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An analytical hierarchy process (AHP)-guided decision model for undergroundmining method selectionSuprakash Gupta a & Uday Kumar ba Department of Mining Engineering, Institute of Technology, BHU,Varanasi, 221 005, Indiab Division of Operation and Maintenance Engineering, LuleåUniversity of Technology, SE–97187, Luleå, SwedenVersion of record first published: 01 May 2012.

To cite this article: Suprakash Gupta & Uday Kumar (2012): An analytical hierarchy process (AHP)-guided decision model for underground mining method selection, International Journal of Mining,Reclamation and Environment, 26:4, 324-336

To link to this article: http://dx.doi.org/10.1080/17480930.2011.622480

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An analytical hierarchy process (AHP)-guided decision model

for underground mining method selection

Suprakash Guptaa* and Uday Kumarb

aDepartment of Mining Engineering, Institute of Technology, BHU, Varanasi 221 005, India;bDivision of Operation and Maintenance Engineering, Lulea University of Technology,

SE – 971 87 Lulea, Sweden

(Received 29 July 2011; final version received 11 April 2012)

Decision making in mining, especially the selection of an appropriate stopingmethod for an ore deposit, is a critical and challenging task owing to itscompliance with a set of criteria. The lack of quantitative data and the qualitativenature of the task forces one to adopt an experience- and intuition -basedtechnique like the analytical hierarchy process (AHP). This article examines theapplication of the AHP for the selection of an appropriate stoping method from agroup of alternatives. The developed model has been verified by a number of casestudies.

Keywords: multi-criteria decision making; analytical hierarchy process; stopingmethods

1. Introduction

Safety and economics are the main concern of any successful mining project. Theselection of an apt mining/stoping method is pivotal for maximising the profitwithout compromising safety. Different parts of an ore deposit normally varywidely in their geological, physical, chemical and structural aspects. Therefore, anumber of stoping methods have been devised, each having its own conditions ofapplicability. The practised stoping method varies from mine to mine and even inthe different parts of the same mine. Depending on the dip, depth, size and shape ofthe deposit, as well as the strength of the ore and host rock, a number of technicallyfeasible methods may be adopted for a particular ore deposit. However, safety,financial bounds, economics and environmental parameters are of the utmostimportance and due attention should be paid to these parameters to select thesafest and most profitable method. Therefore, selecting the most suitable method isa multi-criteria and multi-objective decision binding the process by a set ofconstraints. Furthermore, a number of these criteria and objectives are difficult toquantify.

One possible solution to handling such multiple complexities in decision makingis the use of the expertise of a group of experts through the application of the

*Corresponding author. Email: suprakas@bhu.ac.in

International Journal of Mining, Reclamation and Environment

Vol. 26, No. 4, December 2012, 324–336

ISSN 1748-0930 print/ISSN 1748-0949 online

� 2012 Taylor & Francis

http://dx.doi.org/10.1080/17480930.2011.622480

http://www.tandfonline.com

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analytical hierarchy process (AHP). In the literature, there is a multitude ofapplications of the AHP in diverse areas of multi-criteria and multi-objectivedecision making, e.g. in the selection of front-line management personnel likeforemen [1], maintenance management decision making [2], maintenance policyselection [3], equipment selection in mining [4], comparison of the best catering firms[5] and investment analysis, as well as support and tunnelling systems design, shaftlocation selection and risk assessment in mining [6]. However, there is one drawbackin that the method may suffer from the problem of rank reversal [7,8].

This article details the factors influencing the choice of a stoping method anddeals with the application of the AHP in weighing the contributory factors basedon the experts’ judgements. Finally, the degree of suitability of common stopingmethods for different values of influencing factors was calculated and theapplicability of the developed model was validated through a number of casestudies.

2. Selection of stoping method

The selection of a stoping method is critical for exploiting an ore deposit in the safestand most profitable manner. The chosen method should be flexible enough to adaptto the nature of the deposit, the petrology of the area, the financial status of theowner, the surface structures, the dilution of the extracted ore, and health and safetyissues. This section examines the influence of principal geotechnical and economicfactors in the selection process.

