CIOMIN

Centro de Investigación de Operaciones para la Industria Minera Departamento de Ingeniería de Minas y Departamento de Ingeniería Industrial Facultad de Ciencias Físicas y Matemáticas Universidad de Chile Co-Directores: Enrique Rubio Dpto. Ing. Minas Rafael Epstein Dpto. Ing. Industrial CIOMIN

AGENDA ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

1. EQUIPO DE TRABAJO ,[object Object],[object Object],[object Object],[object Object]

2. LÍNEAS DE INVESTIGACIÓN ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Optimization Approaches to Long Term Mine Planning Seminar OR in Mining, 15 th - 17 th March 2010

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],Background

Background ,[object Object],[object Object],[object Object],[object Object],[object Object]

Problem Description Optimization Approaches to Long Term Mine Planning

Key Elements ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Overview of the Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Methodology of Analysis Optimization Approaches to Long Term Mine Planning

Methodology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Underground Mine PRODUCTION Block caving LHD Block caving ROCK SIZE REDUCTION MAIN TRANSPORTATION (Train) PLANTS (MILLS) COMMERCIAL PRODUCTS Gravity (Tunnel) Drain stage SAG COPPER MOLY

Open Pit Mine Plant Mine Mine Mine Plant Plant Mine Plant Stock Stock

OPEN PIT MINES UNDERGROUND MINES EXTRACTION INITIAL TRASNPORT REDUCTION INSIDE MINE MAIN TRANSPORT DRAIN STAGE REDUCTION OUTSIDE MINE MILLS CONCENTRATION DEMAND DEPOSIT OF VERY-LOW-GRADE ORE AND STOCK Network Flow Representation

Underground Mining Optimization Approaches to Long Term Mine Planning

[object Object],[object Object],[object Object],[object Object],[object Object],Underground mining Indices (sets) ,[object Object],[object Object],[object Object],Decision variables Blocks Sector

[object Object],[object Object],[object Object],Underground mining Main Variables 1 If block n of the column j is extracted at period t 0 ~

[object Object],Underground mining Main Constraints ,[object Object],[object Object]

[object Object],Underground mining ,[object Object],[object Object],Main Constraints

[object Object],[object Object],[object Object],: products at node v Main Constraints Underground mining

[object Object],[object Object],Columns Neighborhoods Underground mining

Neighborhood Underground mining

[object Object],[object Object],[object Object],[object Object],Underground mining

Open Pit Mining Optimization Approaches to Long Term Mine Planning

[object Object],[object Object],[object Object],expansion bench Open Pit Mining

[object Object],[object Object],[object Object],Open Pit Mining ∆ h MIN Rock spillage ∆ h MAX Instability of walls

Deposits of very low-grade ore Crushing Grinding Leaching Dump leaching Flotation SX/EW Stock Network Flow & Design Mine Storage Stage Crushing Stage Preparation plant Plant

Artificial Ending Bench Artificial Starting Bench Artificial Starting Period Artificial Ending Period Leads to less fractional solution than classical formulation. Time Benches Network flow formulation to extract a sequence of benches (includes safety considerations). Network Flow Formulation

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Network Flow Formulation

Open Pit Mining ,[object Object],[object Object],[object Object],[object Object],[object Object]

Solving the Model ,[object Object],Caro et al. - Long Term Optimization of Investment & Production Plans in Open Pit & Underground Copper Mines ,[object Object],Model Nº Constraints Nº Variables 0-1 Variables Underground mine 446,521 535,639 196,386 Open pit mine 245,391 898,742 160,386

[object Object],Rounding Heuristic ,[object Object],Fraction of block n of column j extracted at period t Underground mines

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Underground mines Rounding Heuristic

Applications in CODELCO Optimization Approaches to Long Term Mine Planning

Applications in Codelco ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Uncertainty in Prizes Optimization Approaches to Long Term Mine Planning

Problem ,[object Object],[object Object],[object Object],[object Object]

Methodology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Methodology Stock Plant Plant Plant Plant Plant Stock Plant Including uncertainty in prices generates multiple scenarios. Each scenario configures one complex combinatorial problem.

Robust Planning ,[object Object],[object Object]

Applying Robust Planning ,[object Object],Planning price Evaluation price ,[object Object],[object Object], low high low 9,789 10,715 high 9,773 10,889 -16 -174

Why this asymetry? ,[object Object],[object Object],C’(x) x B x A P A P B x B x A P A P B x B x A P A P B C’(x) C’(x) Loss for producing XA when market price is PB Profit for producing X A when market price is P A

3. OPERATIONS RESEARCH IN MINING NETWORK ( ORMNet) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

4. VISITAS AL EXTERIOR ,[object Object]

5. ORGANIZACIÓN DE SEMINARIOS ,[object Object],[object Object]

6. FINANCIAMIENTO TESIS ,[object Object],[object Object]

Centro de Investigación de Operaciones para la Industria Minera Departamento de Ingeniería de Minas y Departamento de Ingeniería Industrial Facultad de Ciencias Físicas y Matemáticas Universidad de Chile

CIOMIN

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