Mine Planning Chile

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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

[email protected]


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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

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1

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0

20

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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

Documents

Mine Planning Chile