2.1. Factors influencing the decision

Underground mining methods are influenced by a number of factors to varyingdegrees [9–11]. These factors may be broadly divided into two groups:

Intrinsic factors: These are driven by nature or the surroundings and are uncontrollable.Mostly they are dictated by the deposit itself and the host rock. The dip, strength, shape,thickness, grade, depth of the deposit, the strength of the host rock and the presence ofsurface features are the eight attributes which were considered in the development of theproposed model.Extrinsic factors: These are not directly associated with the deposit. Usually the decisionis governed by capital investment, the market and the dilution of the extracted ore, aswell as the availability of labour, and health and safety.

The following section presents all the above-listed influencing factors in greaterdetail.

(1) Dip: The dip of the mineral deposit is classified into three categories, i.e.(a) Flat: 5158(b) Moderate: 158–458(c) Steep: 4458.

(2) Strength of ore: Based on the competence of the ore, as well its ability toform pillars without crumbling or giving in to the overlying rock’s pressure,the ore is divided into three categories, i.e.(a) Weak(b) Moderate(c) Strong.

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(3) Shape of deposit: The deposits may have different shapes and can bebroadly classified as(a) Irregular/discontinuous: the dimensions vary over short distances;(b) Tabular: the true dimensions are many times the thickness (usually

5150 m)(c) Massive: the ore exists as a massive body with no definite shape in

general.(4) Strength of host rock: Depending on the ability of the surrounding rock to

sustain the shocks caused by blasting and other operations, its ability tocave in properly and its water permeability, it may be classified into threecategories, i.e.(a) Weak(b) Moderate(c) Strong.

(5) Thickness of ore body: Highly productive methods need mechanisation thatdepends greatly on the thickness of the orebody. A deposit may be broadlyclassified into three categories on the basis of its thickness, i.e.(a) Narrow: 510 m(b) Intermediate: 10 – 45 m(c) Thick: 445 m.

(6) Presence of surface features: Surface features can preclude the practice ofcaving methods as they cause massive changes in the surface topography.Filling methods are preferred when the deposit underlies an importantstructure like a monument, water reservoir, etc.

(7) Grade of ore: Bulk stoping methods are very sensitive to the variation of thegrade. A deposit with a variable grade needs selective mining. The grade ofthe deposits is categorised as follows:(a) Uniform: the grade at any point in the deposit does not vary

significantly from the mean grade;(b) Gradational: the grade values have zonal characteristics, and the grade

changes gradually from one point to another; and(c) Erratic: the grade values change radically over short distances and do

not exhibit any discernible pattern in their changes.(8) Depth of the deposit: The pressure due to the superincumbent strata increases

with the depth and the adoptable method of stoping changes. Hartman [12]discussed the applicability of different stoping methods by classifying depositsinto three groups based on their depth from the surface, i.e.(a) Shallow: 5450 m(b) Moderate: 450 – 1200 m(c) Deep: 41200 m.

(9) Capital investment: The required investment mostly depends on the extentof mechanisation. Capital-intensive methods cannot be applied if there is adearth of money. Based on the financial capability of the investors, thecapital investment needs for various stoping methods are classified asfollows:(a) High(b) Medium(c) Low.

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(10) Market: Some methods are flexible enough in terms of variation of theproduction to cope with varying market conditions. These methodsallow the mine management to vary the rate of production accordingto the market demand, while others give a fixed rate of production andhave a limited adaptability during ups and downs in the marketconditions.

(11) Dilution of extracted ore: Depending on the average grade of the depositsand the ore processing technology being applied, the acceptable level ofdilution may be classified as(a) High(b) Low.

(12) Labour: Based on the working skill of the available work force, the mineworkers may be grouped as:(a) Skilled(b) Unskilled.

(13) Health and safety: The safety potential of a stoping method is determinedaccording to the conditions of the working environment and is graded asfollows:(a) high – indicating improved working conditions and the fact that the

practised method has less impact on the workers’ health and safety dueto mining-related problems

(b) low – indicating comparatively unsafe working conditions.

