Bidding decision making for construction company using a multi-criteria prospect model/Statybos imones apsisprendimas dalyvauti konkurse naudojant daugiakriterini perspektyvu modeli.
Cheng, Min-Yuan ; Hsiang, Chia-Chi ; Tsai, Hsing-Chih 等
1. Introduction
In the construction industry contractors typically earn
construction contracts through either direct negotiation or competitive
bidding. Government agencies and private sector clients most often
employ competitive bidding, which commonly use the lowest bid price as
the main award criterion. Usually the bid price includes cost of
construction and a markup, the scale of which is typically determined
using a percentage of construction costs. Size of markup impacts upon
the profit, which serves as the primary motivator for a contractor to
win and execute a contract (Dikmen et al. 2007). Research in the area of
competitive bidding strategy models has been conducted since the 1950s
(Friedman 1956). Numerous models have been developed, some of which were
designed specifically for the construction industry. Despite the number
of competitive bidding strategy models that have been developed, few of
these are used in practice, largely as they do not address the practical
needs of construction contractors (Hegazy and Moselhi 1995; Shash 1995).
Therefore, there is a perceived need for models designed in line with
actual construction contractor practices. In the bid process, once a
determination is made to bid, the next step is to select an appropriate
markup (Egemen and Mohamed 2008). A successful contractor is the one
that selects the most optimal bid markup that secures both the contract
and contract profitability (Shash and Abdul-Hadi 1992). Bid markup
decisions currently follow no accepted standards or formal procedures,
but rather consider contractor experience, intuition, and personal
preferences, which are not conducive elements for building an effective
approach for achieving the optimal bid markup (Chua and Li 2000).
Cumulative prospect theory was proposed by Tversky and Kahneman
(1992). Different from the classical theory, CPT adopted a
concave-shaped utility function (UF) for gains and convex for losses and
an inverse S-shaped probability weighting function (PWF) to describe
individual preferences for choosing between risky prospects. Wakker and
Deneffe (1996) proposed a tradeoff (TO) method to improve probability
distortions and misconceptions in utility elicitation. Many studies (Wu
and Gonzalez 1996; Gonzalez and Wu 1999) have worked to elicit the PWF
for particular subjects. Abdellaoui (2000) used TO method concepts to
propose a parameter-free method to elicited subjects' UF and PWF.
Bleichrodt and Pinto (2000) also leveraged the concept to propose a
parameter-free method somewhat different from Abdellaoui's study,
which they applied successfully to medical decision making. Determining
the relative weight of influencing factors is important in
multi-criteria decision making (MCDM). For uncertain events, the
decision maker will find it difficult to form a judgment by relying on
exact numerical values. FPR is a useful tool to express decision
maker's uncertain preference information and define the relative
weight of influencing factors. Significant attention has been given to
fuzzy preference relations in previously studies (Orlovsky 1978; Nurmi
1981; Tanino 1984; Kacprzyk 1986; Chiclana et al. 1998, 2001, 2003; Fan
et al. 2002; Xu and Da 2002, 2005; Herrera-Viedma et al. 2004). Wang and
Chang (2007) adopted FPR to forecast the probability of successful
knowledge management.
The usual practice is to make bid decisions based on
'intuition', which can be described as a derivation of
'gut feelings', experience and guesswork (Ahmad 1990). This
research combined FPR, CPT and MCDM to propose a Multi-Criteria Prospect
Model for Bid Decision making (BD-MCPM) to help construction company
decision makers derive optimal bid decisions. The proposed model
incorporates three phases. Phase I identifies the factors that affect
bidding decisions (i.e., bid/no bid and markup scale). Phase II
introduces FPR to determine bid/no bid. Phase III uses FPR and CPT to
calculate CPT values for given markup scale, then selects the markup
scale with the highest CPT value.
2. Literature review
2.1. Currently available decision making models
Contractors currently make bidding decisions using several relevant
models. Early mark-up scale estimation models (e.g., Friedman 1956;
Gates 1967; Carr 1982) employed probability theory to predict the
probability of winning a particular contract. However, as the bidding
decision is a complex decision-making process affected by numerous
factors, probability theory is unable to describe interactions between
factors.
Researchers have recently introduced bidding decision support
systems based on artificial intelligence (AI), which permit
consideration of identified factors of importance. Such systems include
the expert system (ES) (Ahmad and Minkarah 1988; Tavakoli and Utomo
1989), case-based reasoning (CBR) (Chua et al. 2001), neural network
(NN) (Li 1996; Moselhi et al. 1993; Hegazy and Moselhi 1994; Dias and
Weerasinghe 1996; Li and Love 1999; Li et al. 1999; Wanous et al. 2003),
analytical hierarchy process (AHP) (Seydel and Olson 1990; Cagno et al.
2001), and fuzzy set theory (Eldukair 1990; Fayek 1998; Lai et al. 2002;
Lin and Chen 2004). The ES is one of rule-based systems. The process of
bid decisions are highly unstructured, uncertainty, and subjectivity.
It's too complicated to creating a set of clear rules that would be
suitable for all/most cases. CBR requires a reasonably large set of
cases data from which to draw knowledge to avoid generating inaccurate
results. NN, also called artificial neural network (ANN), is similar to
the CBR, with an important exception that the inference process is
concealed from the decision maker. For such reasons, NN-derived
conclusions are sometimes not particularly convincing to decision
makers. AHP is a decision-making approach that structures
multiple-choice criteria into a hierarchy and assesses relative
importance of each. Unfortunately, AHP employs a complicated process to
obtain consistent assessment results, which makes it unwieldy in
practice.
The complexity and hard-to-define nature of competitive situations
necessitates that most bid decisions rely heavily on decision maker
intuition, experience and guesswork (Ahmad 1990). Fuzzy set theory
provides a useful tool to handle decisions in which phenomena are
imprecise and vague. Eldukair (1990) integrated fuzzy set theory with a
multi-criteria model to select bidding cases. Subsequently, Fayek (1998)
and Lai et al. (2002) used fuzzy set theory to choose optimal mark-up
scales. Lin and Chen (2004) proposed an approach using fuzzy set theory
to obtain a linguistics suggestion result for a bid/no-bid selection.
