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Block Cave Production Planning Using Operation Research Tools

Planificacin de la Produccin Utilizando Herramientas de

Investigacin Operativa en iner!a de Hundimiento por Blo"ues#

$nri"ue Ru%ioPhD candidate, University of British Columbia

Mining consultant, Gemcom Software International

Ton& 'ieringPrincial consultant, Gemcom Software International

Abstract

In the as, manual methods have been used to lan and schedule the e!traction of ore from different bloc" cave

oerations worldwide# $he basic assumtion of these methods has been the validity of a set of heuristics,

traditionally, used to lan and schedule roduction coming out of an active anel# Currently, however, there are

several oerations research tools %reviously used in the manufacturing sector& that could be used in bloc" cavemine lanning# $his aer describes the alication of mathematical rogramming to formulate otimi'ation

roblems whose solution may erhas drive the roduction strategy of a bloc" cave mine# Some of these strategies

such as net resent value otimi'ation, draw rofile otimi'ation and minimi'ation of long ( short term ga have

been formulated#

$he construction of the otimi'ation roblems has re)uired a rational study of which mining constraints are

alicable in each case# In doing so it has been found that the formulation of the ob*ective function as well as the

set of constraints that define the feasible sace of solutions are both critical to effective mine lanning solutions#

+t the moment the full scale algorithms have been incororated into the PCBC bloc" caving commercial ac"age#

-ne of the results of this research has been the integration of the oortunity cost into PCBC to comute best

height of draw in a dynamic manner# $he second result has been the develoment of draw method called .P/

which ma!imi'es the net earnings er eriod# +nother result has been the introduction of a new draw method

called SU01, which aims to minimi'e the difference between actual height of draw and the target reresented by asurface#

Different mathematical techni)ues have been used to solve the otimi'ation roblems such as direct iterative

methods, linear rogramming, golden section search techni)ue and integer rogramming# $he results of alying

otimi'ation to different oerations worldwide will be resented and outlined in this aer# 1inally a discussion

about the role of otimi'ation in bloc" caving will be resented

1 INTRODUCTION

The planning of a %lock cave mine poses

considera%le difficulties in the areas of safet&(

environment( ground control and production

scheduling# )s the industr& is faced *ith more

marginal resources( it is %ecoming imperative to

generate production schedules *hich *ill provide

optimal operating strategies and make the

industr& more competitive +Chanda( ,--./#

Production scheduling of an& mining s&stem

has a profound effect on the economics of the

operation# In a marginal deposit the applicationof the correct scheduling mechanism might affect

the life of the mine# Usuall& the scheduling

pro%lems are comple0 due to the nature and

variet& of the constraints acting upon the s&stem+'en%&( ,--1/# )lthough several authors such as

Caccetta and 2iannini +,-33/( 4ilke et al +,-31/(

2ershon +,-35/ have attempted to develop

methodologies to optimize production schedules(

none has satisfactoril& produced a ro%ust

techni"ue *hich has an accepta%le level of

success# One of the main reasons for this

unsuccessful histor& has %een the failure in

defining the o%6ective function in relation to the

mine planning horizons#

In this research t*o main planning strategies

*ill %e formulated as potential goals to %e

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optimised as part of the long term planning

process# The first one is the ma0imization of net

present value( *hich has %een a traditional

interest of mining companies to optimise in such

a *a& that all the mining( metallurgic and

environmental constraints are fulfilled# The

second strateg& developed in this research isma0imization of mine life( *hich often has %een

associated *ith a societal goal to maintain

emplo&ment levels#

2 OPERATIONS RESEARCH IN

PRODUCTION SCHEDULING

The pro%lem of computing a production

schedule in an underground mine can %e

understood as an operations research pro%lem in

*hich there is an o%6ective function su%6ect tooperational constraints# Trout in ,--1 developed

a model to optimize the c&cle time of the unit

operations related to a long7hole mining method#

)lso Chanda in ,--. developed a model to

optimize production from a slusher %lock cave

method using scrapers as production machines#

Both of these authors concentrated on a short

term planning pro%lems that cover a time horizon

of a fe* *eeks to a fe* months# 8either of these

algorithms have recognized the fact that the set of

constraints is a function of the planning horizonunder stud&( for e0ample( a long term production

schedule should contain much less detail than a

short term plan# Ho*ever the long term plan

includes clear definitions related to mining

reserves( production se"uence( and production

rate# ore sophisticated algorithms have %een

developed %& 2uest +9.../ and atthe*s +9..,/

to anal&se and compute long term plans# 2uest in

9... postulated that %& follo*ing a set of

surfaces that conceptuall& define a dra* control

strateg& dilution can %e minimized and therefore

8P: ma0imized# atthe* also presented an

algorithm *hich could %e used to define the

optimum opening and closure se"uence in a cut

an fill mine# Both of these algorithms recognized

the fact that %& using integer varia%les in their

formulation the computation time often is

inade"uate# )lso %oth authors descri%ed that the

solution for the computing time is rela0ing the

integer varia%le to reach a feasi%le solution in a

reasona%le time# It has %een proven +Terlak&(,--;/ that %& rela0ing the integer varia%les in a

mi0ed integer algorithm the optimum solution

can differ dangerousl& from the solution provided

%& the optimizer#

One of the pro%lems found in the current

literature is that there has %een ver& little anal&sis

of the ade"uate set of constraints applica%le for

different planning horizons# )lso none of these

algorithms have sho*n a case stud& in *hich alarge scale model had %een computed#

Before stating the mathematical pro%lem of

computing a production schedule in a %lock cave

mine( it is important to descri%e the operational

constraints applica%le to %lock cave as a mining

method( the follo*ing list presented %& Ru%io(

9... summarizes a fe* of them