3. Underground mining methods for ore deposits

A number of stoping methods with their variations have been devised to suitparticular ore deposits, and they can be broadly grouped into six commonlypractised stoping methods. The salient features of these methods and theirapplicability conditions are enumerated in this section.

3.1. Room and pillar

In this method, a grid of rooms is developed, leaving pillars to support the back. Therooms and pillars may or may not be uniform in size, and the pillars may or may notbe extracted at a later date.

Focal points:

. Applicable for flat lying deposits.

. Usually not practised in very thick (450 m) deposits.

. The size of the rooms and pillars depends on the depth of the working and thestrength of the ore/host rock.

3.2. Shrinkage

In this stoping method, the ore is drilled and blasted, and most of the blasted muckremains (with only a part being drawn out) in the stope, to provide support for thewalls and working platform until the whole stope has been blasted. The broken ore isdrawn out afterwards.

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Focal points:

. Applicable for narrow deposits.

. Suitable for steep deposits.

. Incompetent host rock cannot stand without support.

3.3. Sublevel stoping

Sublevel stoping is an overhand method where the ore is blasted by drilling longholes from sublevels. The broken ore is drawn out through draw points. The stopesmay or may not be filled after mining, and, if filled, the pillars are usually recoveredusing the same method or the cut and fill stoping method.

Focal points:

. An appropriate geometry must exist, i.e. large and thick deposits.

. The wall rocks must be competent enough to leave open stopes.

. The stope and pillar widths are determined by the rock strength and the depthand height of the stope.

3.4. Cut and fill

Cut and fill is a cyclic stoping method where each slice of ore is removed afterblasting and replaced with fill material. There are a multitude of variations,such as overhand cut and fill, underhand cut and fill, rill stoping and post-pillarcut and fill, which can be selected to suit the conditions. Mostly overhand cutand fill is practised and this method was considered in the proposed modeldevelopment.

Focal points:

. Applicable for narrow ore bodies.

. Suitable for steeply dipping ore deposits.

. The ore can be moderately to highly competent.

. The walls can be weakly to highly competent.

. The cost of the fill must be less than the cost of leaving pillars.

. Applicable for irregular ore bodies.

3.5. Sublevel caving

This is an induced caving method where the ore is blasted by ring drilling fromsublevel drifts. The overlying and the hanging wall are expected to cave in as the oreis drawn out.

Focal points:

. Applicable for deposits with a limited width.

. Suitable when there are incompetent walls (hanging wall and footwall).

. Draw control and maintaining the brow of the face are the key concerns of thismethod.

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3.6. Block caving

In this method, an area of ore is undercut to induce caving under its own weightwhen the overlying waste is expected to cave in as well. A study of the cavability ofthe ore is a prerequisite for employing this method. Prior to practising block caving,a detailed study must be performed to determine the volume of excavation requiredto initiate caving, the size of the caved blocks and whether the hanging wall will cavefast enough. The size distribution of the caved ore is critical for selection of an oredrawing system.

Focal points:

. Applicable when the strength of the ore/wall rock is low.

. The method gives highly fractured ore and good fragmentation.

4. An overview of the analytical hierarchy process

The AHP is a powerful multi-criteria decision making tool developed by ThomasSaaty [13] to accommodate different criteria that influence a decision to varyingdegrees. The AHP can enable decision makers to represent the interaction ofmultiple factors in complex and unstructured situations. It is based on pair-wisecomparisons between criteria/sub-criteria on each level with respect to the goal ofobtaining the best alternative selection. The standard procedure recommended forthe AHP is as follows:

