A vector-dissimilarity-based approach for multi-criteria decision making

REGULAR ARTICLE

A vector-dissimilarity-based approach for multi-criteriadecision making

Suprakash Gupta • Anjum Rahber •

Alireza Ahmadi • Uday Kumar

Received: 5 April 2013 / Revised: 16 July 2013 / Published online: 7 August 2013

� The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and

Maintenance, Lulea University of Technology, Sweden 2013

Abstract Decision making in complex environments is

influenced by a large number of conflicting and incom-

mensurable factors. It is multidimensional and the influ-

encing factors affect the decision process to varying

degrees. The performance measurement of decision alter-

natives in multi-criteria decision making (MCDM) may be

represented as a multidimensional vector in real space. The

technique for order preference by similarity to ideal solu-

tion (TOPSIS) is a popular MCDM tool. However, some-

times this technique shows its inability to differentiate

between decision alternatives. In this paper the limitations

of TOPSIS are examined and an improvement is suggested.

The proposed new method uses the vector dissimilarity

approach to remove the boundary restrictions and achieve

greater sovereignty. The improved method has been dem-

onstrated through a case study of maintenance design for

dump trucks deployed in a large surface mine.

Keywords Decision alternatives � Vectordissimilarity �Maintenance selection �MCDM �Mine

dump trucks

1 Introduction

In today’s highly competitive business environment,

managers have to make numerous decisions within a short

period. Often these decisions are made in complex envi-

ronments and are influenced by a large number of con-

flicting and incommensurable criteria. This compels

managers to take help from guiding tools that assist them in

choosing the right alternative at an acceptable risk. A

suitable multi-criteria decision making (MCDM) approach

helps managers by ranking the available alternatives

through evaluation with respect to multiple appraising

criteria. A decision process normally incorporates the fol-

lowing steps (Opricovic and Tzeng 2004):

(a) Establish the goal or decision objectives.

(b) Develop a list of feasible alternatives that can meet

the decision objectives.

(c) Establish an evaluation methodology, e.g. an MCDM

approach, for assessing the effectiveness of the

alternatives in meeting the objectives.

(d) Select a criteria set and assess the weight of the

criteria.

(e) Evaluate the performance of the alternatives in the

light of the criteria set.

(f) Rank the alternatives and choose the most apt option.

There is no direct and straightforward metric for mea-

suring/assessing the effectiveness of an alternative decision.

It is usually judged indirectly through a set of parameters

called decision making attributes/criteria. The efficacy of a

decision is evaluated through a set of n-attributes. Therefore,

the decision alternatives in a MCDM process may be

regarded as vectors in a real n-dimensional criteria space

where each alternative decision vector is characterised by its

S. Gupta (&) � A. RahberDepartment of Mining Engineering, Indian Institute

of Technology (BHU), Varanasi 221005, India

e-mail: [email protected]

A. Ahmadi � U. Kumar

Division of Operation, Maintenance and Acoustics,

Lulea University of Technology, 97187 Lulea, Sweden

123

Int J Syst Assur Eng Manag (July-Sept 2013) 4(3):249–261

DOI 10.1007/s13198-013-0187-0

Author's personal copy

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direction and magnitude. The evaluation attributes may be

clustered into two groups based on their performance. Some

criteria may be of the benefit type, meaning that the larger

values are preferable to the lower values, while the lesser

values are more preferable than the higher for the cost type

criteria. The influences of these two groups are conflicting in

nature. Conflict management is the core of any MCDM

problem.

These two groups of criteria may be divided into sub-

groups, etc. This gives a list of criteria that influence the

decision to varying degrees. The importance of each cri-

terion may be assessed through a suitable technique like the

analytic hierarchy process (AHP). In MCDM, the alterna-

tives are assessed and compared with each other.

This paper proposes an adapted technique for order

preference by similarity to ideal solution (TOPSIS) meth-

odology which combines both the magnitude and the

direction of a decision vector in the assessment process.

The similarity and dissimilarity of the vector alternatives

are measured by agreement/disagreement in magnitude and

direction. A case study has been performed to illustrate the

use of the proposed methodology for the selection of an apt

maintenance strategy for dump truck components.

The rest of the article is organized as follows. Section 2

describes the AHP, which is used for assessing the relative

importance of different criteria. Section 3 introduces TOP-

SIS as a decision making methodology, while Sect. 4

examines its limitations. In Sect. 5 the proposed adapted

TOPSIS methodology is described. The proposed method-

ology is illustrated through a case study in Sect. 6, which

includes sub-sections on data collection and the development

of the maintenance selection criteria. Section 7 ends the

paper with a discussion and a presentation of conclusions.

2 The analytic hierarchy process (AHP) for assessing

the relative importance of different criteria

The AHP (Saaty 1980) helps the analyst to organize the

critical aspects of a problem into a hierarchical structure.

The method is very popular and interested readers may

refer (Saaty 1980;Gupta and Kumar 2012; Kumar et al.