Fuzzy preference relations (FPRs), which integrate fuzzy logic and
AHP concepts, greatly improve on AHP in terms of relative weight
evaluation. In BD-MCPM, the FPR is used to determine the relative
weights of influencing factors, and the CPT is used to evaluate the
PDM's preference. The BD-MCPM handles factors marked by relatively
higher levels of vagueness to make complicated bidding decisions and
determine PDM risk preference. Results conform to actual bid decisions
generated based on decision maker intuition, experience and guesswork.
Therefore, BD-MCPM can assist decision makers to identify projects with
the greatest profit potential and set an optimal mark-up scale.
2.2. Fuzzy preference relations
Most decision processes are based on preference relations (PR), the
most common representation of information in decision making. In PR, an
expert assigns a value to each pair of alternatives that reflects the
degree of preference for the first alternative over the second. Many
important decision models have been developed using mainly two
preference relation types: (1) Multiplicative Preference Relations (MPR)
and (2) Fuzzy Preference Relations (FPR).
Most decision processes are based on preference relations, the most
common representation of information in decision making. An expert
assigns a value to each pair of alternatives that reflects degree of
preference B as an alternative over others. Many important decision
models have been developed using mainly: (1) multiplicative preference
relations and (2) fuzzy preference relations (Herrera-Viedma et al.
2004).
A multiplicative preference relation on a set of alternatives X is
represented by matrix A, with A usually assumed a multiplicative
reciprocal:
A = [[a.sub.ij] [subset] X x X; (1)
[a.sub.ij] x [a.sub.ji] = 1 [for all]i, j [member of] {1, ..., n}.
(2)
The [a.sub.ij] indicate the preference ratio of alternative
[x.sub.i] to [x.sub.j]. Saaty (1980, 1994) suggested measuring
[a.sub.ij] using a ratio scale 1-9. When [a.sub.ij] = 1 indicates
indifference between [x.sub.i] and [x.sub.j], and [a.sub.ij] = 9
indicates that [x.sub.i] is absolutely preferred to [x.sub.j], then
[a.sub.ij] [member of] [1/9,9].
Fuzzy preference relation B on a set of alternatives X is a fuzzy
set on the product set X x X, characterized by membership function
[[micro].sub.B]: X x X [right arrow][0,1]. Therefore:
B = [b.sub.ij]] [b.sub.ij] = [[mu].sub.B] ([x.sub.i], (x.sub.j])
[for all]i, j [member of]{1, ..., n}; (3)
[b.sub.ij] + [b.sub.ji] = 1 [for all]i, j [member of] { 1, ..., n},
(4)
where [[mu].sub.] is a membership function and [b.sub.ij] is the
preference ratio of alternative [x.sub.i] over [x.sub.j]. A [b.sub.ij]
at 0.5 denotes that [x.sub.i] and [x.sub.j] are indifferent, and a
[b.sub.ij] at 1 represents that [x.sub.i] is preferred absolutely to
[x.sub.j].
The method (Herrera-Viedma et al. 2004) to transformation
multiplicative preference relations A to fuzzy preference relations B
and obtain relative weights presents the following:
(1) Get (n-1) values {[a.sub.12], [a.sub.23], ...,
[a.sub.(n-1].sub.n]} of multiplicative preference relations A;
(2) Diagonal elements of A are values at 1.0, using the equation
(5) to calculate the remaining elements in the upper right part of the
diagonal:
[a.sub.i(j-1)] x [a.sub.(i+ 1).sub.j]/[a.sub.(i+1)(j-1)]. (5)
Elements in the lower left part of the diagonal in were calculated
using the equation shown below:
[a.sub.ij] = 1/[a.sub.ji]; (6)
(3) Let Z = max[A], then transfer multiplicative preference
relations A to a consistently MPR matrix C with a normal to interval
[1/9, 9] with equation (7):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (7)
(4) Apply equation (8) to transform the consistent MPR matrix C to
FPR matrix B:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)
2.3. Cumulative prospect theory
Consider a prospect (mutual fund) X with outcomes [x.sub.1] [less
than or equal to] ... [less than or equal to] [x.sub.k] [less than or
equal to] 0 [x.sub.k+1] [less than or equal to] ... [less than or equal
to] [x.sub.n] that are associated with probability [p.sub.1], ...,
[p.sub.k], [P.sub.k+1], ..., [p.sub.n]. Cumulative prospect theory
predicts that people will choose prospects based on the value (Tversky
and Kahneman 1992):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (9)
where [lambda] > 0 is a loss-aversion parameter and [pi] are
decision weights calculated based on "cumulative"
probabilities associated with the outcomes. In particular, prospect
theory assumes a probability weighting function [w.sup.+] : [0; 1]
[right arrow] [0; 1] for gains and a probability weighting function
[w.sup.-] : [0; 1] [right arrow] [0; 1] for losses. In CPT the utility
function v(x) is unchanged from the original PT (Tversky and Kahneman
1992; Tversky and Fox 1995; Gonzalez and Wu 1999), which is concave for
gains and convex for losses, with the loss function assumed to be
steeper than the gain function ([beta] > 1):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (10)
The decision weights employed in CPT are given by Tversky and
Kahneman (1992):
[[pi].sub.1] = [w.sup.-] ([p.sub.1] and [[pi].sub.n] = [w.sup.+]
([p.sub.n]); (11)
[[pi].sup.-.sub.i] = [i.summation over (j=1)] [w.sup.-]([p.sub.j])
- [i-1.summation over (j=1)] [w.sup.-] ([p.sub.j]) for 2 [less than or
equal to] i [less than or equal to] k
and
[[pi].sup.+.sub.i] = [n.summation over (j=i)] [w.sup.+] ([p.sub.j])
- [n.summation over (j=i+1)] ([p.sub.j]) for k + 1 [less than or equal
to] i [less than or equal to] n - 1, (12)
where probability weighting functions [w.sup.-] and [w.sup.+] are
defined for probabilities associated with losses and gains,
respectively, which may be experimentally estimated using the following
formulae (Tversky and Kahneman 1992; Camerer and Ho 1994; Wu and
Gonzalez 1996):
[w.sup.-] (x) = [x.sup.[delta]]/[([x.sup.[delta]] + (1 -
[x.sup.[delta]])).sup.1/[delta]]
and
[w.sup.+] (x) = [x.sup.[gamma]]/[([x.sup.[gamma]] + (1 -
[x.sup.[gamma]])).sup.1/[gamma]]. (13)
For only gain conditions, equations (9) will transform to:
V[[p.sub.1], [x.sub.1]; [p.sub.2], [x.sub.2]] =
2[summation].sub.j=1] [[pi].sup.+].sub.j] x v([x.sub.j]) =
[[pi].sup.+.sub.1] x v([x.sub.1]) + [[pi].sup.+.sub.2] x v([x.sub.2]).
