AHP as a tool to determine risks to be accounted in the Bidding Price
Dr. Poonam Ahluwalia
MWH India Private Limited
Abstract: Water and Sanitation is a key thrust area in developing nations like India. With inflow of funds
from International bodies such as JICA and World Bank, significant consultancy assignments have been
floated in the past few years. Such projects are under scrutiny by not only pollution control boards, and
the concerned ministries, but also by the media. Several projects in this category have been criticized in
the projects for not achieving/ only partially achieving their goals. As a result for the upcoming projects,
the terms of reference are being made more and more stringent for the consultants. This has increased
the quantum of risks consultancy firms are knowingly taking up. However, all these risks generally are
not accounted for in the quoted cost to competitively quote while bidding for the job. The current paper
discusses how Analytical Hierarchy Process can be used as tool to organizes tangible and intangible
factors in a systematic way, and provides a structured yet relatively simple solution to prioritize the the
risks to competitively bid for projects.
The Analytical Hierarchy Process (AHP) is a decision-aiding method developed by Saaty [1,2]. It aims at
quantifying relative priorities for a given set of alternatives on a ratio scale, based on the judgment of
the decision-maker, and stresses the importance of the intuitive judgments of a decision-maker as well
as the consistency of the comparison of alternatives in the decision-making process . The strength of
this approach is that it organizes tangible and intangible factors in a systematic way, and provides a
structured yet relatively simple solution to the decision-making problems . In addition, by breaking a
problem down in a logical fashion from the large, descending in gradual steps, to the smaller and
smaller, one is able to connect, through simple paired comparison judgments, the small to the large.
The quantum of risks consultancy firms are knowingly taking up in water and wastewater sector is
increasing owing to ambiguous TORs and stringent penalty clauses. Increasing competition is forcing the
bid manager to account for only selected risks to maintain their competitive edge. The current paper
discusses how Analytical Hierarchy Process can be used as tool to organizes tangible and intangible
factors in a systematic way, and provides a structured yet relatively simple solution to the determine
which risks are required to be priced for in the bidding price and which could be excluded.
Schuyler  has stated decision making skill amongst one of most significant skills of project
management , and notices that few of us have had formal training in decision making. Belton 
compared AHP and a simple multi-attribute value (MAV), as two of the multiple criteria approaches. The
study stated that both approaches have been widely used in practice which can be considered as a
measure of success. The greatest weakness of the MAV approach was mentioned as its failure to
incorporate systematic checks on the consistency of judgments. Also for large evaluations, the number
of judgments required by the AHP can be somewhat of a burden. However for fewer evaluations, it is
established as a robust tool for decision making.
The Analytical Hierarchy Process [1, 2]
The process of decision-making involves identification of the objectives, the system components, and
the relations among them. The main theme of the Analytical Hierarchy process is: “Decomposition by
hierarchies and synthesis by finding relations through informed judgment”. Hierarchy is an abstraction
of the structure of a system to study the functional interactions of its components and their impacts on
the entire system. This abstraction of the structure can take several related forms, all of which
essentially descend from an apex (an overall objective), down to sub-objectives, down further to forces
which affect these sub-objectives, down to the objects who influence these forces.
The hierarchical presentation of the system can be used to describe how changes in priority at upper
levels affect the priority of elements in lower levels. But we need to know the potency with which the
various elements in one level influence the elements on the next higher level, so that one may compute
the relative strengths of the impacts of the elements of the lowest level on the overall objectives.
Given the elements of one level, say the 4th
, of a hierarchy and one element, e, of the next higher level,
compare the elements of level 4 pairwise in their strength of influence on e. Insert the agreed upon
numbers, reflecting the comparison, in a matrix and find the eigenvector with the largest eigenvalue.
The eigenvector provides the priority ordering, and the eigenvalue is a measure of the consistency for
The agreed upon numbers art the following, given elements A and B
A and B are equally important, insert 1
A is weakly more important than B, insert 3
A is strongly more important than B, insert 5
A is very strongly more important than B , insert 7
A is absolutely more important than B, insert 9
In the position (A, B) where the row of A meets the column of B.
An element is equally more important when compared with itself, so where the row of A and column of
A meet in position (A,A) insert 1. Thus the main diagonal of a matrix must consist of 1’s. Insert the
appropriate reciprocal 1,1/3,……..,1/9 where the column of A meets the row of B, i.e., position (B,A) for
the reverse comparison of B with A. The numbers 2,4,6,8 and their reciprocals are used to facilitate
compromise between slightly differing judgements.
The next step consists of the computation of a vector of priorities from the given matrix. In
mathematical terms the principal eigenvector is computed, and when normalised becomes the vector of
priorities. To avoid large-scale computation, estimates of that vector can be obtained in the following
1) The crudest: Sum the elements in each row and normalise by dividing each sum by the total of
all sums, thus the results now add up to unity, The first entry of the resulting vector is the
priority of the first activity; the second of the second activity and so on.
2) Better: Take the sun of the elements in each column and form the reciprocals of these sums. To
normalize so that these numbers add to unity, divide each reciprocal by the sum of reciprocals.
