told us that the majority of farmers would not travel long distances to  
Figure 3: Selected demand cities for distributing the agricultural supply of the three agricultural chains. sell their products, and most likely they would only trade at the nearest town. We also corroborated the exponent values with those proposed in [58]. In the experiments, we varied this exponent and observed its effects on the objective function. The other uncertain parameter is the fixed operation hub costs. As said above, we established this value based on estimates made for the Food Security and Supply Master Plan of Bogota (PMASAB in Spanish). However, as these estimates may change, we varied the original estimates in \(\pm\)20%. We carried out a sensitivity analysis in which we varied the hub capacities and the gross profit margins. Although, the RAP-E- officers said that there were no plans for new infrastructure, the increase in capacity can be seen as adding days of operation. In this case, the fixed operation costs were adjusted in the same proportion. We did not vary the transportation costs for the following reasons: First, the sources we used were reliable, and second, the major components of such costs are unlikely to vary: Salaries, taxes, and insurance in the term of fixed transportation cost and gas and tolls in the term of variable transportation cost. Last, we varied the gross margins, and the original figures were reduced in 10%, 25%, and 50%.