(14)
3. Constructing a multi-criteria prospect model for bidding
decisions
3.1. Multi-criteria prospect model for bidding decision
This study adopted BD-MCPM, which combined FPR and CPT, to modeling
the construction company's bidding decision processes using the
three phases shown in Fig. 1.
3.2. Phase I--preparation
The bidding decision process generates two decisions: whether to
submit or not submit a bid (bid/no bid) and, if so, the scale of the
markup component of the bid (markup) (Egemen and Mohamed 2008). Many
factors affect decision making in each phase. Phase I should first
identify the key factors that influence a bidding decision and, based on
such factors, collect and organize relevant project data/information.
[FIGURE 1 OMITTED]
3.2.1. Identify the key factors of influence in a bid decision
Many studies designed to identify the factors that influence
bidding decisions have been conducted in recent years. Some have adopted
a contractor perspective. Others have focused on conditions limited to a
particular, localized situation. Still others have taken a multinational
perspective. All have worked to identify key factors of influence at
work on local contractor bid decisions. The purpose of Phase I in the
BD-MCPM was to identify, respectively, the key factors influencing
bid/no bid and markup decisions. The identification process was a two
step process, which first reduced the total potential number of factors
by identifying and choosing only those referenced consistently in the
literature in order to identify a shortlist of 'pre-adapted'
factors. The second step incorporated these pre-adapted factors into a
questionnaire, which was send to local contractors who were asked to
assess the importance of each factor on a scale from 1 to 9 (1:very
unimportant, 9:very important). Each factor was then assigned an
importance score based on an average of submitted scores. Table 1 shows
44 factors identified in the literature as affecting bid/no bid decision
making (Cook 1985; Skitmore 1985; Marsh 1989; Cooke 1992; Odusote and
Fellows 1992; Shash 1993; Wanous et al. 2000; Chua and Li 2000; Han and
Diekmann 2001; Lewis 2003). Sixteen of these factors were prioritized as
they were mentioned in five or more of the referenced articles. Ten of
these prioritized factors received average scores of importance equal to
or greater than 5, and were ranked from highest to lowest.
Similarly, Table 2 shows the eight factors identified in the
literature as affecting markup decisions (Odusote and Fellows 1992;
Dozzi et al. 1996; Li 1996; Dulaimi and Shah 2002). A shortlist of those
that were mentioned in two or more articles was then made, and those
from the shortlist with average earned scores of importance equal or
greater than 5 were ranked.
3.2.2. Case collection
A case study to test the ability of the BD-MCPM model to solve the
above problem was conducted to illustrate the effectiveness of the
approach in practice. The background of research participants were
considered to be homogeneous in the sense that they were all qualified
professionals in construction field with previous knowledge of bidding
strategies and bidding procedures. Table 3 presents a summary of data
collected on three actual projects.
3.3. Phase II--deciding to bid or not to bid
The goal of Phase II was to make a decision whether or not to bid
on a particular project. The 10 key factors that affect the bid/no bid
decision were identified in Section 3.2.1. By assessing the relative
weights and risk scores for these factors, a bid/no bid score may be
obtained, which can then be used to make the decision whether to bid or
not.
3.3.1. Determining the relative weight of influencing factors for
bid/no bid decisions
The seven steps employed to determine the relative weight of
identified factors of influence are described as follows:
Step 1: Define linguistic variables. This study used 9 linguistic
terms {AM: Absolutely more important, VM: Very strongly more important,
SM: Strongly more important, WM: Weakly more important, EQ: Equally
important, WL: Weakly less important, SL: Strongly less important, VL:
Very strongly less important, AL: Absolutely less Important} associated
with real number {5, 4, 3, 2, 1, 1/2, 1/3, 1/4, 1/5} to compare
corresponding neighboring factors.
Step 2: Obtain questionnaire input. Ten factors of influence
[[BF.sub.i](/=1,2,...,10)] were considered in making the bid / no bid
decision. Via a questionnaire survey or interviews, the kth evaluator
assessed the relative intensity of importance of the two adjoining
factors [BF.sub.i] and [BF.sub.j] to obtain 9 grades of importance
[[a.sup.k.sub.ij] (i = 1,2,...,9, j = i + l), where [a.sup.k.sub.ij] = 1
means indifference between two factors, [a.sup.k.sub.ij] = 2,3,4,5 shows
that factor [BF.sub.i] is relatively important to factor [BF.sub.j],
[a.sup.k.sub.ij] = 1 / 2,1 / 3,1 / 4,1 / 5 and indicates that factor
[BF.sub.i] is less important than factor [BF.sub.j]. Table 4 presents
the relative importance of bid/no bid decision factors assessed by
evaluator 1.
Step 3: Construct the MPR matrix. To construct the kth
evaluator's MPR matrix [A.sup.k], we first translated the
linguistic terms of questionnaire results into real numbers
[a.sup.k.sub.ij] to fill proper diagonal elements, using Eqs (5) and (6)
to calculate the remaining elements of MPR matrix.
