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Long-term Production Scheduling Optimization for Sublevel Caving Mines Using Mixed-Integer Linear Programing (MILP)

Authors: Khazaei, Soroush;

Long-term Production Scheduling Optimization for Sublevel Caving Mines Using Mixed-Integer Linear Programing (MILP)

Abstract

Efficient production scheduling is crucial for the success of mining operations, especially in the face of declining ore quality and depleting reserves. While open-pit mining is cost-effective in terms of fixed costs, it faces significant challenges such as overburden removal, high stripping ratios, pit stability, and reclamation costs. Consequently, underground methods, particularly sublevel caving (SLC), are becoming popular due to their moderate development requirements, high production rates, and adaptability. Advanced techniques have further extended SLC's applicability to hard rock deposits, making it a viable method with the potential to operate like a factory, where development, drilling, charging, blasting, mining, and material handling are conducted independently on separate levels. To optimize profitability in SLC operations, it is crucial to consider the concurrent and independent nature of all activities involved. Previous research has primarily focused on extraction sequencing, often neglecting the integration of all operational activities. This thesis introduces mixed-integer linear programming (MILP) models to optimize long-term SLC mine scheduling. To maximize the net present value (NPV), the models focus on key aspects: scheduling development activities, sequencing mining units (MUs), and managing the material flow between the mine, processing plant, and stockpile. Two comprehensive models were developed and implemented: the Scheduling model and the Holistic model. The Scheduling model incorporates fundamental constraints including mining and processing capacities, active level sequencing, vertical and horizontal precedence relationships between adjacent MUs, and grade blending requirements. The Holistic model extends this framework by integrating mine development scheduling and stockpile management, providing more realistic and implementable schedules by considering the interdependencies between development activities, production sequencing, and material flow management. Both models were evaluated across three mining direction scenarios: Left-to-Right (LtoR), Middle-Out (MID), and Right-to-Left (RtoL). The Scheduling model was validated against GEMS PCSLC commercial software, demonstrating consistent mining capacity utilization (96-97%) and superior economic performance with NPV improvements of 1.7-2.2% over PCSLC-TTL and approximately 15% over PCSLC-TM3D Mixing. Results demonstrate that the MID direction consistently outperformed both LtoR and RtoL approaches across all key performance indicators. In the Scheduling model, MID achieved the highest NPV ($2.561 billion), highest mining utilization (96.6%), and fastest solution times (4-5× faster than other directions). The Holistic model confirmed this superiority, with MID achieving the highest NPV ($1.304 billion), mining utilization (89.6%), plant utilization (97.5%), and dramatically faster solution times (9.1× faster than LtoR and 5.8× faster than RtoL). The Holistic model demonstrated several key advantages: realistic representation of mine development sequencing with proper prioritization, effective stockpile utilization that decoupled processing from mining constraints maintaining high plant utilization (97-98%) despite lower mining utilization (88-90%), and extended mine life (30 years vs. 24 years) due to incorporation of development timeframes. However, the Holistic model's NPV was approximately 49% lower than the Scheduling model's, highlighting the significant economic impact of including development constraints and associated production delays. Sensitivity analysis revealed that parameter settings significantly influenced performance, with the MID direction showing remarkable stability across different configurations while LtoR and RtoL required tighter optimization parameters. The 40-50% Precedence Extraction Ratio (PER) range and 2% gap tolerance provided optimal balance between solution quality and computational efficiency. This research enhances the representation of real-world mining operations by integrating comprehensive SLC development scheduling and material flow management. The main scientific contribution is the development, implementation, and verification of mathematical models for long-term SLC production scheduling that simultaneously integrate development, mining, material transfer, processing, and stockpiling activities. The main industrial contribution is the demonstration that optimization-based approaches can significantly improve economic performance while ensuring operational feasibility, providing valuable guidance for future SLC operations.

Country
Canada
Related Organizations
Keywords

Sublevel Caving, Long-term Production Scheduling Otimization, Mathematical Programing

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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