Morobe Mining Joint Venture (MMJV) is developing the Hidden
Valley mine and the mine is considering several suppliers 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 develops 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
that supplier X is “ equally to strongly
preferred ” to supplier Z, but supplier Z is “equally to very strongly
preferred” 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 prioritized 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 synthetization is done by
adding cost pairwise comparison 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 preferences for each criterion. For
example, 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 comparisons 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 preference 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 summarizing 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
|
|
Y-UWM
|
0.237541
|
Y-UWM
|
0.3505
|
|
Z-Hasting
Deering
|
0.350507
|
Z-Hasting
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 prioritize the criteria, and examine strengths and
weaknesses of different suppliers.