For example, from Table 4 we can obtain a set of 9 values
{[a.sup.1.sub.1 2] = 4, [a.sup.1.sub.2 3] 3=1, [a.sup.1.sub.4 5] 4=1/4,
[a.sup.1.sub.4 5]=1/3, [a.sup.1.sub.5 6] = 1, [a.sup.1.sub.6 7] =1/3,
[a.sup.1.sub.7 8] = 2, [a.sup.1.sub.8 9] = 1/2, [a.sup.1.sub.9 10] =3 },
the MPR matrix of evaluator 1's may be constructed as follows:
[A.sup.1] =
1 4 4.00 1.00 0.33 0.33 0.11 0.22 0.11 0.33
0.25 1 1 0.25 0.08 0.08 0.03 0.06 0.03 0.08
0.25 1.00 1 1/4 0.08 0.08 0.03 0.06 0.03 0.08
1.00 4.00 4.00 1 1/3 0.33 0.11 0.22 0.11 0.33
3.00 12.00 12.00 3.00 1 1 0.33 0.67 0.33 1.00
3.00 12.00 12.00 3.00 1.00 1 1/3 0.67 0.33 1.00
9.00 36.00 36.00 9.00 3.00 3.00 1 2 1.00 3.00
4.50 18.00 18.00 4.50 1.50 0.50 0.50 1 1/2 1.50
9.00 36.00 36.00 9.00 3.00 1.00 1.00 2.00 1 3
3.00 12.00 12.00 3.00 1.00 0.33 0.33 0.67 0.33 1
Let Z = max[[A.sup.k], a consistently MPR matrix [C.sup.k] with a
normal to interval [1/5, 5], the transform function show in Eq. (15)
will change to Eq. (16) :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (15)
For example, the maximum value of evaluator 1's [A.sup.1] MPR
matrix was 36. Applying Eq. (15), a consistently MPR matrix [C.sup.1]
may be obtained as follows:
[C.sup.1] =
1.00 1.86 1.86 1.00 0.61 0.61 0.37 0.51 0.37 0.61
0.54 1.00 1.00 0.54 0.33 0.33 0.20 0.27 0.20 0.33
0.54 1.00 1.00 0.54 0.33 0.33 0.20 0.27 0.20 0.33
1.00 1.86 1.86 1.00 0.61 0.61 0.37 0.51 0.37 0.61
1.64 3.05 3.05 1.64 1.00 1.00 0.61 0.83 0.61 1.00
1.64 3.05 3.05 1.64 1.00 1.00 0.61 0.83 0.61 1.00
2.68 5.00 5.00 2.68 1.64 1.64 1.00 1.37 1.00 1.64
1.97 3.66 3.66 1.97 1.20 1.20 0.73 1.00 0.73 1.20
2.68 5.00 5.00 2.68 1.64 4.64 1.00 1.37 1.00 1.64
1.64 3.05 3.05 1.64 1.00 1.00 0.61 0.83 0.61 1.00
Step 4: Transform the consistent MPR matrix to a fuzzy preference
relation matrix. The consistent MPR matrix [c.sup.k.sub.ij [member of]
[1/5,5], the transform function shown in Eq. (8) will change to Eq. (16)
shown below:
[b.sub.ij] = g ([a.sub.ij]) = (1 + [log.sub.5] [c.sub.ij])/2. (16)
Applying Eq. (16), the evaluator 1's FPR matrix [B.sup.1] may
be obtained as follows:
[B.sup.1] =
0.50 0.69 0.69 0.50 0.35 0.35 0.19 0.29 0.19 0.35
0.31 0.50 0.50 0.31 0.15 0.15 0.00 0.10 0.00 0.15
0.31 0.50 0.50 0.31 0.15 0.15 0.00 0.10 0.00 0.15
0.50 0.69 0.69 0.50 0.35 0.35 0.19 0.29 0.19 0.35
0.65 0.85 0.85 0.65 0.50 0.50 0.35 0.44 0.35 0.50
0.65 0.85 0.85 0.65 0.50 0.50 0.35 0.44 0.35 0.50
0.81 1.00 1.00 0.81 0.65 0.65 0.50 0.60 0.50 0.65
0.71 0.90 0.90 0.71 0.56 0.56 0.40 0.50 0.40 0.56
0.81 1.00 1.00 0.81 0.65 0.65 0.50 0.60 0.50 0.65
0.65 0.85 0.85 0.65 0.50 0.50 0.44 0.44 0.35 0.50
Step 5: Aggregate the FPR matrix for all evaluators. The opinions
of different evaluators were aggregated to obtain an aggregated weight
for each factor of influence. [b.sup.k.sub.ij] was employed to denote
the fuzzy preference relationship value of the kth evaluator to assess
factors i and j. This study used an average value method to integrate
the judgment values of m evaluators and obtain the averaged FPR matrix
[bar.B]. The average function is shown below:
[[bar.b].sub.ij] = 1/m ([b.sup.1.sub.ij] + [b.sup.2.sub.ij] ... +
[b.sup.m.sub.ij]). (17)
For example, [b.sup.k.sub.ij] for 3 evaluators were
[b.sup.1.sub.12] = 0.69, [b.sup.2.sub.12] = 0.72, and [b.sup.3.sub.12] =
0.78. Equation (17) was then applied to generate [[bar.b].sub.12] =
0.73. The same approach was used to obtain an averaged FPR matrix
[bar.B], as follows:
[bar.B] =
0.50 0.73 0.85 0.69 0.50 0.54 0.54 0.64 0.49 0.62
0.27 0.50 0.62 0.46 0.26 0.31 0.31 0.41 0.26 0.38
0.15 0.38 0.50 0.34 0.14 0.19 0.19 0.29 0.14 0.26
0.31 0.54 0.66 0.50 0.30 0.35 0.34 0.45 0.30 0.42
0.50 0.74 0.86 0.70 0.50 0.55 0.54 0.65 0.50 0.62
0.46 0.69 0.81 0.65 0.45 0.50 0.50 0.60 0.45 0.57
0.46 0.69 0.81 0.66 0.46 0.50 0.50 0.61 0.45 0.58
0.36 0.59 0.71 0.55 0.35 0.40 0.39 0.50 0.35 0.47
0.51 0.74 0.86 0.70 0.50 0.55 0.55 0.65 0.50 0.62
0.38 0.62 0.74 0.58 0.38 0.43 0.43 0.53 0.38 0.50
Step 6: Normalize the aggregated FPR matrix. Using R to indicate
the normalized aggregate FPR matrix, the value of element [r.sub.ij] can
be obtained using the function shown below:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (18)
For [[bar.b].sub.12] = 0.73, [10.summation over (i=1)]
[[bar.b].sub.ij] = 6.21 when j = 2, applying equation (18), we can then
get [r.sub.12]=0.118 and, in the same manner, obtain normalize averaged
FPR matrix R as follows:
R =
0.128 0.118 0.115 0.119 0.129 0.125 0.123 0.121 0.129 0.122
0.069 0.081 0.084 0.079 0.069 0.072 0.070 0.077 0.068 0.076
0.038 0.061 0.067 0.059 0.037 0.044 0.042 0.055 0.037 0.052
0.079 0.087 0.089 0.086 0.078 0.081 0.078 0.084 0.078 0.083
0.129 0.118 0.115 0.120 0.130 0.127 0.124 0.122 0.130 0.123
0.117 0.111 0.109 0.112 0.118 0.116 0.113 0.113 0.118 0.113
0.119 0.112 0.110 0.112 0.119 0.117 0.114 0.114 0.119 0.114
