Contractors play an important role in any construction project. Perhaps the most important decision is the selection of contractor by the employer prior to the implementation of the project. AHP is one of the main mathematical models currently available to support the decision theory, particularly for construction contractor prequalification.

1. Nam N. N. Tran
ANALYTIC HIERARCHY PROCESS
(AHP)
#makingdecision #portfoliomanagement

2. WHAT IS
ANALYTIC HIERARCHY PROCESS
(AHP)
Is an effective tool for dealing with
complex Multi Criteria decision
making, and may aid the decision
maker to set priorities and make
the best decision
Thomas Saaty
(introduced in 1970s)

3. 05
Objective: Selectinga contractor
Criteria: Financial,Strategy,Urgency, Stakeholder commitment.
Alternatives: HYU,XYTech,ABCons.
AHP algorithm is basically composed
of two steps:
1. Determine the relative
weights of the decision criteria
2. Determine the relative
rankings (priorities) of alternatives
Ex: ABCONS ?
FINANCIAL
STRATEGY
URGENCY
STAKEHOLDER COMMITMENT
WHAT IS
ANALYTIC HIERARCHY PROCESS
(AHP)

4. HIERARCHY TREE
06
Selectingacontractor
Financial Strategy Urgency Stakeholder commitment
HYU XYTech ABCons

5. RANKING SCALE
07
FORCRITERIAANDALTERNATIVES
Scale Num Rating Reciprocal
Extremely Preferred 9 1/9
Very strong to extremely 8 1/8
Very strongly preferred 7 1/7
Strongly to very strongly 6 1/6
Strongly preferred 5 1/5
Moderately to strongly 4 1/4
Moderately preferred 3 1/3
Equally to moderately 2 1/2
Equally preferred 1 1
Saaty'sScaleofRelativeImportance(Saaty,2005)

6. RANKING OF CRITERIA
08
CRITERIA Financial Strategy Urgency Commitment
Financial 1 1/5 3 4
Strategy 5 1 9 7
Urgency 1/3 1/9 1 2
Commitment 1/4 1/7 1/2 1
S 6.5833 1.4540 13.5 14
CRITERIA Financial Strategy Urgency Commitment
Financial 0.1519 0.1375 0.2222 0.2857
Strategy 0.7595 0.6878 0.6667 0.5000
Urgency 0.0506 0.0764 0.0741 0.1429
Commitment 0.0380 0.0983 0.0370 0.0714
1.000

7. CHECKING FOR CONSISTENCY
09
- AHP evaluations are based on the aasumption that the
decision maker is rational, i.e., if A is preferred to B and B is
preferred to C, then A is preferred to C.
- If the CR is greater than 0.1 the judgments are untrustworthy
because they are too close for comfort to randomness and the
exercise is valueless or must be repeated
The next stage is to calculate a Consistency Ratio (CR) to
measure how consistent the judgments have been relative to
large samples of purely random judgments.

8. CALCULATION OF CONSISTENCY RATIO
09
Consider [Ax = lmaxx] where:
- A is the comparison matrix of size n n, for n criteria, also called the priority
matrix.
- x is the Eigenvector of size n 1, also called the priority vector.
- lmax is the Eigenvalue.
1 1 5 3 4
5 1 9 7
1 3 1 9 1 2
1 4 1 7 1 2 1
0.1993
0.6535
0.0860
0.0612
=
0.8329
2.8524
0.3474
0.2474
𝐶𝑉 =
0.8329
2.8524
0.3474
0.2474
÷
0.1993
0.6535
0.0860
0.0612
=
4.1786
4.3648
4.0401
4.0422

9. CALCULATION OF CONSISTENCY RATIO
09
𝜆max =
4.1786 + 4.3648 + 4.0401 + 4.0422
4
= 4.1564
Consistency index, CI is found by
𝐶. 𝐼 =
𝜆max − 𝑛
𝑛 − 1
=
4.1564 − 4
4 − 1
= 0.0521
Eigenvalue:
C.R. = C.I./R.I. where R.I. is the random index
n 1 2 3 4 5 6 7
R.I. 0 0 .5 .9 1.11 1.25 1.35
-> R.I = 0.9 (n=4, from table)
𝐶. 𝑅 =
𝐶. 𝐼
𝑅. 𝐼
=
0.0521
0.90
= 0.0579 < 0.1
C.R. ≤ 0.1 indicates sufficient consistency for decision

10. RANKING OF PRIORITIES
09
To find the ranking of priorities, namely the Eigen Vector X:
1) Normalize the column entries by dividing each entry by the sum of the
column.
2) Take the overall row averages.
𝐶𝑜𝑚 𝐹𝑖𝑛 𝑆𝑡𝑟𝑎 𝑈𝑟𝑔 𝐶𝑜𝑚𝑚
𝐻𝑌𝑈 0.5012 0.2819 0.1790 0.1561
𝑋𝑌 0.1185 0.0598 0.6850 0.6196
𝐴𝐵 0.3803 0.6583 0.1360 0.2243

11. SORTING DECISION
09
𝐶𝑟𝑒
𝐶𝑜𝑚𝑝𝑎𝑛𝑦 𝐹𝑖𝑛 𝑆𝑡𝑟𝑎 𝑈𝑟𝑔 𝐶𝑜𝑚𝑚 𝑭𝒊𝒏 0.1993
𝐻𝑌𝑈 0.5012 0.2819 0.1790 0.1561 𝑺𝒕𝒓𝒂 0.6535
𝑋𝑌 0.1185 0.0598 0.6850 0.6196 𝑼𝒓𝒈 0.0860
𝐴𝐵 0.3803 0.6583 0.1360 0.2243 𝑪𝒐𝒎𝒎 0.0612
𝐴 = 0.1993 × 0.5012 + 0.6535 × 0.2819 + 0.0860 × 0.1790 + 0.0612 × 0.1561 = 0.3091
𝐵 = 0.1993 × 0.1185 + 0.6535 × 0.0598 + 0.0860 × 0.6850 + 0.0612 × 0.6196 = 0.1595
𝐶 = 0.1993 × 0.3803 + 0.6535 × 0.6583 + 0.0860 × 0.1360 + 0.0612 × 0.2243 = 0.5314

12. THANKS FOR WATCHING THIS PRESENTATION
Nam N. N. Tran
ANALYTIC HIERARCHY PROCESS
(AHP)