Multiple Criteria Models for Evaluation of Competitive Bids ∗
S. L. Liu
School of International Trade and Economics
University of International Business and Economics
Beijing, 100029 P. R. China
E-Mail: slliu@mail.east.net.cn
K. K. Lai
Department of Management Sciences
City University of Hong Kong, Hong Kong
E-Mail: mskklai@cityu.edu.hk
S. Y. Wang
Institute of Systems Science
Academy of Mathematics and Systems Sciences
Chinese Academy of Sciences, Beijing 100080, China
E-Mail: sywang@iss02.iss.ac.cn
Abstract
In this paper, two general bidding systems are proposed to aid an owner to select one contractor based on
multiple attribute decision making models. They are named the general multiple attribute lower bidder system
and the general multiple attribute average-bid system which are an extension and a refreshment of the
multiparameter bidding system and the average-bid method, respectively. The preference of the owner over the
criteria (or attributes) relevant to construction work award is incorporated into the two new systems if necessary
and required by the owner. The values of the attributes (excluding the cost) required to be determined by the
owner in the multiparameter bidding system are not necessarily determined in the general multiple attribute
lower bidder system. This reduces the burden of the owner. The two new bidding systems are demonstrated via
an example, and are compared with the multiparameter bidding system and the average-bid method. The
∗
This paper has been published by IMA Journal of Mathematics Applied in Business and Industry, 11(3),
151-160, 2000.
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comparisons show that the preference of the owner over the attributes relevant to selection of contractors has
significant effect on the bid evaluation. Particularly, the two new systems still remain in the form of the
competitive bidding concept and can easily be applied to practice.
Key words: Competitive bidding, Bids evaluation, Multiple attributes, Lower bidder system, Non-lower
bidder system.
1. Introduction
In many industries, a sizable proportion of business is attained through competitive bidding. For example,
in the construction industry, contract bidding is widely used as a vehicle for distributing construction work to
willing contractors.
Bids evaluation (or selection of contractors) is as important to the owner as bidding strategy formulation to
the contractor (Nguyen, 1985). Contractors observe quite frequently that the lowest bid does not necessarily win
the project, and owners do not always find bids evaluation an easy task.
Currently, given that the owner has received the bids from a number of bidders for a specified project, the
bids evaluation (or the process of selecting a contractor from these bidders) is mainly based on two typical kinds
of systems. One kind of system called the single criterion bidding systems in this paper includes the lower
bidder system with its variations and the non-lower bidder systems (including the averaged-bid methods).
Another kind of systems may be called the multiple criteria (or attributes) bidding systems (including the
multiparameter bidding system).
In the lower bidder system, the bid price (or cost) is the only criterion for determining the successful
bidder (the future contractor), namely, the lowest bidder is awarded to the project. Although this traditional
system protects the public from extravagance, corruption, other improper practice by public officials, and the
bidding process independent from any of pressure (political, social and economic) because of the sole criterion
for evaluating bids, it has certain disadvantage, such as often resulting in unreasonably low bids either
accidentally or deliberately submitted and unqualified contractors which may cause extensive delays in the
planed schedule, cost overrun, very serious problems in quality, the increased number of claims, disputes,
litigation, and so on (Herbsman and Ellis, 1992; Ioannou and Leu, 1993). Over the years, some modifications to
the lower bidder system were made. For example, “responsible bidder”and “public interest”has been added to
the statutes to control the authority to let and award the projects. Other modifications created the concept of
prequalified bidder lists, and so on.
However, not every country around the world is using the lower bidder system. Several countries and areas,
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including Italy, Portugal, Peru, and Taiwan, have developed the non-lower bidder systems to overcome the
disadvantages as indicated above in which the successful bidder is not the lowest one. The philosophy behind
this concept is that the best bid is the most reasonable one, not the lowest one, not the highest one, but the one
closest to some average (Herbsman and Ellis, 1992) or the one that satisfies a certain relationship with the
average of all the bid prices (Ioannou and Leu, 1993). Several variations of this concept have been developed.
For example, one of such variations, the Peruvian government bidding system is presented in Henriod and
Lanteran (1988). Countries such as France and Portugal try to disqualify what they call abnormally low bids.
For more details about the above variations, see Henriod and Lanteran (1988) and Herbersman and Ellis (1992).
In addition, other variations are the average-bid methods being used in Italy and Taiwan (see Ioannou (1993) for
more detail). In Taiwan, the winner might be the contractor whose bid price is closest to the average. In Italy, the
winner might be the contractor whose bid price is closest to, but less than the average.