0.091 0.095 0.096 0.094 0.091 0.092 0.090 0.094 0.091 0.093
0.131 0.119 0.116 0.120 0.131 0.128 0.125 0.122 0.131 0.124
0.099 0.099 0.099 0.099 0.099 0.099 0.121 0.099 0.099 0.099
Step 7: Obtain relative weights. Given that [WB.sub.i] denotes the
priority weight of influencing factor i, the priority weight of each
factor may be obtained using the following function:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (19)
In Case 1, [10.summation over (i=1)] [10.summation over (j=1)]
[r.sub.ij] = 10 and [10.summation over (j=1)] [r.sub.ij] = 1.228 for i =
1,
applying equation (19) obtains a relative weight for influencing
factor [BF.sub.1] of 0.123. Following the same process, the relative
weights of influencing factors in Case 1 as assessed using three
evaluators were obtained as [WB.sub.i] = {0.123, 0.074, 0.049, 0.082,
0.124, 0.114, 0.115, 0.093, 0.125, 0.101}.
3.3.2. Assessing the risk score for factors of influence in bid/no
bid decision making
Risk score [RS.sub.i] represents the degree of risk in the factor
of influence [BF.sub.i], which has been subjectively established by PDM
using predetermined scores {0 - No risk, 25--Low risk, 50--Moderate
risk, 75--High risk, 100--Prohibitive risk}. For Case 1, the value of
risk associated with influencing factors using PDM is illustrated in
Table 5.
3.3.3. Deciding to or not to submit a bid
A total bid/no bid score may then be calculated by summing degrees
of significance:
[V.sub.B] = [10.summation over (i=1)] [WB.sub.i] x [RS.sub.i]. (20)
If [V.sub.B] [less than or equal to] 50, then a "bid"
decision is recommended. Applying equation (20) to bid/no bid scores for
cases 1 through 3 returned, respectively, total scores of 43.8, 52.9 and
45.3. As such, the contractor should bid on Case 1 and Case 3 and
proceed to Phase III (the markup phase) for both.
3.4. Phase III--deciding appropriate markup
Once a decision to bid has been made, the next step is to determine
appropriate markup sizes for bidding projects. Firstly, the PDM assign a
set of markup scales. The evaluator then determines the relative weight
of each factor of influence (see also Section 3.2.1) for each special
markup scale. The resulting assess the probability of winning project
for specify markup scale. The determining process is illustrated below.
3.4.1. Assign specific scale of markup
In construction projects, the scale of a markup is determined based
on relevant contractor policies and project type. In general, markups
tend to represent 3% ~ 7% of a project's total estimated cost,
although in certain cases, markups may be in the 10% ~ 15% range or
higher. This study adopted 5 frequently used markup scales
{[M.sub.1]=3%, [M.sub.2]=4%, [M.sub.3]=5%, [M.sub.4]=7%, [M.sub.5]=10%}
as examples.
3.4.2. Determine relative weight of influencing factors for special
markup scale
The eight key factors previously identified as affecting markup
scale decision making (MF.sub.i]) are listed in Table 2. These also
represent factors of influence on outcome implementation. Assigning
weights to each factor is done in the same manner as that described in
Section 3.3.1. The only difference was the associated factors of
influence used. The relative weight of each influencing factor
[MF.sub.i], assessed using 3 evaluators, were obtained and represented
as [WM.sub.i] = {0.078, 0.078, 0.064, 0.123, 0.191, 0.118, 0.150,
0.198}.
3.4.3. Forecast probability of winning project using markup scale
As bids typically involve multiple potential contractors, assessing
the probability of bid success over competitors at a particular markup
level is critical. Of course, markup scale may be expected to correlate
inversely to probability of bid success. FPR was used here to forecast
project bid success in the same manner as in Section 3.3.1.
For each case and defined markup scale, evaluators used linguistic
terms to judge subjectively the relative importance of each factor in
winning a bid and in losing a bid [MF.sub.i].
For example, in Case 1, when the markup was set to 3%, Evaluator 1
assessed the relative importance to win/lose case probability to be
[b.sup.1.sub.uv] = {5,4,4,3,5,4,5,4}. Using questionnaire results, a 2x2
pair-wise comparison MPR matrix could then be constructed with two
outcomes ("win" and "lose") for each factor of
influence. The pair-wise comparison MPR matrix [B.sup.k] for each
influencing factor was then constructed (see Table 6 below).
Applying the same process described from step 4 to 7 in Section
3.3.1., derived the average rating [PR.sub.i], which described the
potential for winning in light of the identified factors of influence
[MF.sub.i]. For example, in Case 1, at a markup of 3%, win probability
ratings for relevant factors of influence [MF.sub.i] may be obtained
using [PR.sub.i] ={0.81, 0.76, 0.79, 0.69, 0.78, 0.76, 0.83, 0.76}.