(1) Step 1: Decompose the problem hierarchically, i.e. structure the problem intoan L-level hierarchy as presented below:. Level 1: Overall objective/focus of the problem.. Level 2: Criteria used for evaluating the alternatives.. Level 3: Sub-criteria.. . . .. . . .. Level L: Set of decision alternatives to be evaluated with respect to the

overall objective.(2) Step 2: Compare pairs of elements on each level using Saaty’s [13] nine-point

scale. This comparison forms the elements of the n6 n pair-wise comparisonmatrix, where n is the total number of attributes on a particular level ofhierarchy.As human judgements are the basis of the pair-wise comparison approach,some degree of inconsistency may be introduced due to a lack of adequateinformation, improper conceptualisation of the hierarchy, mental fatigue,etc. However, the greatest strength of the AHP method is its ability to detectinconsistency in judgements. For example, if an expert (evaluator) expressesthe opinion that stoping method A is three times more appropriate thanstoping method B, which is two times more appropriate than stoping methodC, then perfect consistency in judgements would imply that stoping methodA should be considered (36 2) six times more appropriate than stopingmethod C. Now, if the value rating of the expert judgement is anything otherthan six, then judgemental errors exist that result in an inconsistency matrix.The consistency of the pair-wise comparison matrix is checked by the ratio

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called the inconsistency ratio or consistency ratio (CR). Judgements areconsidered acceptable if the CR5 0.1. When the CR� 0.1, one shouldinvestigate the problem and try to find out the possible cause of theinconsistency, in the hope of modifying the judgements, hence applyinga modified matrix [14]. The interested reader may refer to [13] for details onthe CR.

(3) Step 3: Aggregate the experts’ judgements to form an aggregated pair-wisecomparison matrix. Each expert generates his or her own pair-wisecomparison matrix for the criteria/sub-criteria. As pointed out by Aczeland Saaty [15], the aggregated pair-wise comparison of each expert can beaggregated into a group comparison by taking the geometric mean ofall the comparisons. Therefore, the weighted mean value of aij is expressedas:

aij ¼Ynk¼1

wk � akij

!1�Pn

k¼1wk

ð1Þ

where akij is the kth expert’s pair-wise comparison value, n is the number ofexperts and wk is the weight of the kth expert. In this study, it was assumedthat all the experts have equal expertise in their judgements and thereforewk¼ 1 8 k.

(4) Step 4: Generate the priority vector at each level in the hierarchy using theeigen-vector method. The normalised principal eigen-vector corresponding tothe principal eigen-value of a pair-wise comparison matrix gives the priorityvector. The eigen-vector for a consistent reciprocal square matrix can beobtained by normalisation of any column vector of the matrix.

(5) Step 5: Synthesise all the priority vectors so that a final priority vector ofthe alternatives will be obtained. Synthesis of the priority vectors from onelevel with those of the next higher level is carried out using the followingexpression:

Wi ¼Xnj¼1

Cj � wij 8i ¼ 1; 2; . . . ;m ð2Þ

where Wi is the weight or priority value of the alternative i, cj is the weight/priority value of the criterion j for j¼ 1, . . . , n, and wij is the priority value ofthe alternative i with respect to the criterion j when m is the number ofdecision alternatives and n is the number of criteria.

5. Structure of the proposed AHP model for the selection of a stoping method

The proposed AHP model, as shown in Figure 1, decomposes the problem into fivelevels hierarchically. The top level represents the main objective of selecting a stopingmethod, while the selection criteria for the fulfilment of the objectives are placedat the second, third and fourth levels, and the lowest level contains the decisionalternatives for the stoping methods. The experts assess the relative strength/importance of each criterion/sub-criterion on a level of the hierarchy in comparisonwith the other criteria/sub-criteria on the very same level, to fulfil the objective of the

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immediately higher level. These experts’ judgements are then translated into numbersfollowing Saaty’s nine-point scale to obtain the pair-wise comparison matrix.

The overall rating of each alternative is calculated by multiplying the relativepriorities along each path of the hierarchy leading to the decision alternative andthen adding these products for each decision alternative.

5.1. Methodology

(1) Step 1: List the intrinsic and extrinsic factors that influence the choice of astoping method.

