## 1 Introduction  
Underground mining is a typical multi-process operation [1]. The design of mining methods generally encompasses processes such as rock drilling, blasting, ventilation, support, and ore drawing, requiring the coordination of multiple types of workers and equipment [2]. The inefficient management of production processes can not only reduce production efficiency but also potentially introduce safety hazards in mining operations. In the past few decades, mines have predominantly adopted an extensive management model. This was primarily due to the relatively favorable mining environments of ore bodies in the past. The ore bodies were typically thick, large, and high-grade, and government regulations regarding mine safety control were less stringent. Mines could achieve high profits without implementing fine-grained management practices. Additionally, the mechanization level of mine production was relatively low in the past. The management process heavily relied on person-to-person communication, which hindered the realization of refined management across the entire production process [3, 4, 5]. With the increasing mining depth of ore bodies, the emergence of high-temperature and high ground pressure conditions has rendered the mining environment increasingly harsh, thereby escalating the risk factors associated with human operations [6; 7; 8]. Alongside the advancement of mechanization, modern mines have started to employ mechanized equipment to replace traditional manual operations across various production processes [9]. During normal production in modern mines, the extensive application of mechanized equipment, particularly within the framework of mine intelligence, implies that production efficiency is predominantly determined by the performance of mechanized equipment, stope geological conditions, and the design of the mining system [10; 11; 12; 13]. For instance, in the rock drilling process, the efficiency of rock drilling equipment is of critical importance [14]. Both drilling speed and equipment failure rates substantially influence the efficiency of the rock drilling process. When encountering fractured rock formations, rock drilling equipment is highly susceptible to jamming during operation, leading to a significant reduction in drilling efficiency. Furthermore, the design of the mining system is of paramount significance [15]. In practical mining operations, it is imperative to conduct timely ventilation, cooling, drainage, and support based on engineering conditions to ensure the safety of mining activities. These factors constitute fundamental considerations in the design of the mining system and directly affect production efficiency [16]. The evolving production environment and shifting management objectives have necessitated that mine production managers enhance the refined management of the entire process. The relevant personnel must carry out in-depth analyses of underground metal mine operations, identify weak links in the mining process, and implement more scientific optimization systems and effective measures to address these issues. Numerous scholars have conducted research on optimizing the production process of underground metal mines using mathematical programming methods. In 2010, [PERSON] et al. [17] proposed a new mixed-integer programming (MIP) model that significantly reduced the solution time for underground mine production scheduling problems while maintaining result accuracy and satisfying all constraint conditions. In 2020, [PERSON] et al. [18] comprehensively reviewed the application of mathematical programming in the production scheduling optimization of sub-level open-stoping mines, providing recommendations for future research and highlighting the crucial role of such methods in optimizing complex systems. In 2023, [PERSON] et al. [19] applied a mixed-integer linear programming framework to comprehensively optimize the development and production scheduling of open-pit mines, aiming to maximize mine life. [PERSON] et al.