## 2 Modeling of Logistic Systems in the Field of Mining
[PERSON] and [PERSON] developed a program in Fortran language that simulated mining operations for room and pillar systems [14; 19]. [PERSON] and [PERSON] applied the simulation model to handle the transport of the winning in the opencast mine [20]. Another example of the first simulation models was the model of transport processes in an opencast copper ore mine. It described the operations of loading the mining product onto the haul trucks with the use of five loaders. The winning was first dumped into an ore crusher and then onto a waste pile or a leaching area. Based on the simulation model, it was determined how the dispatcher should direct the haul trucks to different loaders to minimize the queuing time. The results of the model written in Fortran language showed that the decisions made on its basis would significantly improve the loading process [21]. In the following years, the number of works based on simulation models, built using various simulation languages and commercial software in the field of mining, increased rapidly. Description of Mining Processes in Copper Ore Mines According to Business Process Model and Notation (BPMN)  
The room and pillar mining system, used in underground mines of non-ferrous ores, is adapted to the geological and mining characteristics of the deposit, in particular its thickness. The exploitation of the non-ferrous metal ore deposits with a thickness of up to 5 m is carried out with the use of explosives. For this purpose, the exploitation field is cut with rooms and drifts with the separation of protective pillars--this is the cross-cutting stage. The cross-cutting of the field leaves protective pillars, the task of which is to protect the ceiling. The shorter dimension of the protective pillar is most often located perpendicularly to the works site. As the front progresses, the pillars from the last rows in front of the extraction line are cut into smaller ones, minimizing the losses of the winning from the exploited field--this is the retreating stage. The size of the residual pillars depends on the local geological and mining conditions as they should provide appropriate stable support for the ceiling in the area of the liquidated field. Over time, the ceiling gradually settles on the remaining pillars, closing the exploited space. After blasting the mine face, the mining product is extracted with the use of production loaders (LHD), which load it onto haul trucks (HT) or transport it directly to the dumping point built on a belt conveyor. Then, the excavated material is transported by a network of belt conveyors to the main retention reservoirs at the mining shafts. In the mining system using explosives, technological tasks are carried out in a closed cycle of technological operations (Figure 1):  
* Mine face control and measurements;
* Drilling blast holes;
* Loading explosives;
* Blasting;
* Airing;
* Loading and haulage of the winning (Figure 2);
* Roof dressing;
* Roof anchoring. After the last step of the cycle, the whole process in the mine face starts over. It would not be possible without carrying out several auxiliary operations on an ongoing basis. In deep mines, using explosives for the extraction, mining technologies are based on the use of mobile mining machines on wheeled chassis. In the implementation of mining processes, self-propelled machines of various construction are used for the following groups of works:  
* Mining of the deposit, i.e., drilling trucks (FDR) and blasting vehicles (BV);
* Securing and liquidating mining excavations, i.e., bolting rig (RB) or rock ripping machine (RM);
* Loading and transport of excavated material, i.e., bucket loaders (LHD) and haul trucks of various sizes (HT);
* Transport of personnel, materials, devices and machines as well as tools (including transport, fuel and lubrication vehicles);
* Preparation of transport roads and auxiliary works (including bulldozers, drainage trucks).