Finally, for a specify markup scale, the forecast probability of
winning PM may be obtained using the following function:
PM = [8.summation over (i=1)] [WM.sub.i] x [PR.sub.i], (21)
where [WM.sub.i] and [PR.sub.i] denote the relative weights and the
probability ratings of winning for identified markup scale factors of
influence [MF.sub.i], i [member of] (1,2, ..., 8).
Using the example of Case 1 at a 3% markup and the value for
[WM.sub.i] obtained in Section 3.4.2., we may apply equation (21) to
obtain a win probability forecast PM = 78%. In the same manner, the win
probability forecast at 4%, 5%, 7% and 10% markups were 71%, 63%, 43%
and 25%, respectively, for Case 1. In Case 3, win probability forecasts
were 77%, 68%, 60%, 46% and 28% for defined markups in the 3~10% range.
As defined in the model construct, probability of winning a project
is kept and probability of losing a project is ignored, the latter
yields a prospect value equal to 0.
3.4.4. Elicit the PDM utility function for the markup scale
This study adopted the TO method proposed by Wakker and Deneffe
(1996) to elicit the PDM utility function for the markup scale. This
paper will not describe the mechanisms by which such was accomplished,
as the method has been described previously in the literature
(Bleichrodt and Pinto 2000; Abdellaoui 2000; Abdellaoui et al. 2005).
The elicited result for the PDM utility function is shown in Fig. 2.
[FIGURE 2 OMITTED]
3.4.5. Elicit the PDM probability weighting function
Bleichrodt and Pinto (2000) proposed a method to elicit PWF based
on the TO method. This method first set p' [less than or equal to]
0.5 for low probabilities and p '>0.5 for high probabilities,
then chose two prospects which were queried to subjects in order to
assess an outcome. For probabilities p' [less than or equal to] 05,
subjects were asked to assess an outcome [z.sub.y] such that the
difference between [p', [x.sub.i]; 1 - p', [x.sub.j]] and
[p', [x.sub.k]; 1 - p', [z.sub.r]] with [X.sub.k] [greater
than or equal to] [x.sub.i] > [x.sub.j], [x.sub.k], [x.sub.i], and
[x.sub.j] are elements of the standard sequence elicited in 3.4.4. The
weighting of probabilities w (p') were determined using:
w(p') = u([x.sub.j]) - u([z.sub.r])/[u([x.sub.j]) -
u([z.sub.r])] + [u([x.sub.k]) - u([x.sub.i]). (22)
For probabilities p '>0.5, subjects were asked to assess an
outcome [z.sub.s] such that there is indifference between [p',
[x.sub.m]; 1 - p', [x.sub.n]] and [[p', [z.sub.s]; 1-[p',
[x.sub.q]] with [x.sub.m] [greater than or equal to] [x.sub.n] [greater
than or equal to] [x.sub.q], [x.sub.m], [x.sub.n], and [x.sub.q] are
elements of the standard sequence. Weighting of probabilities w(p')
were determined by:
w(p') = u([x.sub.n]) - u([x.sub.q])/[u([z.sub.s]) -
u)[x.sub.m])] + [u([x.sub.n]) - u([x.sub.q])]. (23)
This study used the same probabilities p' ={0.10, 0.25, 0.50,
0.75, 0.90} as those in Bleichrodt's study to elicit PDM's
PWF. In the elicitation procedure, the PDM may be used to assess an
outcome for the two prospects in probabilities that range from 0.10 to
0.90. If the first assumption assumes a low setting probability p',
then the PDM will be asked to assess [z.sub.y] for the prospect of
p', [x.sub.i]; 1 - p', [x.sub.j]] and [p', [x.sub.k]; 1 -
p', [z.sub.r]], and apply equation (23) to calculate w(p'). If
w(p') [greater than or equal to] 0 and p' [greater than or
equal to] w (p'), then p' represents a low probability.
Otherwise, p' should be high probability, and PDM will be asked in
the same p' again to assess [z.sub.s] with prospects [p',
[x.sub.m]; 1 - p', [x.sub.n]] and [p', [z.sub.s]; 1 -
[p', [x.sub.q]], and apply equation (28) to calculate w(p') .
Other probabilities of p' are assumed at a high probability to
elicit w (p') . Fig. 3 shows the elicited PWF of the PDM in this
study.
[FIGURE 3 OMITTED]
3.4.6. Determine the prospect value of the markup scale
Under CPT and FPR, the Prospect Value [V.sub.CPT] ([M.sub.i]) at a
specified markup scale [M.sub.i] may be determined using the CPT
equation:
[V.sub.CPT] ([M.sub.i]) = U ([M.sub.i]) x W (P[M.sub.i]), (24)
where U ([M.sub.i]) and W ([PM.sub.i]) may be found by
interpolation:
U([M.sub.i]) = [M.sub.i] - [M.sub.j]/[M.sub.j+1] - [M.sub.j]
[U([M.sub.j+1]) - U([M.sub.j])] + U([M.sub.j]); (25)
W([PM.sub.i]) = [PM.sub.i] - [PM.sub.j]/[PM.sub.j+1] -
[PM.sub.j][W([PM].sub.j+1]])-W([PM.sub.j])]+W([PM.sub.j]). (26)
The calculated CPT value for each markup scale in Case 1 and Case 3
were listed in Table 7.
3.4.7. Comparison and decision making
Selecting the highest markup scale CPT value (Table 7) determined
the markup scale in each case (i.e., 5% for Case 1 and 7% for Case 3).
Estimated profit and bid price for Cases 1 and 3 were calculated and are
shown in Table 8. Under circumstances in which contractors may only
choose one case on which to bid, other consideration factors may be
brought into play (e.g., duration, funding requirements, etc.).
4. Discussions
BD-MCPM was used successfully to help PDM determine which case(s)
should be bid and the optimal markup. Knowing competitor markup scales
prior to tender submission would be helpful in modifying the markup
recommendations generated by BD-MCPM and allow for adjustments critical
to winning the bid (markup adjustment downward) or increasing profit
(markup adjustment upward). In practice, however, it is difficult to
elicit a competitor's UF and PWF. Therefore, an effective
methodology with which to infer such represents a valuable direction for
future research.
