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Mine Planning:
Finding Optimal Sequences of Extraction by Using
Mathematical Models and HPC
Jorge Amaya (CMM)
Pierre Nancel-Penard (CMM)Nelson Morales (DELPHOS-AMTC)
Universidad de Chile
BS Grupo
Lima, October 8, 2011
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Contents
1. The problem
2. Objectives3. The steps
4. The mathematical model
5. Algorithms and software
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1. The problem Strategic planning plays a very relevant role in the mine business. The
general strategy of extraction in the long term determines the subsequent
steps in the production process.
In particular, the robustness of the proposed sequences must be
incorporated for a fine evaluation of the business (quality of data, prices
variations, stochastic behavior of the market).
To find the optimal blocks sequence for the extraction of the ore from themine site is a very complex mathematical problem, having a huge number
of decision variables and prohibited computer execution time.
We aim to construct computer tools for the generation of and robust
optimal sequences, in terms of discounted economic value.
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Block model
Idealized image
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2. Objective: mine planning in open pit mines
The general problem can be essentially formulated as follows: given an
estimation of the value (grade) distribution in situ, the decision-maker needs
to determine the order of extraction of the basic production units (blocks).
The aim of the planning is to define the economic sequence of blocks,
satisfying logical, physical, and capacity constraints.
Capacities (extraction, transport, process)
Wall slope of the pit (stability) Waste/ore rate
Destinations of the blocks (plant, stock, process)
This gives rise to very large (linear) binary Optimization problems.
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Planningscheme
Proposed
min ing p lan
Validation
Block / Reblock
Operation plan
Optimized
sequence
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3. The steps
Development of mathematical optimization for the mine planning of
open pit mines.
HPC-Software for the resolution of very large mine planning
problems.
Web applications based on these methodologies for consulting and
remote services.
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0
0.2
0.4
0.6
0.8
1
1.2
0
20
40
60
80
100
120
1 2 3 4 5
Cu
(%),Au(ppm)
Tonelaje(Mt/ao)
Periodo (aos)Mineral Waste Cu Au
VAN: 840.5 MUS$
Production plan
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Cubes aprox. 20x20x20 m3
4. Mathematical Modelling
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The information in the data base for our purposes is essentially:
coordinates (x, y, z)grade at each block (% of Copper/Total mass) and other characteristics
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Graph GSub-Graph G
FINAL PIT MAXIMAL CLOSURE
To f ind a sub-graph sat isfying th e precedence relat ions and maximal benef ice.
FIRST PROBLEM
ii PjGjGiAjijP '' then,),(/If
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Graph GSub-Graph G
53343
422211
5
4 1
SEQUENCE
To find a feasible sequence of bloc ks having maximal disco unted value.
SECOND PROBLEM
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The static problem
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5. Algorithms and software
Multi-strategy based on High Performance Computing
Multidisciplinary Approach (mathematics, mining, HPC)
Calculations based on a block model (definition of the geometry, data)
Software system based on clustercomputing
Modular system and remote service
Software compatible with market standards.
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a. Linear programming
b. Branch and Bound
c. Heuristics: Greedy, Local search, Relaxation and Expected period of
extraction
d. Pre-processing: eliminating variables and redundancies, via final pit orfirst period of possible extraction for or each block.
Mathematical model: resolution
Main possible (and relevant) extensions
a. Robust optimization (large number of instances due to samplingprocess of random data)
b. Multiple destinations of blocks (very large number of variables and
constraints)
c. Multi-mine (several mines, sharing plant facilities, some capacities and
demands)
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DB
Blocks models
SERVER
Web
BrowserWeb
Application
Consulting
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SIMULACION 1
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SIMULACION 2
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SIMULACION 3
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The Web Application
OverView of the application
Specifications of the application
Features
Specifications of the clusters
Test results
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Overview of the Application
Intenet explorer
Or chromeOr firefox
Or Opera on
Linux or windows
Cryptation with gpg
www.secuenciapit.cmm.uchile.cl
Cluster Syntagma Head Node
syntagma.dim.uchile.cl
Batch system: Sun Grid Engine
Cryptacion with gpg
Compute node:
Secuencia pit compute
Job with decrypted input data
Job with crypted input data
Crypted output results, secuenciapit public key
Crypted Input data,user public key
uncrypted output results
Crypted output results
Cluster : syntagma
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Specifications of the application
Application mono user
Php pages website on a linux-apache web server
Cryptation input/output data with gpg
Communication between the website and the cluster with
ssh
Easy to use Interface
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Features of the application
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THANK YOU