2010) for details. The salient points of the AHP are as

follows:

The AHP employs pair-wise comparison in which

experts compare the importance of two factors on a rela-

tively subjective scale. These pair-wise comparisons are

carried out for all the attributes using a scale of absolute

judgments that represents ‘how much more’ one element

dominates another with respect to a given attribute. The

number of attributes is limited to seven on a level, fol-

lowing the concepts espoused by Miller (1956) for the

limits of human information processing capacity. The

judgment matrix A ¼ aij� �

of importance is built according

to the relative importance given by the experts. The

weighted mean value of aij for a group response is:

aij ¼Ynk¼1

wk � akij !1=wk

ð1Þ

where akij is the k-th expert’s paired comparison value, n is

the number of experts, and wk is the weight of the k-th

expert. In this study, it was assumed that all the experts had

equal expertise in their judgments and therefore wk ¼ 18k.Since human judgments are the basis of the AHP, some

degree of inconsistency may be introduced due to a lack of

adequate information, improper conceptualization, and

mental fatigue. Therefore, one needs to measure the con-

sistency of judgments, which is accomplished by calcu-

lating the consistency ratio (CR), i.e. by comparing the

consistency index (CI ¼ kmax�nn�1

, where kmax is the largest

Eigen value of the n 9 n pair-wise comparison matrix) in

relation to random index (RI). The judgments can be

considered acceptable if and only if the consistency ratio

(CR ¼ CIRI) is less than 0.1. If the CR is much in excess of

0.1, the judgments are untrustworthy, as they are too close

for comfort to randomness and the exercise is worthless or

must be repeated.

3 Decision making through TOPSIS

Multi-criteria decision making (MCDM) is used to select

an alternative from several alternatives according to vari-

ous criteria. The feasible set of alternatives may be regar-

ded as an array of n-dimensional vectors, when n is the

number of decision criteria. Each alternative is a point in n-

dimensional real space. Hwang and Yoon (1981) first

developed the TOPSIS to help the decision maker in

complex situations arising out of multiple criteria and

multiple perspectives. The TOPSIS approach is based on

the idea that the chosen alternative should have the shortest

distance from the positive ideal solution (PIS) and the

farthest from the negative ideal solution (NIS). The aim of

TOPSIS is to find the best values of the alternatives for the

PIS when the NIS is the minimal benefit solution and

incorporates all the worst values of the alternatives. Sub-

sequently the alternatives are ranked with respect to their

relative closeness to the ideal solutions. The calculation

procedure of TOPSIS is as follows.

3.1 Normalize the appraisal matrix

Experts assess different criteria in different units and use

different scales according to their individual perception and

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subjective estimation. The basic prerequisite for compari-

son and aggregation or applying other mathematical oper-

ations on the collected appraisal data is the transformation

of different incommensurable criteria into common unit-

less functions. A normalization process transforms differ-

ent incommensurable criteria into n-dimensional criteria to

allow mathematical relations and operations. This sets their

values in the closed interval [0, 1]. Assume that xij is an

element of the appraisal matrix D ¼ xij� �

for the value of

the i-th appraisal criterion function of alternative Aj. xijindicates the rating of alternative Aj with respect to crite-

rion i. The element rij of the normalized appraisal matrix R

is usually calculated by the vector normalization method as

was originally proposed by Hwang and Yoon (1981) in

TOPSIS. Observing its unit dependence (Opricovic and

Tzeng 2004) and following Lai et al. (1994) and Ahmadi

et al. (2010), linear normalization has been vouched for

concerning sovereignty and the elimination of a scaling and

unit effect as given below:

rij ¼ xij � x�ixþi � x�i

for benifit criterion and

rij ¼ xþi � xij

xþi � x�ifor cost criterion

ð2Þ

where, i ¼ 1; 2; 3; . . .; n and j ¼ 1; 2; 3; . . .;m and xþiand x�i are the maximum and the minimum values of the i-

th criterion function for all the alternatives, respectively.

3.2 Construct the weighted normalized appraisal

matrix

All the appraisal criteria may not have an equal impor-

tance, because the different appraisal criteria have various

meanings and influence decisions to different degrees.

Various methods are used to determine importance/

weights, such as the Eigen vector method, weighted least

square method, entropy method, and AHP, as well as linear

programming techniques for multidimensional analysis of

preference (LINMAP). The AHP has been used here to

assess the corresponding weight of the criteria. The

weighted normalized appraisal matrix can be calculated by

multiplying the normalized appraisal matrix ½rij� by the

corresponding weight matrix W ¼ ½wi�. The weighted

normalized appraisal matrix V ¼ ½vij� or decision matrix is

formulated as follows:

vij ¼ rij � wi ð3Þ3.3 Determine the positive and negative ideal solutions

In TOPSIS, n-dimensional vector solution space is boun-

ded by two cardinal points, the PIS Aþð Þ and the NIS A�ð Þ.The PIS Aþð Þ is the most preferable alternative and has the

coordinates of all the best attainable values of the mono-

tonically increasing criterion function, while the NIS A� is

the least preferable alternative and is made up of all the

worst attainable values of the monotonically decreasing

criterion function. These two cardinal points form the basis

for calculating a separation measure. The expressions are

as follows: Aþ ¼ fðMaxjvijji 2 IÞ; ðMinjvijji 2 I0Þji ¼1; 2; 3; . . .; ng ¼ fv�1 ; vþ2 ; . . .v�i ; . . .v�n g—coordinates of the

positive ideal alternative solution in n-dimensional criteria

space. A� ¼ fðMinjvijji 2 IÞ; ðMaxjvijji 2 I0Þji ¼ 1; 2; 3;

. . .; ng ¼ fv�1 ; v�2 ; . . .v�i ; . . .v�n g—coordinates of the nega-

tive ideal alternative solution in n-dimensional criteria

space.

