## 1 Introduction  
One of the most essential activities in mining operations is ore hauling; this process involves moving fragmented rock from the blasting site using loading and hauling equipment [1]. The ore rocks are then transported to the crushing process to reduce their size before being sent to the recovery plant, where valuable metals such as copper, gold, molybdenum, and aluminum, among others, are extracted [2; 3; 4]. Figure 1 illustrates the schematic of the described process. Poor planning of ore hauling operations can decrease productivity levels, affect the achievement of production targets within the established timelines, and consequently impact operational costs. Several factors must be considered to effectively plan ore hauling operations, such as the amount of available loading and hauling equipment and their scheduled maintenance [5]. It is also essential to account for the established production targets, working hours, and topographic levels. Other important aspects include the ore grade, the number of available loading ramps for loading operations, and the environmental impact [6]. Mining companies have a defined amount of loading and hauling equipment allocated based on the production targets set for a specific period. It is crucial to determine the necessary amount of this equipment to efficiently transport ore rocks to control associated costs, which can be substantial depending on the time required to meet these targets [7]. Knowing the minimum amount of equipment needed optimizes operations and facilitates tactical analysis. This analysis enables better decision-making in the face of contingencies, ensuring the achievement of production targets at the lowest possible cost. As shown in Figure 1, the ore hauling process involves assigning hauling equipment to loading equipment. These do not necessarily operate at the same loading speed because some equipment have different loading capacities. The loading is performed simultaneously, and is described as a system of parallel machines with different speeds. Since the number of hauling equipment is finite, they are used as many times as necessary to meet the production target. However, they are unavailable while transporting the ore to the crushing process, having a \"release time\" before they are available again to be reloaded. Thus, this scenario can be adapted to a problem of parallel machines with different speeds and release times. The novelty of this work lies in incorporating different speeds and release times into the mathematical model for parallel machine scheduling in mineral hauling operations (PMSPOHO). These features allow for a more realistic and accurate representation of operational conditions in the mining environment. The speed of the loading equipment plays a crucial role in this model. Variations in loading speeds can significantly impact the efficiency of the ore hauling operation. By considering different loading speeds, the model can more precisely allocate resources to match the dynamic nature of mining operations. This ensures that faster-loading equipment is utilized to its maximum potential while slower equipment is assigned tasks that better suit its capabilities, optimizing the overall workflow. Incorporating the speed of the loading equipment into the scheduling algorithm maximizes equipment use and minimizes idle time for the hauling equipment. This enhances operational efficiency by reducing delays and ensuring a continuous flow of materials. The developed mathematical model addresses these critical variables, optimizing the allocation of hauling equipment, maximizing their use, and reducing idle time. This approach ensures greater operational efficiency by aligning equipment capabilities with the demands of the mining process. The strategic allocation of resources, guided by the speed and availability of each loading machine, contributes to a more streamlined and cost-effective operation, highlighting the importance of these variables in achieving optimal performance.