MINING METHOD SELECTION METODOLOGY BY MULTIPLE CRITERIA DECISION ANALYSIS - CASE STUDY IN COLOMBIAN...

ISAHP Article: Mu, Saaty/A Style Guide for Paper Proposals To Be Submitted to the

International Symposium of the Analytic Hierarchy Process 2014, Washington D.C., U.S.A.

International Journal of the

Analytic Hierarchy Process

1 Washington, D.C.

June 29 – July 2, 2014

MINING METHOD SELECTION METODOLOGY BY MULTIPLE

CRITERIA DECISION ANALYSIS - CASE STUDY IN

COLOMBIAN COAL MINING

Eng. Jorge Ivan Romero Gelvez M.I.

Escuela Colombiana de Carreras industriales

Bogotá, Colombia.

E-mail: [email protected]

Eng. Felix Antonio Cortes Aldana. Phd

Universidad Nacional de Colombia

Bogotá, Colombia.

E-mail: [email protected]

ABSTRACT

The purpose of this paper is to present an application of the AHP technique to a mining

method selection problem faced by a Colombian mining company; in this case we use

five decision makers. Next, a final aggregation of criteria priorities by AHP and

ENTROPY is proposed for include subjective and objective weighting. Next, VIKOR

method is performed to present a compromise solution; VIKOR is used to solve the

problem without decision makers dependence; the weights for VIKOR are aggregated

using an a priori λj subjective weighting obtained from AHP method. Whereas entropy weighting provides a dynamic and objective assessment of all criteria, AHP weighting

determine all decision makers preferences. Finally, an analysis of the results is carried out

to derive conclusions in relation to the effects of the modeling processes of both

techniques.

Keywords: Multicriteria decision making, selection problem, AHP, VIKOR, Entropy

weighting.

1. Introduction

This study wants to contribute to mining planning and design process. The problem of

selecting the mining method becomes the most important aspect of mining activities, and

you should select the method that best fits the unique criteria of each location, such as

spatial, geological, hydrogeological, geotechnical and other considerations such as

economic, technological and environmental factors. The performance of a subjective and

objective methodology will try to support the hard process of select the most suitable

mining extraction alternative.

Selecting the extractive method becomes the most important aspect of mining activities;

the selected method need to fits with unique criteria of each location, such spatial,

geological, hydrogeological, geotechnical and other considerations like economic,

technological and environmental factors. Such considerations or also called criteria,

usually in conflict have multiple stakeholders: environmental authorities, mining

IJAHP Article: Mu, Saaty/A Style Guide for Paper Proposals To Be Submitted to the


International Symposium of

the Analytic Hierarchy

Process

2 Washington, D. C.

June 29 – July 2, 2014

authorities, mining companies, communities and others. In Colombia usually the final

decision maker becomes the Mining Engineer who works for the extractive company.

A mining company wants to choose the most suitable alternative for extracting coal

deposit located on the western side of Cerro Tasajero, Norte de Santander, Colombia.

This site was carefully studied by an interdisciplinary group of Geologists and Engineers

(among others). All data parameters of this deposit can be observed in Table 1. And also

can be proved by consulting the document: Regions and areas with coal in Colombia,

developed by (Mejia-umana & Pulido-gonzalez, 1993)

Table 1

Technical parameters Seam 20

Source: Own development based on information from the mining company

2. Literature Review

The selection of extraction methods in mining is one of the oldest challenges of humanity

and has been studied widely; about the most relevant scientific literature begins with the

first qualitative classification schemes extractive methods selection (Boshkov & Wright,

1973). In subsequent studies a classification system divides underground mining into

three groups based on ground conditions assigning each type of support required

(Morrison, 1976). (Laubscher, 1981) proposes a selection methodology for underground

mining method based on the RMR system (rock mass rating).

The first approach to a quantitative selection method is developed by (Nicholas, 1993)

with a numerical approach for the selection of extractive method (Selection Procedure -

A Numerical Approach); in this method a scale is formulated for the weighting of each

extraction method. Subsequently Hartman (H. Hartman & Mutmansky, 2002) developed

a qualitative selection scheme based on reservoir geometry and ground conditions to

choose the extractive method. Next, (Miller-Tait, Pakalnis, & Poulin, 1995) modified the

Nicholas method adding several criteria.