Here I is the set of benefit (max. type) criteria, I0 is theset of cost (min. type) criteria and vþi is the best feasible

value of the i-th criterion function, while v�i is the worst

attainable value of the i-th criterion function.

3.4 Calculate the separation measure

The separation distances of a feasible alternative solution,

Aj, from the PIS Aþð Þ and the NIS A�ð Þ are usually cal-

culated as Euclidean distances of n-criteria from cardinal

points as given below:

Sþj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1

vij � vþi� �2s

; i ¼ 1; 2; 3; . . .N, ð4Þ

S�j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1

vij � v�i� �2s

; i ¼ 1; 2; 3; . . .N: ð5Þ

3.5 Calculate the relative closeness to the ideal solution

The relative closeness of the j-th alternative with respect to

the ideal solution A? is defined as C�j , with the following

being valid: 1�C�j � 0. If alternative j is the PIS, then

C�j ¼ 1; however, if alternative j is the NIS, then C�

j ¼ 0.

In other words, if the value of C�j is closer to 1, the alter-

native j will be closer to the PIS.

C�j ¼ S�j = Sþj þ S�j

� �: ð6Þ

3.6 Rank the priority

A set of alternatives are then ranked according to the

descending order of C�j values.

4 Limitations of TOPSIS

The ranking of alternatives according to the descending

order of C�j values has some limitations, as pointed out by

Opricovic and Tzeng (2004). Referring to Fig. 1, Aþ and

Int J Syst Assur Eng Manag (July-Sept 2013) 4(3):249–261 251

123


A� are the two cardinal points in the feasible solution space

AþPA�Q. The Euclidean distances AþD1 and A�D1 used

as separation measures (Sþj and S�j ) consider only the

magnitude of the vectors. As a result, both the alternatives

Aj and Ak have equal C�j values and possess the same rank

in TOPSIS. The ranking of the alternatives using the rel-

ative closeness value C�j puts all the alternatives on the line

D1AcD2 on the same rank as all C�j ¼ 0:5. Any alternative

in the region E1AcE2D2AcD1E1 (the area hatched in blue)

has C�j [ 0:5 and therefore has a better rank than alterna-

tive Ac, although Ac is comparatively closer to Aþ. Simi-

larly, all the alternatives in the region F1AcF2D2AcD1F1

(the area hatched in red) have C�j \0:5 and therefore pos-

sess an inferior rank than alternative Ac, although they are

comparatively farther from A�.

5 Proposed adapted TOPSIS methodology

Having observed the limitations of the prevailing approach,

a modified approach is proposed here. The proposed

methodology represents all the alternative decisions as n-

dimensional vectors. The included angles between the

alternative decision vectors may be used as measures of

conflict. The closeness of an alternative decision vector to

the cardinal points is influenced by the direction and

magnitude of the separation vectors. Therefore, both of

these parameters will be included in the calculation. The

coordinates of the PIS and NIS are obtained following the

same procedure described in TOPSIS (step 1–3). Now the

cardinal points (PIS and NIS) and all the alternative deci-

sion points are assumed to be on concentric circles with the

origin as the centre. Let the radii of the circles for the

alternative decision points and the PIS be represented as r1and r2, respectively (Fig. 2). The angle between the alter-

native decision vector and the PIS vector is represented by

hþ. The value of hþ is calculated from the co-ordinates of

the cardinal points and the alternative decision points using

the expression given below:

h ¼ cos�1 AþAj

Aþk k Aj

!

¼ cos�1

Pni¼1 v

þi � vijffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i¼1ðvþi Þ2 �Pn

i¼1ðvijÞ2q

0B@

1CA: ð7Þ

The separation measure is estimated as the arc length

r � h, where r is the equivalent mean radius and is esti-

mated as r ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffir1 � r2

p. The use of a geometric mean

normalizes the effect of the range domination of different

attributes and averaging data. This arc length is represented

by SMþðrþ � hþÞ. Similarly, the separation measure from

the NIS is calculated and represented by SM�ðr� � h�Þ.Now the preference index (PI) of the j-th alternative ðS�j Þ iscalculated as:

S�j ¼ SM�j =ðSMþ

j þ SM�j Þ ð8Þ

The values of S�j lie between 0 and 1. The closer the

value of S�j is to 1, the greater is its acceptability. S�j is

calculated as a ratio of separation arc lengths. Arc lengths

are influenced both by the vector magnitude and the

direction. Therefore, PI has a higher sensitivity.

6 Case study

Modern surface mining projects deploy gigantic machines

which involve huge capital investments. A steady pro-

duction assurance is a prerequisite for their economic

sustainability. The production rate is directly influenced by

the health and condition of the equipment, i.e. its func-

tionality and availability. Hence, maintenance plays an

important role for the healthy operation of an industrial

organization, and the maintenance cost represents 15–40 %

of the production cost (Al-Najjar and Alsyouf 2003). The

objective of maintenance is to maximize the utilization of a

component’s life by minimizing the number of failures and

replacements. Attaching insufficient importance to main-

tenance strategies has resulted in low maintenance effi-

ciency in the past (Wang et al. 2007). Moreover, one-third

of the maintenance cost may be saved by discarding

unjustifiable and unnecessary maintenance-related activi-

ties (Mobley 2002 cited by Wang et al. 2007).

