## 1 Introduction  
The loading and hauling process in a mining operation is one of the most important stages, as it represents around 50% to 60% of the total operating cost in an open-pit mine [1, 2]. On the other hand, due to the variability in the nature of the variables that make up a shovel-truck system, the application of DES is feasible because it satisfactorily allows the recreation and estimation of system performance through time by means of the development of a simulation model [3, 4]. Furthermore, there is a wide range in the application areas of the simulation because the consulted works addressed problems, such as minimization of maintenance cost and maximization of shovel availabilities, estimation of the haul truck fleet productivity, mining cost reduction, modeling and optimization of fuel consumption, and the optimization of the truck fleet size in an open-pit mine [5, 6, 7, 8, 9]. Nonetheless, regarding the truck fleet size estimation in open-pit mines, numerous studies employed complex methodologies, though innovative and effective, that involved an advanced understanding of programming languages, the development of neural network algorithms, or deterministic approaches [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. For example, [PERSON] & [PERSON] [19] developed an algorithm with VBA that included allocation planning--which found the maximum mining capacity and optimal truck fleet size--and dynamic allocation to find the best allocation scheduler. [PERSON] et al. [13] compared a flexible dispatching system to a Firefly Metaheuristic Algorithm using ARENA and MATLAB; the latter method increased production and reduced costs in an Iranian mine. [PERSON] et al. [10] developed a multiple-objective model with IBM CPLEX, ARENA, and MS Excel, maintaining the number of shovels during the simulation for one year, and the results showed a decrease in the required fleet size by 16% compared to a deterministic fleet size. Moreover, commercial software packages addressing this problem are available in the market, including HaulSim, Talpac, and Haulage [22; 23; 24]. Some relevant features of these packages are that Talpac only works with a single loading unit at the time, Haulage can connect the cuts obtained from a mine plan through haul road profiles, and HaulSim allows the users to model bunching [3]. Because these solutions were designed exclusively for shovel-truck systems, they are closed-source simulation software. Nowadays, given the presence of tools that enable the modeling of any process through the development of DES for free, such as Arena Software [25], and the extended literature covering this topic, the present work attempts to develop a non-dispatch methodology easy to understand for any user, new or experienced, in which having advanced programming language skills is not mandatory, but that allows the quick identification of possible errors during the simulation of truck-shovel systems. In addition, such an approach can be applied to other industries, such as manufacturing, shipping, and transport. In this work, the deterministic methodology employed in the case study was compared with the stochastic approach applied to a mine located at 4500 masl where scarce works have been developed. It was demonstrated that the former approach replicated the variability of the operating conditions, such as the fixed times and loaded tonnages by hauling equipment in an expanding open-pit copper mine located in Peru. Thus, to solve the truck fleet estimation problem, probability distribution functions (PDF) and deviations from the random variables were collected as input, and from these distributions, the stochastic simulation developed different scenarios. Additionally, the Dijkstra algorithm was employed to solve the shortest path problem between origins and destinations [26]. On the other hand, the time required by loaded or unloaded trucks to travel was calculated with the different velocities by gradient.