## 2 Literature Review
### The Location Routing Problem
[12], who address the problem of locating battery swap stations and routing electric vehicles with stochastic demands. This problem is solved using a hybrid approach that combines a variable neighborhood search with a binary particle swarm optimization algorithm. The problem's complexity increases when considering the low autonomy of this type of vehicles, since route failures can frequently be present when demands are not known in an accurate manner. Uncertainty in the LRP has been studied using either stochastic or fuzzy parameters. Table 1 shows an overview of works addressing this topic, which includes: (i) whether the uncertainty is addressed stochastically or in a fuzzy fashion; (ii) the considered uncertain parameter; (iii) the mathematical modeling approach; (iv) the approach used to solve the problem; and (v) the objective function. Analyzed works show a clear preference for considering an uncertain demand, as well as for using fuzzy chance constrained models. Given both the considered uncertainty and the combinatorial nature of the LRP, most works employ a hybrid approach combining simulation with a metaheuristic algorithm. Finally, cost minimization is the prevalent objective, although a few works also consider the minimization of risk or the minimization of the additional travel distance due to route failures. Regarding works on fuzzy parameters, [PERSON] et al. (2017) propose a hybrid particle swarm optimization (PSO) algorithm to solve a capacitated LRP with fuzzy triangular demands (CLRP-FD). The hybrid PSO algorithm is composed of three phases including a local search method and stochastic simulation. In addition, the authors propose a chance-constrained programming model for the CLRP-FD. [PERSON] et al. (2018) consider a multidepot LRP with fixed depot capacity and fuzzy travel times. [PERSON] and [PERSON] (2018) present a fuzzy chance constrained programming model where demands are modeled as fuzzy numbers. A four-phase method called \"greedy clustering\" is proposed, in which both an ant colony system metaheuristic and stochastic simulation are included. [PERSON] et al. (2019) propose an LRP with time windows and fuzzy demands as the delivery part of a multimodal transport network. The mixed integer mathematical fuzzy model is coded and solved using GAMS and compared to the results provided by a genetic algorithm. [PERSON] and [PERSON] (2018) analyze a LRP with simultaneous pick-up and delivery in the context of reverse logistics. Both types of demands (pick-up and deliveries) are fuzzy variables. A fuzzy chance constrained programming model is proposed to represent the problem, and a greedy clustering method is used to solve it. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  
The analyzed works show that uncertainty in the LRP has been addressed either by using stochastic or fuzzy demands but never considering both types of uncertainty at the same time--e.g., that some customers' demands are modeled as stochastic variables while others are modeled as fuzzy values. In addition, to the best of our knowledge, there are no previous studies on the LRP with facility sizing decisions and hybrid fuzzy-stochastic demands. Only [PERSON] et al. (2013) have studied a similar LRP variant, although considering all customers' demands as stochastic. Thus, our work aims to fulfill the existing gap by considering a flexible-size LRP and two different types of uncertain parameters: stochastic and fuzzy demands.