Maintenance plays a key role in achieving organiza-

tional goals and objectives. Maintenance management is

E1 D1 F1

E2

AJ

AK

D2 F2

AC

C2

C1

Fig. 1 A two-dimensional representation of Euclidean distances from

PIS and NIS


123


complex and the output of maintenance is hard to measure

and quantify. The maintenance costs are usually high due

to the high costs for restoring equipment, secondary dam-

age and safety/health hazards caused by the failure of

equipment (Yang 2003). Inadequate maintenance can result

in higher levels of unplanned asset failure, which entails

many inherent costs for the organization, including costs

for reworking, labour, loss of production, scrap, etc.

(Moore and Starr 2006).

Different types of maintenance policy have been

developed. The selection of an apt maintenance policy is

important in reducing equipment maintenance cost and

downtime, improving quality and increasing productivity.

A large number of maintenance types, such as reactive,

predictive, preventive, pro-active, total-productive, design-

out and opportunistic maintenance, are practised in indus-

try. A number of factors, such as the type of component, its

importance, the stock cost, the availability of spares, etc.,

influence maintenance. Each type of maintenance has its

own advantages and disadvantages, as well as applicability

and effectiveness criteria. The selection of a suitable

maintenance policy needs detailed examination of the

effectiveness of alternative maintenance types.

The selection of a maintenance strategy depends on a

large number of factors/attributes and many reported

research studies, such as a study by Triantaphyllou et al.

(1997), support the use of MCDM. The effects of these

attributes are to be critically analyzed before selecting any

type of maintenance. These attributes may be tangible or

intangible and influence maintenance decisions to different

degrees.

The choice of the right set of criteria plays an important

role in the decision making process. This involves experts

from various functional activities in the organization. The

effectiveness of a maintenance policy is appraised mainly

according to two types of criteria: (1) a set of criteria that

can measure the value added to the assets by practising the

maintenance policy concerned, i.e. the benefit criteria, and

(2) a set of criteria that evaluates the price/cost of the

maintenance policy in question, i.e. the burden or the cost

criteria. The benefit appraisal attributes are mainly a

reduction in the maintenance downtime, an increase in the

maintenance deferral, an increase in the life of the unit,

etc., while the various maintenance cost heads are the

burden appraisal attributes. Hence, the selection of a

maintenance policy is a MCDM process.

The dump truck is an important piece of equipment in

surface mines. This type of machinery meets with frequent

breakdowns, predominantly due to rough road conditions

and a harsh environment. The maintenance of dump trucks

constitutes a lion’s share of the maintenance cost in surface

mines. The design of an apt maintenance policy for dump

r1

r 2

r

Positive Ideal Solution point

Solution by one of the alternative decision point

n-dimensional coordinate system

θ

Rθ = S1

Fig. 2 Graphical representation

of separation distances


123


trucks is very important. Maintenance policies differ from

component to component depending on their functionality,

cost, criticality, importance, working environment, etc.

This case study aims at the design of maintenance for the

three most critical components, i.e. the engine, tyre, and

transmission. The case study was conducted in a large

surface coal mine in India. This mine deployed a large fleet

of dump trucks of different capacities, varying from 85 to

120 t and manufactured by Terex, Caterpillar, Hulpack,

Komatsu and BEML.

The mine had three maintenance workshops, namely a

base workshop, a field workshop and a mine workshop.

The mine workshop dealt with small repair jobs near the

mine itself, while the field workshop took care of the more

critical problems and was involved only if it was not

possible to deal with the fault in the mine workshop. The

base workshop was mainly involved in supplying spares,

carrying out repairs and keeping stocks of equipment. A

survey was conducted and information was gathered

regarding the various types of maintenance techniques

applied in the main workshop. It was found that 4 main

types of maintenance strategies were implemented in the

main base workshop. These were as follows:-

(a) Corrective maintenance This can be defined as the

maintenance which is required when an item has

failed or is worn out, to bring it back to working

order. Corrective maintenance is the most commonly

used maintenance approach, but it has associated

demerits. Sudden equipment failures lead to excessive

downtime, affecting production and occasionally

damaging other parts. In most cases, this is expensive.

When a component needs replacement, the cost of the

replacement alone is substantial. Corrective mainte-

nance also leads to low availability figures and is

usually carried out on items for which the conse-

quences of failure or wearing out are not significant

(less important items).

(b) Periodic maintenance This is also known as sched-

uled maintenance. It has a fixed cost and is carried out

following the designer’s or manufacturer’s recom-

mendations. Here significant activities are carried out

regularly (following a certain predetermined sche-

dule) to maintain the condition or operational status

of a piece of equipment, machine, plant, or system.

(c) Preventive maintenance Preventive maintenance

actions are performed according to a clock-time-

based or machine-run-based schedule. They detect,

preclude, or mitigate the degradation of a component

or system with the aim of sustaining or extending its

useful life through controlling the degradation to an

acceptable level. While preventive maintenance is not

the optimum maintenance programme, it does have

several advantages over a purely reactive programme.

