## 3 Literature Review  
In this section, we explore the mathematical foundations of hub location problems. This is a particular case of the facility location problem (FLP) that consists of both establishing the location of one or more facilities and the assignment of customers to such facilities [20]. Most problems studied in the literature derive from the classical \(p\)-medians,  
Figure 1: Characterization of the Central Region in terms of (**a**) population size and (**b**) production quantities of all five agricultural chains considered in this paper. fixed charge and set covering problems [20]. The \(p\)-medians consist of establishing the location of exactly \(p\) facilities among a set of \(n>p\) possible sites with the objective of minimizing the total weighted distance. The fixed charge cost is a natural extension of the \(p\)-medians in which the number of facilities is a decision variable itself. In this model, in addition to transportation costs, there are fixed charge costs associated with the opening/operation of the facilities. The set covering problem (SCP) differs from the above two in the sense that the objective is minimizing the number of facilities subject to the constraint that all customers must be served [21]. Facilities can only serve customers located within a predefined radius of influence (i.e., customers are covered). A different approach to coverage are the Huff's gravity [22] and the logistics regression (logit) [23] models. These models, instead of having the sharp coverage distinction of the SCP (i.e., covered or not), establish the probability that a customer patronizes a facility. This probability is related to some measure of attractiveness of the facility. The first papers considered only retail stores [22]. Later models included other services [24]. There are many variants of the FLP and it is not the purpose of this paper to cover them all. For a complete review, please see [25; 26]. An extension of the FLP used in this paper is the competitive facility location problem in which the decision maker does not have control on the choices of the customers, but rather has estimations of their shopping behavior [27; 28; 29]. In general, these choices are modeled through either the Huff or the logit formulas. Most papers consider Mixed Integer Linear Programming (MILP) formulations and use either standard MILP solvers [30] or decomposition algorithms [31; 32]. Other approaches use metaheuristics algorithms [33; 34; 35]. Facility location models are also common for fresh food and agriculture supply chain design [36; 37]: This topic of has attracted many researchers that have addressed multiple problems [38; 39]. Some examples related to emerging countries are: [PERSON] et al. [12] proposed a bi-level algorithm for the location of purchasing centers in the coffee belt region of Colombia. The two objectives considered were the cost minimization and the coverage maximization. [PERSON] et al. [40] presented a MILP model for supply chain design with JIT planning and scheduling with perishability constraints. [PERSON] [8] proposed a MILP model for the location of fruit processing centers in the central region of Colombia. This model included humidity and temperature related constraints of the potential sites. [PERSON] and [PERSON] [41] introduced a MILP model for the network design of urban distribution centers of fruits and vegetables in Bankok (Thailand). They investigated not only location, but also vehicle routing extensions. Later, [PERSON] [42] presented a real-life application model for the location of a catering distribution problem in urban schools in Mexico considering waiting times. In most of these papers, the objective function was the cost minimization including fixed, transportation, and other costs related to quality, and/or delivery. Several extensions in food supply chain combine facility location with combinatorial another problem: Examples are the location and routing [43; 44] and the inventory location [45] problems.