5. Conclusions
This study developed a Multi-Criteria Prospect Model for Bidding
Decision (BD-MCPM) to help contractors determine whether to submit a bid
and, when the answer is in the affirmative, set an optimal markup scale.
Research contributions include:
1. Identification of ten and eight key influencing factors used by
contractors in Vietnam to make decisions, respectively, on bid/no bid
and mark-up scales using literature review and questionnaire survey
techniques.
2. Introduction of a new Multi-Criteria Prospect Model for Bidding
Decision (BD-MCPM), which combines fuzzy preference relations (FPR),
cumulative prospect theory (CPT), and Multi-Criteria Prospect Model
(MCPM). The BD-MCPM is a systematic bidding model designed to help
construction companies make strategic bid / no bid decisions and to
determine the optimal markup scale for each project bid.
3. FPR using only a small number of expert input variables provides
consistency in fuzzy preference relations that simplifies the process of
evaluating relative factor weights to deciding bid/no bid phase and
forecast probability project win for specific mark-up size. Moreover,
applying FPR to evaluation and forecasting can connote the
characteristic of evaluator's "experience" and
"guesswork".
4. CPT evaluates the primary decision maker's risk prospects
in terms of utility functions and probability weighting functions. CPT
calculates preference values for assigned mark-up scales and probability
of a project win based on prior forecasts. It further selects the
mark-up scale delivering the optimal preference value so that the
decision maker can make an optimal decision that takes into account the
PDM's intuition.
5. The study validated the BD-MCPM using actual bidding projects
obtained from construction companies in Vietnam and successfully helping
the PDM to select cases on which to bid and to set optimal markup scale.
doi: 10.3846/13923730.2011.598337
References
Abdellaoui, M. 2000. Parameter-free elicitation of utility and
probability weighting functions, Management Science 46(11): 1497-1512.
doi:10.1287/mnsc.46.11.1497.12080
Abdellaoui, M.; Vossmann, F.; Weber, M. 2005. Choice-based
elicitation and decomposition of decision weights for gains and losses
under uncertainty, Management Science 51(9): 1384-1399.
doi:10.1287/mnsc.1050.0388
Ahmad, I. 1990. Decision support system for modeling bid/no bid
decision problem, Journal of Construction Engineering and Management
ASCE 116(4): 595-608. doi:10.1061/(ASCE)0733-9364(1990)116:4(595)
Ahmad, I.; Minkarah, I. 1988. An expert system for selecting bid
markups, in Proc. of the Fifth Conference on Computing in Civil
Engineering: Microcomputers to Supercomputers ASCE, 229-238.
Bleichrodt, H.; Pinto, J. L. 2000. A parameter-free elicitation of
the probability weighting function in medical decision analysis,
Management Science 46(11): 1485-1496. doi: 10.1287/mnsc.46.11.1485.12086
Cagno, E.; Caron, F.; Perego, A. 2001. Multi-criteria assessment of
the probability of winning in the competitive bidding process,
International Journal of Project Management 19(6): 313-324.
doi:10.1016/S0263-7863(00)00020-X
Camerer, C. F.; Ho, T.-H. 1994. Violations of the betweenness axiom
and nonlinearity in probability, Journal of Risk and Uncertainty 8(2):
167-196. doi:10.1007/BF01065371
Carr, R. I. 1982. General bidding model, Journal of the
Construction Division ASCE 108 (4): 639-650.
Chiclana, F.; Herrera, F.; Herrera-Viedma, E. 1998. Integrating
three representation models in fuzzy multipurpose deci sion making based
on fuzzy preference relations, Fuzzy Sets and Systems 97(1): 33-18.
doi:10.1016/S0165-0114(96)00339-9
Chiclana, F.; Herrera, F.; Herrera-Viedma, E. 2001. Integrating
multiplicative preference relations in a multipurpose decision-making
model based on fuzzy preference relations, Fuzzy Sets and Systems
122(2): 277-291. doi:10.1016/S0165-0114(00)00004-X
Chiclana, F.; Herrera, F.; Herrera-Viedma, E.; Martinez, L. 2003. A
note on the reciprocity in the aggregation of fuzzy preference relations
using OWA operators, Fuzzy Sets and Systems 137(1): 71-83.
doi:10.1016/S0165-0114(02)0043 3-5
Chua, D. K. H.; Li, D. 2000. Key factors in bid reasoning model,
Journal of Construction Engineering and Management ASCE 126(5): 349-357.
doi:10.1061/(ASCE)0733-9364(2000)126:5(349)
Chua, D. K. H.; Li, D. Z.; Chan, W. T. 2001. Case-based reasoning
approach in bid decision making, Journal of Construction Engineering and
Management ASCE 127(1): 3545. doi:10.1061/(ASCE)0733-9364(2001)127:1(35)
Cooke, B. 1992. Contract Planning and Contractual Procedures. 3rd
Ed. Palgrave Macmillan. 259 p.
Cook, P. J. 1985. Bidding for the General Contractor, Kingston,
Mass.: R. S. Means. 224 p.
Dias, W. P. S.; Weerasinghe, R. L. D. 1996. Artificial neural
network for construction bid decisions, Civil Engineering and
Environmental Systems 13(3): 239-253. doi:10.1080/02630259608970200
Dikmen, I.; Birgonul, M. T.; Gur, A. K. 2007. A case-based decision
support tool for bid mark-up estimation of international construction
projects, Automation in Construction 17(1): 30-44.
doi:10.1016/j.autcon.2007.02.009
Dozzi, S. P.; AbouRizk, S. M.; Schroeder, S. L. 1996. Utility
theory model for bid markup decisions, Journal of Construction
Engineering and Management ASCE 122(2): 119-124.
doi:10.1061/(ASCE)0733-9364(1996)122:2(119)
Dulaimi, M. F.; Shah, H. G. 2002. The factors influencing bid
markup decisions of large- and medium-size contractors in Singapore,
Construction Management and Economics 20(7): 601-610.
doi:10.1080/01446190210159890
Egemen, M.; Mohamed, A. 2008. SCBMD: A knowledge-based system
software for strategically correct bid/no bid and mark-up size
decisions, Automation in Construction 17(7): 864-872.
doi:10.1016/j.autcon.2008.02.013
Eldukair, Z. A. 1990. Fuzzy decisions in bidding strategies, in
Proc. of the First International Symposium on Uncertainty Modeling and
Analysis, Maryland, USA, 3-5 December, 1990, 591-594.