In order to overcome the disadvantage of the single criterion bidding system, a number of authors such as
Diekmann, Herbsman and Ellis, Henriod and Lanteran, and Nguyen have developed another kind of bidding
systems based on multiple attributes. The key idea of this kind of systems is that the selection process of the
contractors is based on more attributes, such as bid price or cost, time, quality, managerial safety accountability,
competence, and efficiency of contractors (Diekmann, 1981; Herbsman and Ellis, 1992; Nguyen, 1985). The
successful bidder is selected according to aggregation of scores or rankings on these attributes (Herbsman and
Ellis, 1992; Nguyen, 1985), as commonly used in multiple attribute decision modeling.
Diekmann (1981) presented a study of contractor selection for a cost-plus contract based on multiple
attributes. In his study, a wide range of attributes that may be used in selecting a contractor were discussed.
Nguyen (1985) proposed a systematic procedure for the selection of contractors based on fuzzy set theory
and multicriteria modeling.
Herbeman and Ellis (1992) analyzed the non-lower bidder systems and came to the conclusion that the
non-lower bidder systems would not be generally accepted in the United States because of 150 years of a
traditional competitive bidding system even though they have their merits. They were convinced that a total
change from the lower bidder system would not be feasible in the short range and would be even more difficult
to sustain in the long range. Only a major modification that would remain in the form of the competitive bidding
concept would be accepted. In view of these consideration, they proposed a so-called multiparameter bidding
system based on the idea that the selection process of the contractors will be based on more parameters (or
attributes) than just cost. The successful bidder will be selected according to the lowest combined bidding value
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of the chosen multiple attributes.
However, there are still some problems existing in the multiparameter bidding system. For example, the
method for determining the total bid scores for each bidder violates the independent principle between all the
attributes in the multiple attribute decis ion modeling. The preference of the owner over the attributes is not
incorporated into their system though it is mentioned in their system. In addition, the proposed system requires
the owner to determine three multipliers (time value, quality value and safe value) which vary with different
owners and different projects and difficult to be determined. This certainly burdens the owner greatly and is not
suitable for practical application.
In this paper, based on the principle of multiple attribute decision modeling we will propose two general
bidding systems (called the general multiple attribute lower bidder system and the general multiple attribute
average-bid system, respectively) which are extensions and refreshments of the multiparameter bidding system
and the average-bid method, respectively. The preference of the owner over the criteria (or attributes) is
incorporated into the two new systems if necessary or required by the owner. Particularly, the values of the
attributes (not including bid price) required to be determined in the multiparameter bidding system are not
necessarily determined in the general multiple attribute average-bid system. As a result, the first system reduces
the owner’
s burden. Particularly, the two new systems still remain in the form of the competitive bidding
concept and can easily be applied in practice. Finally, the data given in Herbman and Ellis (1992) will be used to
demonstrate the two new systems and compare them with the previous two systems mentioned above.
2. Review and Modification to the Multiparameter Bidding System
In order to state our ideas and compare them with the multiparameter bidding system, it is necessary to
review the multiparameter bidding system in Herbman and Ellis (1992). The main idea of the multipara meter
bidding system is that the selection process of the contractors will be based on more attributes than just cost, and
the successful bidder will be the one who has the lowest combined bidding value of the multiple attributes. The
major attributes selected by the owner are, cost, time, quality, and safety. The scores of these four attributes are
transformed into values by multiplying some factors (namely, their unit values). Then the values of all the
attributes for each bidder are totaled to get the combined bidding value for that bidder. Mathematically, the
multiparameter bidding system can be expressed as below:
Bi = C i + VT T i + (100 − Qi )C i / 100 + V S S i ,
(2.1)
where Bi s are the combined bidding values for determining award, Ci s refer to the bid prices submitted by the
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bidders and are measured in dollars, Ti s are the time amounts in calendar days proposed by the bidder for
performance of the work, Qi s and Si s are the quality and safety items established from the bidders’previous
performance records by the owner, respectively. The attribute quality is measured in “points per 100”, and the
attribute safety is measured in “points per $1,000,000”based on number of accidents per $1,000,000 cost and
depending on the severity of the accidents (3 points for severe accidents, 2 points for medium ones, and 1 point
for light ones). The factors VT and V S refer to the respective unit values of the attributes time and safety,
respectively.
Herbeman and Ellis (1992) pointed out that in addition to the above attributes, there may be additional
attributes, for example, safety (very important in tunnel and dam projects), security (in military projects), and so
on, which would be specific to particular industries and can be incorporated into the system. Certainly, the
agencies using the system would have the responsibility of figuring the weights and the quantification methods
for these attributes.