3) Good: Divide the elements of each column by the sum of that column (i.e., normalize the
column) and then add the elements in each resulting row and divide this sum by the number of
elements in the row. This is a process of averaging over normalized columns.
4) Good: Multiply the n elements in each row and take the nth root. Normalize the resulting
Judgment consistency can be checked by taking the consistency ratio (CR) of CI with the appropriate
value in Table 2. The CR is acceptable, if it does not exceed 0.10. If it is more, the judgment matrix is
inconsistent. To obtain a consistent matrix, judgments should be reviewed and improved.
Table 1: Pair-wise comparison scale for AHP preferences
Numerical Rating Verbal judgments of preference
9 Extremely Important
8 Very Strongly Important to Extremely Important
7 Very Strongly Important
6 Strongly to Very Strongly Important
5 Strongly Important
4 Moderately to Strongly Important
3 Moderately Important
2 Equally to moderately Important
1 Equally Important
Table 2: Average random consistency (RI)
Size of matrix Random consistency
Example: A bid manager at the outset has to consider the following before any bid submission:
Check for conflicts of interest
Discuss with Internal approving authorities to arrive at “Go / No Go decision”
If a “Go Ahead” is decided, Identify strategy for winning bid, which includes
Optimum resource selection- to ensure competitive cost and maximize technical score
Identify hidden cost implications (Risks)
Determine acceptability of risks and based on the same proceed ahead with bid submission
The Risk Management Process consists of three stages:
– Risk Identification
– Risk Analysis- Assessment of Impact
– Risk Treatment- Providing for mitigation
The following are some of the key risks the consultancy firms in the water/ wastewater sector are
accepting to ensure they have key projects on their portfolio, to help them qualify for similar projects in
Risk of non payment due to shortage of fund allocation for proposed project. One way to reduce
that risk is to ensure the owner has the financial wherewithal to pay before the project is even
started. If the information is not available this risk needs to be suitably built in [Risk A]
Availability of human resources right through the project cycle [Risk B].
Time frame mentioned in the ToR is inadequate. Penalty clause for non timely delivery [Risk C]
Vague criteria for acceptance of deliverables- Likelihood of revision in deliverables/ delay in
acceptance of submitted deliverables [Risk D]
Conflicting priorities/ suggestions of various stakeholders having a say in acceptance of
deliverables [Risk E].
Client is not technically sound - Likelihood of revision in deliverables [Risk F].
Availability of required data and its authenticity- Additional Investigations over and above those
stated in the ToR may be required [Risk G].
The ideal scenario is that each risk is accounted for in the bid price. However, owing to more and more
stringent terms of reference and highly competitive bidding, currently the trend is to either decide on a
quote and see which risks are being covered or prioritize the risks and see covering which set of risks
impacts the bidding price in what quantum.
Generally risks are quantified as product of probability and consequences (impact). Further whether
mitigation can be effectively planned or not is another important aspect to consider. Product of these
three factors can be an effective indication to deliberate further and make guided decision to arrive at
risk priorities. For example the following numbers were arrived at using Delphi technique for the
various risks identified above.
Likelihood Consequence Mitigation LCM score
Risk A 0.5 0.8 0.9 0.36
Risk B 0.8 0.5/0.8 0.3 0.12
Risk C 0.5 0.5 0.3 0.075
Risk D 0.8 0.5 0.7 0.28
Risk E 1 0.5 0.3 0.15
Risk F 0.8 0.5 0.5 0.20
Risk G 0.8 0.8 0.7 0.28
The following correlation between subjective judgment and numerical representation was provided to
Highly unlikely 0.1
Unlikely to happen 0.3
Could happen 0.5
Will probably happen 0.8
Will happen 1
No effect 0.1
Minimal effect 0.3
Moderate effect 0.5
Significant effect 0.8
Low effectiveness 0.8
The following pairwise matric comparison was arrived at for various risks:
Risk A Risk B Risk C Risk D Risk E Risk F Risk G
Risk A 1 3 9 1.29 2.25 1.8 1.28
Risk B 0.333 1 3 0.43 0.75 0.6 0.428
Risk C 0.111 0.333 1 0.142 0.25 0.2 0.14
Risk D 0.777 2.33 7 1 1.75 1.4 1.25
Risk E 0.444 1.333 4 0.571 1 0.8 0.571
Risk F 0.555 1.666 5 0.714 1.25 1 0.714
Risk G 0.777 2.333 7 0.8 1.75 1.4 1
Risk A 0.2498
Risk B 0.0833
Risk C 0.0277
Risk D 0.2009
Risk E 0.1110
Risk F 0.1388
Risk G 0.1885
Consistency Index (CI)= 3.6367 x 10-6
Random Consistency ratio (RI)= 1.32
Consistency ratio (CR) = CI/ RI= 2.75508 x 10-6
As the value of CR is less than 0.1, the judgments are acceptable.
Results: The following priorities were arrived which show consistency between values obtained by LCM
score and AHP.
Priority by AHP Priority by LCM score
Priority Risk Priority Risk
1 Risk A 1 Risk A
2 Risk D 2 Risk D; Risk G
3 Risk G 3 Risk F
4 Risk F 4 Risk E
5 Risk E 5 Risk B
6 Risk B 6 Risk C
7 Risk C
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