Practising preventive maintenance helps to extend the

life of the equipment and bring it closer to the

designed life. Preventive maintenance will generally

make the equipment run more efficiently. Although

catastrophic equipment failures cannot be averted, the

failure frequency may decrease through well-defined

preventive maintenance. Minimizing failures trans-

lates into maintenance and capital cost savings. The

major advantages of this type of maintenance strategy

are that it is cost-effective in many capital-intensive

processes, that its flexibility allows an adjustment of

the maintenance periodicity, and that it leads to an

increased component life cycle, energy savings and

reduced equipment or process failure. However, the

process suffers from a number of disadvantages:

catastrophic failures are still likely to occur; the

method is labour-intensive; occasionally it may

include over-maintenance; and there is a potential

risk of incidental damage to components in carrying

out the maintenance.

(d) Pro-active maintenance This is basically a type of

approach or attitude, rather than a technique. Pro-active

maintenance is the cheapest strategy of all and is based

on experience. With this strategy, if a particular type of

problem is encountered in a component/piece of

equipment, then as a preventive measure, all similar

components/equipment are upgraded.

6.1 Data collection

Failure and maintenance information on dump trucks was

collected from the field and classified as shown in Table 1.

Here one can observe that the engine, tyres and transmis-

sion are the most critical components of the dump trucks,

as they needed more maintenance hours and hence required

most attention. These three components have been con-

sidered for further study.

6.2 Development of the hierarchical structure

of the maintenance selection criteria

Structuring the problem into a hierarchy serves two pur-

poses. First it provides an overall view of the complex

relationship between the variables inherent in the problem,

and second, it helps the decision maker in making judg-

ments concerning the comparison of elements that are

homogenous and on the same level of the decision hier-

archy (Arunraj and Maiti 2010). The performance of a

maintenance strategy is reflected by various indicators

called decision attributes. The choice of these attributes

and sub-attributes affects the type of maintenance policy


123


adopted. The factors considered in this study were selected

in due consultation with the field experts of the case study

and are described below (Fig. 3).

6.2.1 Production

It is always desirable that the maintenance of any compo-

nent should have the least possible effect on the production

capacity. The target level of incessant production is man-

datory for the economic sustainability of any project. This

is mainly a reflection of the criticality of the component.

The failure of a critical component of any equipment may

lead to high downtime and must be avoided. Consequently,

the effect of failure of the component on production is of

the utmost importance for production equipment and

should be given due weightage when selecting a mainte-

nance policy. This issue takes into account continuous

output and high quality (the desired level of production in

conformance with the acceptable standards). Both factors

are important from the point of view of market demand and

the reputation of the firm, and hence should be focused

upon.

6.2.2 Feasibility

The feasibility or acceptability of a maintenance strategy is

one of the important criteria to be considered. This includes

the acceptability of a particular maintenance policy by

Table 1 Failure and maintenance information for various components of the dump trucks during the study period

Sl.

no.

Names of

system parts

Frequency of

maintenance

Total hours of

maintenance

Average

maintenance time

Minimum maintenance

time (h)

Maximum maintenance

time (h)

1 Tyre 218 3,965 18 2 160

2 Engine 20 3,090 154 16 1,106

3 Transmission 8 2,777 347 76 2,698

4 Hub seal 3 2,418 806 141 1,307

5 Hy-o-ring/tube/

valve

61 2,300 37 2 216

6 Suspension 41 1,950 47 7 191

7 Nose cone

bearing

1 1,848 1,848 Not available 1,848

8 NTL 255 1,749 7 2 Not available

9 Drive shaft/

spider

2 1,516 758 28 1,488

10 Linings 19 1,397 73 4 720

11 Coolant pump 9 1,035 115 30 104

12 Electrical circuit 32 957 29 10 159

13 Hyd-T/M hoses 14 628 45 Not available Not available

14 Battery 7 611 87 10 308

15 Hoist cylinder 3 527 175 130 249

16 Horn 79 504 6 2 Not available

17 Air ckt piping/

valves

59 504 8 2 216

18 Fan pulley/

bearing

4 313 78 14 205

19 Str/orbitrol

valve

2 222 111 28 194

20 Chassis 6 214 35 6 114

21 Coolant hoses 10 213 21 10 306

22 Air compressor 4 207 51 24 79

23 Tie rod/bushing 9 206 22 8 80

24 Tank mountings 7 195 27 5 71

25 Radiator 1 168 168 168 168

26 Steering hyd

pump

1 156 156 156 156

27 Dump body pin/

lock

7 152 21 4 46


123


work groups, especially the maintenance personnel. Any

maintenance policy can be implemented only if the per-

sonnel are interested in practising it. This can also be called

the ease with which the policy can be adopted and prac-

tised. It is a natural human tendency to continue practices

in which one is well-versed, and hence the more primitive

maintenance practices are much more preferred than the

newer ones.

6.2.3 Safety and reliability

Safety plays a vital role in choosing the type of mainte-

nance policy to be used. For any organization, the safety of

its personnel and its equipment and installations is of great

importance, and therefore the chosen maintenance strategy

should ensure a high level of safety to avoid any hazardous

incidents. If the failure of a particular component may

cause a severe accident and fatal injury, every attempt

should be made to avoid such a situation and that should be

reflected in the maintenance policy. The adopted mainte-

nance policy must be well tested and reliable enough.

