A New Approach to Optimize Ultimate Geometry of Open Pit Mines with Variable Overall Slope Angles

The optimization method for determining open pit limit is important, as it is crucial to achieve the most profitable outcome from the limited amount of reserves available. However, importance must be also given to geotechnical aspects to ensure that safety requirements are met. Thus, overall slope angle (OSAs) must be incorporated in the optimization process. In the conventional methods, there were problems in incorporating various OSAs, or they were included in the pit design after the completion of the optimization procedure. To include variable OSAs in the optimization, cone-based method is still considered as one of the most suitable approaches. To apply this method, a new mathematical model incorporating various OSAs into the ultimate pit problem through mixed integer programming (MIP) and simulated annealing is proposed. Four different cases of change in OSAs in the pit were included in the algorithm. The proposed method was verified by applying it to five different cases, and the OSA was achieved with a considerably low difference of 0°–2° while optimizing the ultimate pit. The comparison between the introduced algorithm and the Lerchs–Grossman algorithm indicated that an improvement within a range of 8–20% can be achieved.