(2) Step 2: Prepare the questionnaires for collecting the experts’ opinions.(3) Step 3: Select a group of experts from the mining industry, academia and

research institutions.(4) Step 4: Collect the experts’ assessments regarding the strength of the influence

of different factors in choosing the suitable stoping method.(5) Step 5: Verify the consistency of the experts’ judgements through the

consistency ratio.(6) Step 6: Construct the aggregated judgement matrix using expression (1) and

calculate the priority value of each influencing factor (Cj).(7) Step 7: Collect the values of the influencing factors for the case study mines

and calculate the overall priority value (Wi) for each stoping method withexpression (2). The methods with the highest Wi value are chosen.

5.2. Model development

A questionnaire with a set of multiple choice questions was prepared to collect theexperts’ opinions on the relative importance of eight intrinsic and five extrinsicfactors that influence the choice of a stoping method. Five experts (two fromindustry, two from a research institute and one from academia) were asked tomark their opinions on the questionnaires. The individual experts’ judgementswere aggregated using expression (1), and the aggregated pair-wise comparison

Figure 1. Structure of the AHP model for the selection of a stoping method.

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Table

1.

Aggregatedpair-w

isecomparisonmatrix

fortheim

portance

oftheeightintrinsicfactors.

Intrinsicfactor

Dip

ofthe

deposit

Strength

ofore

Strength

of

host

rock

Depth

of

thedeposit

Shapeof

thedeposit

Presence

of

surface

feature

Grade

ofore

Thicknessof

thedeposit

Dip

ofthedeposit

1.00

0.46

0.37

0.39

2.77

3.78

2.77

2.17

Strength

ofore

2.17

1.00

1.00

1.00

2.00

6.09

3.37

2.00

Strength

ofhost

rock

2.70

1.00

1.00

2.00

3.00

7.47

4.37

2.00

Depth

ofthedeposit

2.55

1.00

0.50

1.00

2.00

6.73

3.96

3.00

Shapeofthedeposit

0.36

0.50

0.33

0.50

1.00

1.25

0.50

1.00

Presence

ofsurface

feature

0.26

0.16

0.13

0.15

0.80

1.00

0.50

0.50

Gradeofore

0.36

0.30

0.23

0.25

2.00

2.00

1.00

1.00

Thicknessofthedeposit

0.46

0.50

0.50

0.33

1.00

0.10

1.00

1.00

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Table

2.

Priority

values

forthedifferentinfluencingfactors.

