Mining Equipment Supplier Selection - Mine Management Questions and Answers Series (7)

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.