Methods

This section describes optimisation workflows and algorithms implemented in Optamine.

Mixed-Integer Programming (MIP) for Open-Pit Production Planning

Mixed-Integer Programming (MIP) is a common and powerful method for solving strategic and tactical mine planning problems, including open-pit production scheduling and pushback sequencing.

Typical MIP formulation (open-pit scheduling)

• Decision variables: binary variables indicating whether a block/bench is mined in a given period; continuous variables for tonnage, grade, and processing flows.
• Objective: maximise discounted cash flow (NPV) or another economic metric subject to operational and regulatory constraints.
• Constraints: precedence (respecting pit slope and block removal order), processing capacity, blending and product quality, fleet availability, resource constraints, and ESG limits.

Solution approaches

• Exact solvers: branch-and-bound with cutting planes and heuristics to handle large-scale MIPs.
• Decomposition techniques: Lagrangian relaxation, Benders decomposition, and time/space decomposition to reduce problem size.
• Heuristics: greedy pushback construction, local search, and metaheuristics for very large instances or real-time use.

Modelling tips

• Encode precedence explicitly via closure graphs to reduce symmetric solutions.
• Aggregate blocks into benches or parent blocks for strategic horizons, then refine schedules at tactical horizons.
• Use rolling-horizon or multi-stage formulations to balance long-term strategy and short-term operability.
• Include soft constraints with penalty terms to preserve feasibility while retaining model interpretability.

Integrating MIP with other methods

Combine MIP with graph-based ultimate-pit methods (e.g., Lerchs–Grossmann-derived shells) and with machine learning (for dynamic value estimation and recovery forecasting). See the tools page for solver recommendations and modelling libraries.