Parameters

Dip

Strength

ofore

Strength

ofcountry

rock

Surface

features

Shape

Grade

Thick-ness

Depth

Labour

Market

Health

Dilution

Capital

Methods

Flat

Medium

Steep

Weak

Medium

Strong

Weak

Medium

Strong

Relevant

Irrelevant

Irregular

Tabular

Massive

Uniform

Graded

Erratic

Thick

Thin

Shallow

Moderate

Deep

Skilled

Unskilled

––––

High

Low

High

Low

High

Medium

Low

Room

and

pillar

0.0081

0.0108

0.0073

0.0044

0.0030

0.0081

0.0047

0.0105

0.0040

0.0106

0.0101

0.0018

0.0027

0.0019

0.0098

0.0189

0.0151

0.0012

0.0215

0.0036

0.0081

0.0108

0.0073

0.0044

0.0030

0.0081

0.0047

0.0105

0.0040

0.0106

0.0101

0.0018

Shrinkage

stoping

0.0092

0.0082

0.0065

0.0044

0.0030

0.0081

0.0047

0.0105

0.0054

0.0143

0.0032

0.0004

0.0015

0.0050

0.0032

0.0189

0.0383

0.0082

0.0025

0.0065

0.0092

0.0082

0.0065

0.0044

0.0030

0.0081

0.0047

0.0105

0.0054

0.0143

0.0032

0.0004

Sublevel

stoping

0.0021

0.0054

0.0087

0.0044

0.0030

0.0120

0.0082

0.0021

0.0130

0.0061

0.0305

0.0025

0.0030

0.0019

0.0382

0.0211

0.0038

0.0050

0.0059

0.0015

0.0021

0.0054

0.0087

0.0044

0.0030

0.0120

0.0082

0.0021

0.0130

0.0061

0.0305

0.0025

Cutand

fill

0.0185

0.0082

0.0033

0.0097

0.0030

0.0012

0.0133

0.0200

0.0062

0.0109

0.0164

0.0015

0.0034

0.0028

0.0067

0.0271

0.0272

0.0124

0.0019

0.0069

0.0185

0.0082

0.0033

0.0097

0.0030

0.0012

0.0133

0.0200

0.0062

0.0109

0.0164

0.0015

Sublevel

caving

0.0062

0.0069

0.0109

0.0007

0.0061

0.0090

0.0082

0.0021

0.0080

0.0029

0.0282

0.0035

0.0015

0.0009

0.0341

0.0211

0.0148

0.0073

0.0054

0.0008

0.0062

0.0069

0.0109

0.0007

0.0061

0.0090

0.0082

0.0021

0.0080

0.0029

0.0282

0.0035

Block caving

0.0021

0.0067

0.0097

0.0007

0.0061

0.0090

0.0082

0.0021

0.0106

0.0024

0.0174

0.0038

0.0015

0.0008

0.0257

0.0105

0.0185

0.0075

0.0044

0.0023

0.0021

0.0067

0.0097

0.0007

0.0061

0.0090

0.0082

0.0021

0.0106

0.0024

0.0174

0.0038

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Table

3.

Resultsforthecase

studymines.

Case

studymine

Sourceofinputparameter

value

Overallpriority

valuefor

stopingmethod

Rem

arks

StrassaIronOre

Deposit,

Bergslagen,Sweden

Thevalues

ofthevariousinput

parametersweretaken

from

Bjorkstedt[16]

Room

andpillar–0.1820

Shrinkagestoping–0.1743

Sublevel

stoping–0.2137

Cutandfill–0.1535

Sublevel

caving–0.1606

Block

caving–0.1158

Thedeveloped

methodsupportsthe

practised

sublevel

stopingmethod.

KolarGold

Deposit

(NundyroogMine),

Karnataka,India

Inputparameter

values

asper

Deshmukh[17]

Room

andpillar–0.1390

Shrinkagestoping–0.1645

Sublevel

stoping–0.2043

Cutandfill–0.2164

Sublevel

caving–0.1521

Block

caving–0.1238

Thecalculatedpriority

values

are

infavourofthepractised

cutandfill

method.

KhetriCopper

Ore

Deposit,

Rajasthan,India

Inputparameter

values

asper

Deshmukh[17]

Room

andpillar–0.1427

Shrinkagestoping–0.1678

Sublevel

stoping–0.2284

Cutandfill–0.1787

Sublevel

caving–0.1687

Block

caving–0.1137

Thedeveloped

model

supportsthe

practised

sublevel

stopingmethod.

LuckyFridayUnderground

Silver

andLeadmine,Coeur

d’A

lene,

Idaho,USA

Inputparameterssource:

www.hecla-m

ining.com

[18]

Room

andpillar–0.1334

Shrinkagestoping–0.1409

Sublevel

stoping–0.1554

Cutandfill–0.2151

Sublevel

caving–0.1571

Block

caving–0.1981

Theresultssupport

thepractised

cut

andfillmethod.

GreensCreek

Mine,Admiralty

Island,USA

Inputparameterssource:

www.hecla-m

ining.com

[18]

Room

andpillar–0.1364

Shrinkagestoping–0.1419

Sublevel

stoping–0.1534

Cutandfill–0.2253

Sublevel

caving–0.1496

Block

caving–0.1933

Theresultssupport

thepractised

cut

andfillmethod.

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matrix for the importance of the eight intrinsic factors is given in Table 1. The CRvalues of the pair-wise comparison matrices vary between 2% and 5%. Finally, thecalculated priority values for the different influencing factors are presented inTable 2.

6. Validation of the developed model

The efficacy of the developed model was verified through case studies in five workeddeposits scattered all over the world. The results are summarised in Table 3.