The above system can be generalize to the case when the owner considers that the four attributes have
different weights ω1 , ω 2 , ω 3 and ω 4 . That is
Bi0 = ω 1Ci + ω 2VT Ti + ω 3 (100 − Qi ) Ci /100 + ω 4V S S i ,
(2.2)
From the viewpoint of multiple attribute decision making (Hwang and Yoon, 1981), the equation (2.1) is
not sound and reasonable because of the dependence of the value of attribute quality on cost. In addition, the
factors VT and V S are difficult for the owner to determine because of their variations with the different owners
and different projects, and the unit value of any new attribute is required to determine by the owner whenever
the attribute is incorporated into the system.
3. Two General Multiple Attribute Bidding Systems
3.1 Preliminaries
The selection of contractors (or evaluation of bids) is viewed as a multiple attribute decision making
problem. The contractors are the alternatives, the parameters used to evaluate the bidders are the attributes,
and the objective for the owner is to choose a bidder as a contractor who has the lowest combined bidding
score or utility value. Certainly, the owner using these two systems would have the responsibility of
selecting all the relevant attributes and figuring the weights and the quantification methods for these
attributes in order to express his/her ideas. For example, some attributes (such as bid prices and time)
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should be quantified by the bidders and some attributes (such as quality and safety) by the owner based on
the bidder’s past performance, and so on.
Suppose that there are m bidders who are bidding for a project and the owner has selected n attributes
(including cost or bid price), X j , j=1, 2, …, n, to evaluate m bidders. Assume that X ij is the score of attribute
X j with respect to bidder i. .Suppose that the weights of the attributes are ω1 , ω 2 , …, ω n . All the above data
are shown in Table 1.
Table 1. Evaluation matrix for the bidders
Attribute
X1
X2
…
Xn
1
X 11
X 12
…
X 1n
2
X 21
X 22
…
X 2n
…
m
…
X m1
…
X m2
…
…
…
X mn
Bidder
3.2 Determination for the weights of the attributes
With respect to the determination of weights of the attributes, there are many methods that can be used. For
example, AHP is a good method among them. Also, the method in Liu et al (1999) can be used. Of course, the
weights can be given directly by the owner.
3.3 Normalization for the attributes
Generally, different attributes have different scales of measurement; all the attributes often conflict with
each other and are incomparable. A normalization aims at obtaining comparable scales.. The normalization of
the attainment levels of the attributes is not necessary, but it may be essential for some methods like Simple
Additive Weighting Method (Hwang and Yoon, 1981; Liu and Qiu, 1998).
For a profit attribute X j , the normalized value, yij , for a given attainment level of xij will be
yij =
max i x ij − xij
max i x ij − min i x ij
.
(3.1)
Similarly, for a cost attribute X j , the normalized value, yij , for a given attainment level of xij will be
yij =
x ij − min i xij
max i x ij − min i x ij
.
(3.2)
The fixation attribute presented in Liu and Qiu (1998) means that the closer the attainment levels are to
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some fixed real number, the more preference for them. Thus, in the following general multiple attribute
average-bid system to be proposed, the average bid is a fixation attribute.
For a fixation attribute X j with the average bid price, x j , of all the bid prices xij s, the normalized value,
yij , for a given attainment level of xij will be
yij =
x ij − x j − min i x ij − x j
max i x ij − x j − min i x ij − x j
,
(3.3)
where the average bid price x j = ∑ m
i =1 xij / m .
The formulae (3.1), (3.2) and (3.3) for normalizing attributes can guarantee that the better the attainment
levels of the attributes, the lower the corresponding normalized values. The reason for using the above equations
to normalize a given attainment level for a given criterion will be explained later. However, we should indicate
that the above methods for normalizing the attributes are not different from the normal methods as used in
Hwang and Yoon (1981) and Liu and Qiu (1998) where the better the attainment levels of the attributes the
higher the corresponding normalized values.
3.4 A general multiple attribute lower bidder system
The combined bidding score of n attributes for bidder i, denoted by B1i , is computed by the Simple
Additive Weighting Method as follow (Hwang and Yoon, 1981):
n
B1i = ∑ ω j yij ,
j=1
(3.4)
where the bid price is a cost attribute, and yij can be determined by (3.1) for the profit attribute(s) and (3.2) for
the cost attribute(s).
