Morobe Mining Joint Venture (MMJV) is developing the Hiddem
Valley mine and the mine is considering several supplieirs of machinery and
equipment and continual service at the mine site. From experience and data
available, the premier suppliers are Caterpillar, UWM Machinery and Hasting Deering.
The manager identified the criterion for selecting the best service providers
are based on cost, product quality, productivity and life/durability. The
manager developes the following pairwise comparison matrices for each of the
three four criteria.
X = CAT,Y= UWM,Z=Hastings Deering.
Cost

P/Quality

Productivity

Life/Durability


X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z


X

1

2

5

X

1

0.25

0.2

X

1

5

4

X

1

0.143

0.2

Y

0.5

1

7

Y

4

1

0.125

Y

0.2

1

3

Y

7

1

0.125

Z

0.2

0.1429

1

Z

5

8

1

Z

0.25

0.333

1

Z

5

8

1

From the above table, the cost matrix shows
thatsupplier X is “ equally to strongly
preferred ” to supplier Z, but supplier Z is “equally to very strongly
perferred” to supplier Y. Diagonally, it is equally preferred as it has the
value of 1 which indicates one supplier is compared to itself.
The suppliers are prioritised within each
criterion. For example, the manager intend to know which is the most preferred
supplier, the second, third within each
of the four criteria. Mathematically, it is complex but it only employ
approximation method to estimate preference scores. The first step is to sum
the values in each column of pairwise comparison matrix as shown below for cost
matrix(a).
Step 1

(a)

(b)


Cost

Cost


Supplier

X

Y

Z

Supplier

X

Y

Z

Row Average


X

1

2

5

X

0.588

0.6364

0.3846

0.5364


Y

0.5

1

7

Y

0.294

0.3182

0.5385

0.3836


Z

0.2

0.1429

1

Z

0.118

0.0455

0.0769

0.08


Sum

1.7

3.143

13

Sum

1

In (a) the cost synthesization is done by
adding cost pairwise comparision rating matrix. In (b) each column of cost
pairwise comparison rating matrix is divided by the corresponding column sums
(i.e. 0.5/1.7 = 0.294). it is also notice that at (b), each column sums to 1.
Next, the values in each row are averaged as shown on the right hand side of
the table above. Also column sum is 1 for the average values.
Step 2. Compare qualities.
The procedures applied above in cost
comparison matrix is applied to the other comparison criterion and only the
results (row averages) are tabulated for each supplier as given below. The row
averages provide the company with its prefernces for each criterion. For
examlpe, for the cost criterion, supplier
X is most preferred followed by supplier Y and supplier Z.
Supplier

Cost

P/Quality

Productivity

Life/Durability

X

0.5364

0.0927

0.6597

0.0812

Y

0.3836

0.2008

0.2236

0.2474

Z

0.08

0.7065

0.1167

0.6714

Sum

1

1

1

1

The prioritized decision criteria according
to pairwise comparisions are shown below. Note that the corresponding columns
are summed.
Criteria

Cost

P/Quality

Productivity

Life/Durability

Cost

1

0.1667

0.25

0.125

p/Quality

6

1

0.1429

0.1111

Productivity

4

7

1

6

Life/Durability

8

9

0.1667

1

Sum

19

17.167

1.5595

7.2361

The
column values of the above table have been divided by the column sums
correspondingly and then averaged the rows as shown below.
Criteria

Cost

P/Quality

Productivity

Life/Durability

Row Average

Cost

0.05263

0.0097

0.1603

0.0173

0.05998

P /Quality

0.31579

0.0583

0.0916

0.0154

0.12025

Productivity

0.21053

0.4078

0.6412

0.8292

0.52217

Life/Durability

0.42105

0.5243

0.1069

0.1382

0.2976

Sum

1

The prefereence vector for the criteria
consists of the row averages.
Criteria


Cost

0.05998

P /Quality

0.12025

Productivity

0.52217

Life/Durability

0.2976

It can be clearly seen that the
productivity of machines is the most important criterion with its life/durability
the second in decision making. The overall score for each supplier is obtained
by multiplying the matrix summarising MMJV’s preference for each supplier
criterion which was developed previously by the preference vector for the four
criteria above. This is illustrated in
the table below.
Criteria


Supplier

Cost

P/Quality

Productivity

Life /Durability

Criteria


X

0.5364

0.0927

0.6597

0.0812

Cost

0.05998


Y

0.38359

0.2008

0.2236

0.2474

x

P/Quality

0.12025

Z

0.08001

0.7065

0.1167

0.6714

Productivity

0.52217


Life/Durability

0.2976

Below are the scores each supplier was
rated.
Supplier

Score

Order of score


X CAT

0.411952

X CAT

0.412


YUWM

0.237541

YUWM

0.3505


ZHasting
Deering

0.350507

ZHasting
Deering

0.2375

By seeing the scores above, CAT is the most
preferred supplier of machineries for MMJV. MMJV must be confidence in the
judgements made in pairwise comparisons if MMJV will rely on the result above.
But even if the company doesn’t make its selection based on the analytical
hierarchy process (AHP) result, following this process results in identifying
appropriate and reliable supplier to meet company’s production needs. Hence,
AHP can help identify and prioritse the criteria, and examine strenghts and
weaknesses of different suppliers.
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