6.2.4 Maintenance opportunity

Certain maintenance practices require special equipment

and facilities that should be ensured beforehand before

adopting these policies. Sometimes the maintenance work

load may justify the installation of costly facilities.

6.2.5 Time delay

It is desirable that all the equipment should have the

minimum downtime. Each maintenance type has a pattern

and some fixed steps to be followed. The time taken to

carry out any type of maintenance depends not only on

these steps, but also on the availability of maintenance

facilities, the designed maintainability of the equipment

concerned, the crew and materials, the total delay due to

Ease of implementation

Maintenance effectiveness

Direct-criteria (Benefit )

Inverse-criteria (Cost)

Maintenance characteristics

Cost of maintenance

Time delay

Production

Feasibility

Safety & reliability

Maintenance opportunity

Production regularity

Production quality

Acceptability of technique

Safety of facilities & personnel

Reliability of the procedure

Fleet of equipment

Facility available

Duration of maintenance

Logistic delay

Administrative delay

Delay in fault identification

Frequency of maintenance

Cost of manpower

Cost of mater ial

Corrective maintenance

Periodic maintenance

Preventive maintenance

Pro-active maintenance

Decision goal 1st

level criteria 2nd

level criteria 3rd

level criteriaMaintenance alternatives

Fig. 3 List of alternatives and hierarchy diagram of evaluating criteria


123


administrative reasons, logistic delays, and other reasons

connected with the procurement of the required spare parts.

It is always desirable to reduce these delays to a minimum

and the maintenance type that allows the minimum

downtime is the most favourable one and is to be preferred.

6.2.6 Maintenance characteristics

This attribute includes the maintenance and failure pattern

of a component. If a component bears a huge load or

rotates at a high speed, there is a risk of it being deterio-

rated by friction at a high rate. Such components are more

exposed to the risk of failure than others and should

therefore be more critically dealt with. These components

require frequent maintenance to be performed more than

other components. Similarly, the increased duration of the

maintenance has an adverse effect on the equipment

availability and the system production figures.

6.2.7 Cost of maintenance

The cost of each maintenance type includes the expenses

incurred in the basic setup required for the implementation

of any maintenance type, which include the cost of the

hardware, software, material and labour required for the

maintenance. If the maintenance of a particular component

is very costly, then it is always desirable to avoid its failure.

Hence it is desired that such components should be main-

tained before they undergo any failure. Preventive main-

tenance may help in saving time, money and production

losses in this case.

The first four criteria were grouped under the category

‘‘direct criteria’’ and the remaining three under ‘‘inverse

criteria’’. The relative importance of these criteria was

assessed, the one over the other, with the help of the AHP.

To estimate the relative importance of the various criteria

using the AHP, the problem was transformed into a deci-

sion hierarchical structure (Fig. 3) where the goal of the

decision was placed on the top of the tree, and then the

decision criteria were placed on successive levels, starting

from a broad perspective and continuing through the

intermediate levels (criteria on which subsequent sub-cri-

teria depend) to the lowest level (which is usually the set of

alternatives).

6.3 Collection of the judgments from experts

To construct the pair-wise comparison matrix, a question-

naire was prepared and distributed to three field experts of

the case study mine to collect their opinions and percep-

tions. These questionnaires concerned the pair-wise com-

parison of the attributes and the sub-attributes on each level

of hierarchy. The relative importance of all the attributes of

each level was calculated on the basis of the experts’

responses to the above questionnaire.

For pair-wise comparison between the two criteria on

the first level of the hierarchy diagram, i.e. benefit (direct

criteria) and total cost (inverse criteria), the following

question was asked:

6.3.1 Question A

‘‘To select the most effective maintenance policy for the

proposed unit, whose failure affects the normal operation

of the dump truck, we have identified two main criteria: (1)

the benefit that the selected maintenance policy creates and

(2) the total cost under the specific maintenance policy. In

your opinion, with respect to the overall goal, ‘selection of

the most effective maintenance policy’, which of these two

criteria is of greater importance (or priority) in the selec-

tion of a maintenance policy according to the following

scale of importance?’’

Likewise, a pair-wise comparison was made between the

criteria on the second and third levels of the evaluating

criteria. For example, for pair-wise comparison among the

four criteria of benefit on the second level, the following

question was asked:

6.3.2 Question B

‘‘The relevant factors defining the criteria of benefit are

identified as the contribution to production, feasibility,

safety and reliability and maintenance opportunity. In your

opinion, with respect to 1st level criterion 1, benefit, how

important is 2nd level criterion 1 (production) when com-

pared with 2nd level criterion 2 (feasibility)?’’ The ques-

tion was repeated, after adaptation, for the other attributes.

To assess the efficacy of each maintenance policy,

another set of questionnaires was prepared and distributed

to the field experts of the case study mine to collect their

opinions and perceptions concerning the extent to which

each maintenance policy, when implemented, would be

effective in achieving the target level of the decision

attributes.

The feedback and responses collected from the field

experts were analyzed to decide the importance of each

attribute for the decision. Table 2 gives the calculated

weight of the attributes of different levels obtained from

the responses of Expert 1, with the values of kmax, CI, RI

and CR. It shows that Expert 1 is quite consistent in his

judgment, as is evident from the CR values. The average

importance values for all the attributes, calculated from the

aggregated judgment matrix of all the experts, are pre-

sented in Table 3.