At present there are some approaches to the problem of mining method selection by

MCDA which include the application of fuzzy logic (Bitarafan & Ataei, 2004) and

(Karadogan, Kahriman, & Ozer, 2008) and we can find varied applications of AHP

(Alpay & Yavuz, 2009), (Azadeh, Osanloo, & Ataei, 2010) , (Bogdanovic, Nikolic, &

Ilic, 2012) and (Gelvez, Triana, & Aldana, 2012).

Parameter Quality

Thickness between 0.90 m y 2.10 m

Depth 600 m

Type Patty/Tabular

Grade distribution Uniform

Plunge Entre 12° y 20°

RSS (rock substance strength) Very Narrow

RMR (rock mass rating) between 21 y 40





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3. Ubc method

The UBC (University of British Columbia) method was developed by (Miller-Tait

et al., 1995). This method rises by the need of improve the Nicholas technique

(Nicholas, 1993). As new add Miller introduces a -10 value for assign a negative

weight without discard completely any alternative. Moreover the rock mechanics

values are modify whit new ones. For more details can consult (Miller-Tait et al.,

1995)

4. Entropy method

The entropy method was developed by (Zeleny, 1982) as an objective method for

weighting criteria. This method assigns weights to each criterion based on the

decision matrix information, without reflect any decision maker preference

(Pomerol & Barba-Romero, 1997). The relative importance of the criteria j in a

decision situation, measured by weight wj, is directly related to the amount of

data inherently provided by the set of alternatives for this criterion. The more

diversity there is in the evaluations of the alternatives; greater importance should

be the criterion. The extent of this diversity is based on the concept of entropy in

an information channel proposed by (Shannon & Weaver, 2002). The procedure is

as follows:

Evaluations ija (i=1,m)(j=1,n) are normalized by sum fraction iji

a∑ of the

original evaluations of each j criterion. Entropy is determined by: (Ej).

1/log * *logj ij ijiE m a a− ∑ (1)

Where m= Number of alternatives in the normalized matrix, and ija = Normalized

criteria. Next, calculate the diversity (Dj).

1j jD E= − (2)

Normalized weight is calculated (Wj).

/ 1.0j j jjW D D= =∑

(3)

5.Vikor method

This method was developed by Serafim Opricovic in 1998. The VlseKriterijumska

Optimizcija I Kompromisno Resenje VIKOR method was developed for multicriteria

optimization of complex systems. It determines the compromise ranking-list, the

compromise solution, and the weight stability intervals for preference stability of the

compromise solution obtained with the initial (given) weights. This method focuses on

ranking and selecting from a set of alternatives in the presence of conflicting criteria. It

introduces the multicriteria ranking index based on the particular measure of ‘‘close-

ness’’ to the ‘‘ideal’’ solution (Serafim Opricovic & Tzeng, 2004). Acording (Quijano

Hurtado, 2012), based on (S Opricovic, 1998), Assuming that each alternative is

evaluated according to each criterion function, the compromise ranking could be





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performed by comparing the measure of closeness to the ideal alternative. The

multicriteria measure for compromise ranking is developed from the Lp-metric used as an

aggregating function in a compromise programming method (Yu, 1973; Zeleny, 1982).

The set of alternatives “J” are noted by A1, A2, Aj……..Am. For alternative Aj, The

rating of ith aspect is noted byijf , for example ijf is the ith value of the criterion for

alternative Aj; m is the number of alternatives, n is the number of criteria. Development

of the VIKOR method started with the following form of Lp-metric:

( ) ( )1/

* *

,

1

/

ppn

p j i i ij i i

i

L w f f f f −

=

= − − ∑

(4)

1 ; j 1, 2,...., J .p≤ ≤ ∞ =

This Lp distance concept, represents the Manhattan and Chevishev distances for and

values. Uses the L1 norm, where p=1 and corresponds to the mayor distance between two

points. In the second case, for calculation vikor uses the chevishev norm that is the

short distance between two points, where (Bellver & Martinez, 2013; Serafim

Opricovic & Tzeng, 2004). According (Quijano Hurtado, 2012) based on (Serafim

Opricovic & Tzeng, 2007) the procedure is as follows:

a) Determine the best *

if and the worst if− values of all criterion functions i=1,2,….,n,

If the ith function represents a benefit then * maxi ijf f= and mini ijf f− = .