The owner using this system (abbreviated as GMALBS) should select the bidder with the lowest combined
value of n attributes. Its reason is that the equations (3.1) and (3.2) for normalizing the profit and cost attributes
are based on the idea that the better the attainment levels of attribute X j , xij , the lower the corresponding
normalized value yij . Thus, this system still remains within the framework of the competitive bidding concept.
3.5 A general multiple attribute average-bid bidder system
The combined bidding score of n attributes for bidder i, denoted by B 2i , is calculated by the Simple
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Additive Weighting Method as follow (Hwang and Yoon, 1981):
n
B 2i = ∑ ω j yij ,
(3.5)
j=1
where the bid price is a fixation attribute and yij can be determined from (3.1) and (3.2) for the profit and cost
attributes, respectively, and from (3.3) for the attribute bid price or cost.
Similarly, the owner using this system (abbreviated as GMAABS) should select the bidder with the lowest
combined value of n attributes and the reason is the same as the general multiple attribute lower bidder system.
In addition, this system still remains within the framework of the competitive bidding concept.
4. Comparisons of Our Two Systems with Multiparameter Bidding System
and the Average-Bid Method
Our two systems are demonstrated with the data in Herbersman and Ellis (1992) and are compared with
both the multiple parameter bidding system and the average-bid method. Herbersman and Ellis assume that the
owner will select a contractor based on four attributes ( cost, time, quality and safety). The evaluations of these
attributes on each bidder are listed in Table 2.
Table 2. Evaluations of the attributes for the bidders
Attribute
Bidder
A
B
C
D
Cost ($)
Time
(Cal-Days)
Quality
(Points per 100)
1,100,000
1,300,000
1,250,000
1,100,000
250
230
240
300
89
97
91
85
Safety
(number of accidents
per 1,000,000)
12
9
17
25
4.1 Comparisons of the GMALBS with the multiparameter bidding system
Herberman and Ellis (1992) assumed that the parameters VT =$2000/day and V S =$1000/point and the
four attributes are assumed to have same importance, i.e.,
ω 1 = ω 2 = ω 3 = ω 4 =0.25. The evaluations of the
four attributes in Table 2 are normalized as the following Table 3 by using (3.1) and (3.2).
Table 3. Normalization for the attributes for the bidders
Attribute
Cost
Bidder
A
B
C
0
1
0.75
Time
Quality
Safety
0.2857
0
0.1429
0.6667
0
0.5
0.1875
0
0.5
8
D
0
1
1
1
Thus, we have B11 =0.2850, B12 =0.2500, B13 =0.4732, B14 =0.7500 by (3.4) when using the GMALBS.
Hence, in increasing order of preference the bidders is bidder B, bidder A, bidder C, bidder D for the GMALBS,
and bidder A, bidder B, bidder C, bidder D for the multiparameter bidding system. The difference between the
results for the GMALBS and the multiparameter bidding system consists in that the former is independent of the
values (such as
VT and VS ) of the attributes of time, quality and safety and the latter is dependent of them. In
addition, the best bidder B for GMALBS accords with our visual observations, namely, the values of the three
attributes (time, quality and safety) for bidder B are the best ones among the four bidders and the four attributes
have the same weights.
However, if the owner considers that the weights of the attributes should be ω1 =0.6,
ω 2 =0.2, ω 3 =0.15,
ω 4 =0.05, then we have B11 =0.1665, B12 =0.6, B13 =0.5786, B14 =0.4 by the GMALBS, and B10 =778,750,
B20 =878,300, B30 =863,725, B40 =806,000 by the general multiparameter bidding system. Thus, in increasing
order of preference the bidders is bidder A, bidder D, bidder C, bidder B for both our system and .the
multiparameter bidding system. Our preference ordering of the bidders is due to the larger weight of the
attribute cost of 0.6 and the lowest costs of bidder A and bidder D. This shows the significant effect of weights
of the attributes on selection of contractors. In practice, the attribute cost is more important than any other
attributes.
Remark 1. An extreme case of the GMALBS is the lower bidder system where the weight of attribute cost
or bid price is 1 and the weights of all the other attributes are zero.
Remark 2. From Table 2 we can easily conclude that bidder A is preferred to bidder D for any weights of
the attributes.
4.2 Comparisons of the GMAABS with the average-bid system
The evaluations of the four attributes in Table 2 are normalized as the following Table 4 by using (3.1) (3.2)
and (3.3) for the profit cost and fixation attributes, respectively.