123


Table 2 AHP judgment matrix given by Expert 1 with calculated importance values and consistency measures

Production

regularity

Production

quality

Weight of criteria kmax CI RI CR

Total Net

Production

regularity

1 0.5 0.333333 0.115406 2 0 0 0

Production quality 2 1 0.666667 0.230812

Acceptability of technique Ease of implementation Weight of criteria kmax CI RI CR

Total Net

Acceptability of technique 1 3 0.75 0.091548 2 0 0 0

Ease of implementation 0.333333 1 0.25 0.030516

Safety of facilities and personnel Reliability of the procedure Weight of criteria kmax CI RI CR

Total Net

Safety of facilities and personnel 1 0.111111 0.1 0.034622 2 0 0 0

Reliability of the procedure 9 1 0.9 0.311596

Fleet of equipment Facility availability Weight of criteria kmax CI RI CR

Total Net

Fleet of equipment 1 0.5 0.333333 0.014214 2 0 0 0

Facility availability 2 1 0.666667 0.028429

Delay in fault identification Administrative

delay

Logistic

delay


Total Net

Delay in fault identification 1 0.5 2 0.265152 0.026178 3.114286 0.057143 0.58 0.098522

Administrative delay 2 1 5 0.606061 0.059835

Logistic delay 0.5 0.2 1 0.128788 0.012715

Frequency of maintenance Duration of maintenance Weight of criteria kmax CI RI CR

Total Net

Frequency of maintenance 1 7 0.875 0.025524 2 0 0 0

Duration of maintenance 0.142857 1 0.125 0.003646

Cost of manpower Cost of material Weight of criteria kmax CI RI CR

Total Net

Cost of manpower 1 0.25 0.2 0.002992 2 0 0 0

Cost of material 4 1 0.8 0.011967

Production Feasibility Safety and reliability Maintenance

opportunity


Total Net

Production 1 3 1 8 0.403921 0.346218 4.04304 0.014347 0.9 0.015941

Feasibility 0.333333 1 0.25 3 0.142408 0.122064

Safety and reliability 1 4 1 7 0.403921 0.346218

Maintenance opportunity 0.125 0.333333 0.142857 1 0.04975 0.042643

Time delay Maintenance

characteristics

Cost of

maintenance


Total Net

Time delay 1 4 6 0.691099 0.098728 3.090909 0.045455 0.58 0.07837

Maintenance characteristics 0.25 1 2 0.204188 0.02917

Cost of maintenance 0.166667 0.5 1 0.104712 0.014959


123


The results show that procedural reliability has the

highest importance, followed by production regularity and

maintenance frequency. Therefore, the chosen maintenance

policy must be reliable enough and assure a continuous

production which reaches the target amount and quality

level with a smaller number of failures.

6.4 Ranking of the alternative maintenance strategies

In order to collect the data required to rank the alternatives,

a second set of questionnaires was developed. The purpose

was to collect engineering judgments regarding the capa-

bility of each maintenance alternative to realize the ideal

level of each evaluating criterion. For example, to identify

the ability of the maintenance alternatives to enhance the

‘‘production regularity’’, the following question was asked:

6.4.1 Question C

‘‘What score (0–100) do you assign to each maintenance

policy with respect to the criterion ‘production irregulari-

ties’?’’ The question inquires about the extent to which the

alternative is capable of enhancing the production irregu-

larity. If it is capable of eliminating production irregulari-

ties completely, a score of 100 will be assigned, and if it is

unable to contribute to any reduction, a score of ‘‘0’’ will

be assigned. If the expert is not sure about a specific score,

he can assign his judgments as a range, e.g. 65–80. The

results of various calculations in different steps of TOPSIS

and the proposed new method are shown in Table 4, along

with the judgments obtained from the experts.

The results of the MCDM for selection of the best

maintenance type for the engine, transmission and tyres of

a dump truck using TOPSIS and the modified TOPSIS are

presented in Table 5 below.

7 Discussion and conclusions

This type of study can help management to analyze dif-

ferent maintenance types for the optimization of trade-offs

between cost and benefit. In the case study mine, the

management presently implements preventive mainte-

nance for the engine (the most critical part), pro-active

maintenance for the transmission and corrective mainte-

nance for the tyres. An analysis of the collected decision

responses from the field experts using the TOPSIS

method suggests that the present maintenance practices

for the engine should be continued, whereas the proposed

new method suggests a change to periodic maintenance

for the engine. The proposed method suggests that one

should stick to the present pro-active maintenance for the

transmission and the present corrective maintenance for

the tyres. However, an analysis with the TOPSIS method

favours an alteration of the present maintenance practices

to preventive maintenance for the transmission and pro-

active maintenance for the tyres. This analysis provides

the management with scope for revising the present

maintenance practices.