b) Compute the values Sj and Rj, j = 1,2,……,J by the relations

( ) ( )* *

0/

n

j i i ij i iS w f f f f −= − −∑ (5)

( ) ( )* *max /j i i i ij i iR w f f f f − = − − (6)

c) Compute

jQ values by the relation

( )( ) ( )

( )( )

* *

* *1

j

j jS S R Rv

S S R RQ v

− −

− −+ −

− −=

(7)

d) Rank the alternatives, sorting by the values S, R and Q, in decreasing order. The

results are three ranking lists. S, R y Q.

e) A(1) = Q (mín) is the compromise solution if:

I. Acceptable advantage. (2) (1)( ) ( ) ,Q A Q A DQ− ≥

Where 1/ ( 1)DQ J= − and (2)A is the second alternative in the Q ranking

list.





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II. Acceptable stability in decision making. Alternative (1)A must be the best

also in S or R.

6.Research Design/Methodology

According Saaty and Peniwaty when the members of a group are all experts who do not

wish to participate in the judgment process but prefer to obtain their own answer after the

group has structured a decision, we can apply the geometric mean or the mean weighted

by the importance of the experts to the different individuals’ final outcome to obtain an

overall final outcome (Saaty & Peniwati, 2008). In this paper 5 decision makers play the

role of experts and solve the problem individually, next all judgments are unify by the

geometric mean.

For MCDA will be taken as valid alternatives which have a positive weighting to apply

the technique UBC (Miller-Tait et al., 1995) thereby eliminating alternatives that are not

only technically feasible and applicable alternatives left. While there are a good amount

of extractive methods, this problem only considers 9 of the 10 methods described in

(Nicholas 1993) and (Hartman & Mutmansky 2002): Alternative 1 (Open pit), alternative

2 (Block caving), alternative 3 (Sublevel Stopping), alternative 4 (sublevel caving),

alternative 5 (long wall), alternative 6 (room and pillar), alternative 7 (Shrinkage

Stopping), alternative 8 (Cut and fill), alternative 9 (Square set).

Criterion 1 Spatial characteristics of the

deposit.

Sc1. Size - Maximize

Sc2. Shape - Maximize

Sc3. Plunge - Maximize

Sc4. Depth - Maximize

Criterion 2 Geological and

hydrogeological conditions and

geotechnical properties.

Sc5. Distribution - Maximize

Sc6. Rock mass ratings (RMR) -

Maximize

Sc7. Rock substance strength (RSS) -

Maximize

Criterion 3 Economic considerations

Sc8. Performance rate - Maximize

Sc9. Production - Maximize

Sc10. Capital Investment - Minimize

Sc11. Productivity - Maximize

Sc12. Comparative costs of possible

mining methods. Minimize

Criterion 4 Technological factors

Sc13. Mine Recuperation - Maximize

Sc14. Dilution - Minimize

Sc15. Flexibility - Maximize

Sc16. Selectivity - Maximize

Criterion5 Environmental

Considerations

Sc17. Stability of the openings -

Maximize

Sc18. Subsidence or effects on the

surface of excavation - Maximize

Sc19. Health and safety conditions –

Maximize

In (Gelvez et al., 2012) is proposed a generic decision matrix as we can see in Table 2,

this matrix is based on (H. L. Hartman & Mutmansky, 2002) values. The scale: Higuest

5, High 4, Moderate 3, Low 2, Lowest 1; Escala 2: Good 3, Moderate 2, Poor 1; Escala 3:

Large scale 4, Large 3, Moderate 2, Small 1; Escala 4: Large 4, High 3, Moderate 2 and

Small 1 is transformed in objective values, see table 3

Table 2. Generic decision matrix. Source: Own development based on (H. L. Hartman &

Mutmansky, 2002; Miller-Tait et al., 1995)





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C Sc A1 A2 A3 A4 A5 A6 A7 A8 A9

Sc1

Sc2

Sc3

Sc4

Sc5

Sc6

Sc7

Sc8 Rapid Slow Moderate Moderate Moderate Rapid Rapid Moderate Slow

Sc9 Large Scale Large Large Large Large Large Moderate Moderate Small

Sc10 Large High Moderate Moderate High High Low Moderate Low

Sc11 High Low Low Moderate High High Low Moderate Low

Sc12 5 10 20 15 15 20 45 55 100

Sc13 High High Moderate High High Moderate High High Higuest

Sc14 Moderate High Moderate Moderate Low Moderate Low Low Lowest

Sc15 Moderate Low Low Moderate Low Moderate Moderate Moderate High

Sc16 Low Low Low Low Low Low Moderate High High

Sc17 High Moderate High Moderate High Moderate High High High

Sc18 High High Low High High Moderate Low Low Low

Sc19 Good Good Good Good Good Good Good Moderate Poor

C1

C2

C3

C4

C5

Table 3. Numeric generic decision matrix. Source: Own development based on (H. L.