Table 4. Normalization for the attributes for the bidders
Attribute
Bidder
A
B
Cost
0.5
1
Time
0.2857
0
9
Quality
0.6667
0
Safety
0.1875
0
C
D
0
0.5
0.1429
1
0.5
1
0.5
1
Thus, we have B21 =0.4100, B22 =0.2500, B23 =0.2857, B24 =0.8750 by (3.5) when assuming that the four
attributes have the same weights and using the GMAABS. Hence, in increasing order of preference the bidders
is bidder B, bidder C, bidder A, and bidder D for GMAABS, and bidder C, bidders A and D, bidder B for the
average-bid method because of the equalities |1,250,000− x 1 |<|1,100,000− x 1 |<|1,300,000− x 1 | (where
x1 =
1,187,500). The difference between the results for the GMANBS and the average-bid system consists in (i) the
former is independent of the value (such as VT and V S ) of the attributes Time, Quality and Safety, and the latter
is dependent of them; (ii) the former is based on four attributes with same importance and the latter is based on
only one attribute----cost. Similarly, the best bidder B for GMAABS accords with our visual judgment, namely,
the values of the three attributes (time, quality and safety) for bidder B are the best ones among the four bidders
and the four attributes have the same weights.
If the owner assumes thatω 1 =0.6,
ω 2 =0.2, ω 3 =0.15, ω 4 =0.05, then we have B21 =0.4665, B22 =
0.6000, B23 =0.1286, B24 =0.7000 by the GMAABS. Thus, in increasing order of preference the bidders are
bidder C, bidder A, bidder B, bidder D for the GMAABS and bidder C is the most preferred.
These results are due to the larger weight of the attribute cost of 0.6 and the bid price of bidder C is closest to
the average of $1,187,500 among all the bidder’
s bid prices.
This illustrates the importance of weights of the attributes in contractor selection. In practice, the attribute
cost is more important than any other attributes.
5. Conclusions
The competitive bid systems by which the project is awarded based on the sole criterion ( i.e., bid price or
cost) has created many problems in past years. We consider that the main reason is that it ignores the importance
of other attributes, such as quality, time, safety, and so forth.
Many authors have modified the original competitive concept and proposed some special systems in which
some other important attributes such as quality time and safety are incorporated into the original competitive
bidding concept (Diekmann, 1981; Herbsman and Ellis, 1992; Nguyen, 1985).
In this paper, the bids evaluation problem is viewed as a general multiple attribute decision problem. The
Simple Additive Weighting method is used to solve this problem. Certainly, according to the specific
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environment we can also solve the bids evaluation problem by the other methods in Hwang and Yoon (1981) for
multiple attribute decision making problem: (i) the methods for no preference given such as Dominance,
Maximin and Maximax; (ii) the methods for standard level of attribute given such as Conjunctive and
Disjunctive methods; (iii) the methods for ordinal preference of attribute given such as Lexicographic method
and Permutation method; (iv) the methods for cardinal preference of attribute given such as Linear Assignment
method, Hierarchical Additive Weighting method or AHP, ELECTRE methods , TOPSIS, and Simple Additive
Weighting method as used in this paper; (v) the methods for information on alternative given, and so on.
The two general multiple attribute bidding systems (i.e., GMALBS and GMAABS) proposed in this paper
provide good improvements on the multiparameter bidding system and the average-bid method, respectively.
The lower bidder system is a special case of the GMALBS and the average-bid method a special case of the
GMAABS. The preference of the owner over the attributes (namely, the weights of the attributes) is easily
incorporated into the GMALBS and GMAABS. Particularly, the value of the attributes (not including cost)
required to be determined in the multiparameter bidding system need not to be determined in the GMALBS.
Thus, GMALBS reduces the owner’
s burden. The data in Herberman and Ellis (1992) is used to demonstrate our
two bidding systems and compare them with the multiparameter bidding system and the average-bid method.
The results of comparison have showed that the preference of the owner over the attributes relevant to contractor
selection has significant effect on the bids evaluation. In addition, much emphasis should be on the importance
of doing more research on quantification methods for the other attributes such as quality safety and security.
The proposed two systems have the potential of selecting a better contractor for the owner and improving
construction performance of the chosen contractor. Their merits are the flexibility of the systems. As long as the
attributes chosen, their system of measurement and their relativity weights are stipulated in the bid documents in
detail, our two systems are still in accordance with the existing legal status of the current competitive bidding
system.
Acknowledgement
This work was supported by the National Natural Science Foundation of China under Grant 79800006 and
the Strategic Grant of City University of Hong Kong under Grant 7000915.
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