Table 2 continued

Benefit Cost Weight of criteria kmax CI RI CR

Total Net

Benefit 1 6 0.857143 0.857143 2 0 0 0

Cost 0.166667 1 0.142857 0.142857

Table 3 Calculated aggregated weights of the attributes from the

opinions of three experts

Attributes Aggregated weight

Production regularity (PR) 0.081039

Production quality (PQ) 0.185533

Acceptability of technique (AT) 0.05027

Ease of implementation (EI) 0.015224

Safety of facilities and personnel (SFP) 0.021634

Reliability of the procedure (RP) 0.18721

Fleet of equipment (FE) 0.026803

Facility availability (FA) 0.077314

Delay in fault identification (DFI) 0.037972

Administrative delay (AD) 0.021945

Logistic delay (LD) 0.030638

Frequency of maintenance (FM) 0.123367

Duration of maintenance (DM) 0.064491

Cost of manpower (CMP) 0.029589

Cost of material (CM) 0.046969

Production (P) 0.266572

Feasibility (F) 0.065494

Safety and reliability (SR) 0.208844

Maintenance opportunity (MO) 0.104117

Time of delay (TD) 0.090556

Maintenance characteristics (MC) 0.187858

Cost of maintenance (C) 0.076558

Direct criteria (DC) 0.645028

Inverse criteria (IC) 0.354972


123


Table

4Combined

judgmentobtained

from

expertsfortheengineandthecalculationsforTOPSIS

andtheproposednew

method

Alternatives

Attribute

PR

PQ

AT

EI

SFP

RP

FE

FA

DFI

AD

LD

FM

DM

CMP

CM

x ijvalues

Corrective

70

80

85

80

80

85

90

90

75

85

80

70

85

90

75

Periodic

95

95

90

95

95

90

90

95

85

90

100

90

90

80

80

Preventive

100

100

100

100

90

95

80

100

100

100

90

95

95

95

90

Pro-active

80

100

70

95

85

80

95

85

90

75

90

80

80

70

85

r ijvalues

Corrective

0.401974

0.425045

0.488918

0.431018

0.456213

0.484726

0.506089

0.485601

0.426315

0.483157

0.443079

0.415191

0.484726

0.533817

0.453506

Periodic

0.545536

0.504741

0.517678

0.511834

0.541753

0.513239

0.506089

0.512578

0.483157

0.511578

0.553849

0.533817

0.513239

0.474504

0.483739

Preventive

0.574248

0.531306

0.575197

0.538772

0.513239

0.541753

0.449857

0.539556

0.56842

0.56842

0.498464

0.563473

0.541753

0.563473

0.544207

Pro-active

0.459399

0.531306

0.402638

0.511834

0.484726

0.456213

0.534205

0.458623

0.511578

0.426315

0.498464

0.474504

0.456213

0.415191

0.513973

v ijvalues

Corrective

0.020161

0.048771

0.014886

0.003978

0.006729

0.061735

0.009376

0.025925

0.011853

0.007728

0.005994

0.019844

0.012119

0.008782

0.011838

Periodic

0.027362

0.057915

0.015761

0.004724

0.00799

0.065367

0.009376

0.027365

0.013434

0.008183

0.007492

0.025514

0.012832

0.007806

0.012627

Preventive

0.028802

0.060964

0.017513

0.004973

0.00757

0.068998

0.008334

0.028805

0.015804

0.009092

0.006743

0.026931

0.013545

0.00927

0.014205

Pro-active

0.023042

0.060964

0.012259

0.004724

0.007149

0.058104

0.009897

0.024485

0.014224

0.006819

0.006743

0.022679

0.011406

0.00683

0.013416

Aþ

0.028802

0.060964

0.017513

0.004973

0.00799

0.068998

0.009897

0.028805

0.011853

0.006819

0.005994

0.019844

0.011406

0.00683

0.011838

A�

0.020161

0.048771

0.012259

0.003978

0.006729

0.058104

0.008334

0.024485

0.015804

0.009092

0.007492

0.026931

0.013545

0.00927

0.014205

Sþ j

S� j

C� i

coshþ

hþcosh�

h�rþ

r�SM

þSM

�S� i

Corrective

0.017299

0.010053

0.367543

0.995719

0.092566

0.994144

0.108272

0.099957

0.092897

0.009253

0.010058

0.520855

Periodic

0.008508

0.015021

0.6384

0.997229

0.07446

0.995135

0.098681

0.105924

0.098442

0.007887

0.009714

0.551905

Preventive

0.009503

0.019762

0.675269

0.996519

0.083461

0.995776

0.091948

0.108915

0.101222

0.00909

0.009307

0.505896

Pro-active

0.014684

0.014057

0.489085

0.993643

0.112821

0.990956

0.134594

0.102832

0.095569

0.011602

0.012863

0.525779

Bold

values

indicatethenearest

to1andthesuggestalternative


123


The proposed new approach adequately addresses the

concern about the ranking of alternatives solely on the

basis of Euclidean distances. The modification regarding

the separation measure will strengthen the comprehen-

siveness and reasonableness of the ranking order for

alternatives, and hence the decision making process will be

enhanced by implementing the proposed new method.

Maintenance practices of any mining equipment like

shovels, drills, draglines, dozers, etc. can be analysed

though the proposed model. The application domain of the

model can be extended through modification of the attri-

bute lists. This may prove to be an effective tool in conflict

management in MCDM.

References

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Table 5 Comparison of the decision results obtained using TOPSIS

and the proposed modified approach

Selection tool Component

Engine Transmission Tyres

TOPSIS Preventive Preventive Pro-active

Proposed method Periodic Pro-active Corrective

Present practice Preventive Pro-active Corrective


123


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