A New Mixed-Integer Linear Programming Model for Ultimate Pit Limit Determination and Production Planning of Open Pit Mines Considering Effective Operational Constraints

Strategic mine planning is essential for attracting investment and ensuring efficient resource utilization. Long-term production scheduling determines the sequence of ore and waste block extraction to maximize economic returns while satisfying operational constraints. In addition to estimating the Net Present Value (NPV), it provides a foundation for medium- and short-term planning.This study presents a Mixed-Integer Linear Programming (MILP) model for determining the ultimate pit limit and performing long-term production scheduling under two scenarios: with and without the use of a stockpile. The model aims to maximize project NPV while incorporating seven key constraints—four geometric (block precedence, pit floor width, block extraction continuity, and non-repetition of block selection) and three demand-based (extraction capacity, ore block requirement, and minimum feed grade per period). The model was implemented in GAMS and tested on a hypothetical ۵×۷ block dataset to evaluate its feasibility and performance. Sensitivity analysis showed that increasing the pit floor width from one to four blocks resulted in a ۴۴.۸% reduction in the objective function value. A demand sensitivity analysis (۱–۳ blocks per period) under the non-stockpile scenario revealed that a ۳-block demand was infeasible, while the best result was achieved at ۱ block. To address infeasibility, stockpile inventory and shortage variables were introduced. The updated model identified ۲ blocks per period as the optimal plant capacity, balancing stockpile holding costs and shortage penalties. If demand exceeds production, a penalty is applied to the objective function; if production exceeds demand, the surplus is added to the stockpile for future use. This mechanism enhances scheduling flexibility and supports more robust decision-making under real-world constraints.

Keywords:

Open-pit mine , Determination of the ultimate pit limit , Production Planning , Sensitivity analysis , Mixed-Integer Linear Programming