7. Conclusions and proposals for future research work

The selection of a mining method is a complex and multi-attribute decision makingprocess. No one method is able to meet all the requirements and conditions, butrather the appropriate mining method is the one that is technically feasible for theore geometry and ground conditions concerned, while also providing a low-risk andlow-cost operation. This means that the best mining method is the one with thetechnical problems that are the cheapest to deal with. The proposed AHP-guidedmodel is simple and based on the knowledge of experts. The knowledge of theexperts is coded in the form of priority values. The list of attributes is not exhaustive,but is flexible enough to accommodate any alterations. It can be further improved byinclusion or exclusion of attributes, and similarly the priority values can be improvedby incorporating the opinions of a set of experts. A sensitivity analysis may beconducted to check the robustness of the proposed model.

References

[1] B. Samanta, B. Sarkar, S.K. Mukherjee and J. Das, An application of AHP for selection ofmaintenance personnel in mine, J. Mines. Metals Fuels, Vol. 52, December (2004), pp.420–424.

[2] A. Haj Shrimohammadi and W.C. Wedley, Maintenance management – An AHPapplication for centralization/decentralization, J. Qual. Mainten. Eng. 10 (2004), pp. 16–25.

[3] A.W. Labib, A decision analysis model for maintenance policy selection using a CMMS,J. Qual. Mainten. Eng. 10 (2004), pp. 191–202.

[4] B. Samanta, B. Sarkar and S.K. Mukherjee, Selection of opencast mining equipment bymulti-criteria decision making process, Trans. Inst. Mining Metall. Sec. A: MiningTechnol. 111 (2002), pp. A136–A142.

[5] C. Kahraman, U. Cebeci and D. Ruan, Multi-attribute comparison of catering servicecompanies using fuzzy AHP: The case of Turkey, Int. J. Prod. Econ. 87 (2004), pp. 171–184.

[6] V.N. Kazakidis, Z. Mayer and M.J. Scoble, Decision making using the analytic hierarchyprocess in mining engineering, Trans. Inst. Mining Metall. Sec. A: Mining Technol. 113(2004), pp. A30–A42.

[7] V. Belton and T. Gear, On a short-coming of Saaty’s method of analytic hierarchies,Omega 11 (1983), pp. 228–230.

[8] J.S. Dyer, Remarks on the analytic hierarchy process, Manag. Sci. 36 (1990), pp. 259–268.

[9] S. Planeta, J. Paraszczak and J. Szymanski, Selection criteria for underground stopingmethods in narrow vein deposits, Mine Plan. Equip. Sel. 2001: proceedings of the TenthInternational Symposium on Mine Planning and Equipment Selection, edited by R.K.Singhal and B.P. Singh (2001), pp. 233–241.

[10] P.W. MacMillan and B.A. Ferguson, Principles of stope planning and layout for groundcontrol, in Underground Mining Methods Handbook, W.A. Hustrulid, ed., SME-AIME,New York, 1982, pp. 526–530.

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[11] D.E. Nicholas, Selection procedure, in SME Mining Engineering Handbook, 2nd ed., H.L.Hartman, ed., SME, Littleton, CO., 1992, p. 2090.

[12] H.L. Hartmann, Introductory Mining Engineering, John Wiley & Sons, Inc., New York,1987.

[13] T.L. Saaty, Analytical Hierarchy Process: Planning, Priority Setting, Resource Allocation,McGraw Hill, New York, 1980.

[14] H.A. Taha, Operation Research – An Introduction, 7th ed., Pearson Education Inc.,New Delhi, 2002.

[15] J. Aczel and T.L. Saaty, Procedures for synthesizing ratio judgments, J. Math. Psychol. 27(1983), pp. 93–102.

[16] K.A. Bjorkstedt, Strassa Mine, in Underground Mining Methods Handbook, W.A.Hustrulid, ed., SME-AIME, New York, 1982, pp. 414–434.

[17] D.J. Deshmukh, Elements of Mining Technology, Vol. 2, Vidyasewa Prakashan, Nagpur,India, 1988.

[18] http//www.hecla-mining.com as accessed on July 17, 2010.

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