Hartman & Mutmansky, 2002; Miller-Tait et al., 1995)

C Sc A1 A2 A3 A4 A5 A6 A7 A8 A9

Sc1

Sc2

Sc3

Sc4

Sc5

Sc6

Sc7

Sc8 3 1 2 2 2 3 3 2 1

Sc9 4 3 3 3 3 3 2 2 1

Sc10 4 3 2 2 3 3 1 2 1

Sc11 4 2 2 3 4 4 2 3 2

Sc12 5 10 20 15 15 20 45 55 100

Sc13 4 4 3 4 4 3 4 4 5

Sc14 3 4 3 3 2 3 2 2 1

Sc15 3 2 2 3 2 3 3 3 4

Sc16 2 2 2 2 2 2 3 4 4

Sc17 4 3 4 3 4 3 4 4 4

Sc18 4 4 2 4 4 3 2 2 2

Sc19 3 3 3 3 3 3 3 2 1

C1

C2

C3

C4

C5

IJAHP Article: Mu, Saaty/A Style Guide for Papers Submitted to the International Journal of the




7 Vol. 3 Issue 1 2011

ISSN 1936-6744

Figure 1. Proposed methodology for mining method selection Source: Own development

based on information from the mining

7. Data/Model Analysis

Table 4. Decision Matrix. Source: Own development

sc1 sc2 sc3 sc4 sc5 sc6 sc7 sc8 sc9 sc10 sc11 sc12 sc13 sc14 sc15 sc16 sc17 sc18 sc19

wj 4,28% 4,42% 4,28% 4,28% 4,29% 4,34% 4,41% 5,50% 5,78% 5,75% 5,34% 10,58% 4,72% 5,75% 5,10% 5,67% 4,41% 5,32% 5,78%

A1 54 40 52 52 54 53 50 2 3 2 2 20 3 3 2 2 4 2 3

A2 54 54 54 53 54 61 62 2 3 3 4 15 4 2 2 2 4 4 3

A3 54 54 54 52 54 50 50 3 3 3 4 20 3 3 3 2 3 3 3

A4 54 54 51 54 52 59 64 2 2 2 3 55 4 2 3 4 4 2 2

A5 51 54 52 52 50 59 61 1 1 1 2 100 5 1 4 4 4 2 1

ma

x

ma

x

ma

x

ma

x

ma

x

ma

x

ma

x

ma

x

ma

x

min

ma

x

min

ma

x

min

ma

x

Ma

x

Ma

x

min

ma

x

c1 c2 c3 c5c4

Figure 2. Assigning weights by entropy method Source: Own development





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Figure 3. Aggregation of AHP decision makers and Entropy weigths Source: Own

development based on information from the mining company

Figure 4. Hierarchy and AHP results Source: Own development based on information

from the mining company

Table 2. VIKOR results. Source: Own development

Q S R

Sublevel Stoping 0,56874757 0,519571919 0,05748521

Longwall 0,06874757 0,325995775 0,05748521

Room and Pillar 0,39339684 0,451684482 0,05748521

Cut and Fill 0,0374675 0,340501405 0,04978445

Square Set 0,95987655 0,504038032 0,10579196





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Figure 5. Vikor performance analysis. Source: Own development

8. Conclusions

The results Vikor, show a set of compromise solutions (cut and fill - long wall) which are

accepted by experts involved in the decision process. The results of the AHP method

show decision makers preferences for “long wall” in this particular problem. The overall

inconsistency was 5%. Finally for this deposit the company used long wall method, a

finding consistent with the subjective and objective analysis proposed in this

methodology.

The results obtained in this work allow evidence as this Methodology Vikor-AHP, works

to improve the process of decision-making, since it allows structured in a logical way a

lot of information, both the problem and the possible solutions that can be pose.

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