Fan, Z.-P.; Ma, J.; Zhang, Q. 2002. An approach to multiple
attribute decision making based on fuzzy preference information on
alternatives, Fuzzy Sets and Systems 131(1): 101-106.
doi:10.1016/S0165-0114(01)00258-5
Fayek, A. 1998. Competitive bidding strategy model and software
system for bid preparation, Journal of Construction Engineering and
Management ASCE 124(1): 1-10. doi:10.1061/(ASCE)0733-9364(1998)124:1(1)
Friedman, L. 1956. A Competitive Bidding Strategy, Operations
Research 4(1): 104-112. doi:10.1287/opre.4.1.104
Gates, M. 1967. Bidding strategy and probabilities, Journal of the
Construction Division, Proceedings of the American Society of Civil
Engineers 93 (CO1): 75-107.
Gonzalez, R.; Wu, G. 1999. On the shape of the probability
weighting function, Cognitive Psychology 38(1): 129- 166.
doi:10.1006/cogp.1998.0710
Han, S. H.; Diekmann, J. E. 2001. Making a risk-based bid decision
for overseas construction projects, Construction Management and
Economics 19(8): 765-776. doi:10.1080/01446190110072860
Hegazy, T.; Moselhi, O. 1994. Analogy-based solution to markup
estimation problem, Journal of Computing in Civil Engineering ASCE 8(1):
72-87. doi: 10.1061/(ASCE)0887-3801(1994)8:1(72)
Hegazy, T.; Moselhi, O. 1995. Elements of cost estimation: A survey
in Canada and the United States, Cost Engineering 37(5): 27-33.
Herrera-Viedma, E.; Herrera, F.; Chiclana, F.; Luque, M. 2004. Some
issues on consistency of fuzzy preference relations, European Journal of
Operational Research 154(1): 98-109. doi: 10.1016/S0377-2217(02)00725-7
Kacprzyk, J. 1986. Group decision making with a fuzzy linguistic
majority, Fuzzy Sets and Systems 18(2): 105-118.
doi:10.1016/0165-0114(86)90014-X
Lai, K. K.; Liu, S. L.; Wang, S. 2002. Bid Markup Selection Models
by Use of Multiple Criteria, IEEE Transactions on Engineering Management
49(2): 155-160. doi:10.1109/TEM.2002.1010883
Lewis, H. 2003. Bids, tenders & proposals: Writing business
through best practice. London, Sterling, VA: Kogan Page Ltd. 276 p.
Li, H. 1996. Neural network models for intelligent support of
markup estimation, Engineering, Construction and Architectural
Management 3(1/2): 69-81. doi:10.1108/eb021023
Li, H.; Love, P. E. D. 1999. Combining rule-based expert systems
and artificial neural networks for mark-up estimation, Construction
Management and Economics 17(2): 169-176. doi:10.1080/014461999371664
Li, H.; Shen, L. Y., Love, P. E. D. 1999. Ann-based mark-up
estimation system with self-explanatory capacities, Journal of
Construction Engineering and Management ASCE 125 (3): 185-189.
doi:10.1061/(ASCE)0733-9364(1999)125:3(185)
Lin, C.-T.; Chen, Y.-T. 2004. Bid/no-bid decision-making--a fuzzy
linguistic approach, International Journal of Project Management 22(7):
585-593. doi:10.1016/j.ijproman.2004.01.005
Marsh, P. D. V. 1989. Successful bidding and tendering, England:
Wildwood House. 171 p.
Moselhi, O.; Hegazy, T.; Fazio, P. 1993. DBID: Analogy-based DSS
for bidding in construction, Journal of Construction Engineering and
Management 119(3): 466-479. doi:10.1061/(ASCE)0733-9364(1993)119:3(466)
Nurmi, H. 1981. Approaches to collective decision making with fuzzy
preference relations, Fuzzy Sets and Systems 6(3): 249-259.
doi:10.1016/0165-0114(81)90003-8
Odusote, O. O.; Fellows, R. F. 1992. An examination of the
importance of resource considerations when contractors make project
selection decisions, Construction Management and Economics 10(2):
137-151. doi:10.1080/01446199200000013
Orlovsky, S. A. 1978. Decision-making with a fuzzy preference
relation, Fuzzy Sets and Systems 1(3): 155-167.
doi:10.1016/0165-0114(78)90001-5
Saaty, T. L. 1980. The Analytic Hierarchy Process. McGraw Hill, New
York. 287 p.
Saaty, T. L. 1994. Fundamentals of Decision Making and Priority
Theory with the AHP. RWS Publications, Pittsburgh. 447 p.
Seydel, J.; Olson, D. L. 1990. Bids considering multiple criteria,
Journal of Construction Engineering and Management ASCE 116(4): 609-623.
doi: 10.1061/(ASCE)0733-9364(1990) 116:4(609)
Shash, A. A. 1993. Factors considered in tendering decisions by top
UK contractors, Construction Management and Economics 11(2): 111-118.
Shash, A. A. 1995. Competitive bidding system, Cost Engineering
37(2): 19-20. doi:10.1080/01446199300000004
Shash, A. A.; Abdul-Hadi, N. H. 1992. Factors affecting a
contractor's markup size decision in Saudi Arabia, Construction
Management and Economics 10(5): 415-429. doi: 10.1080/01446199200000039
Skitmore, R. M. 1985. The influence of professional expertise in
construction price forecasts. Department of Civil Engineering,
University of Salford, UK. 250 p.
Tanino, T.; 1984. Fuzzy preference orderings in group decision
making, Fuzzy Sets and Systems 12(2): 117-131.
doi:10.1016/0165-0114(84)90032-0
Tavakoli, A.; Utomo, J. L. 1989. Bid markup assistant: An expert
system, Cost Engineering 31(6): 28-33.
Tversky, A.; Fox, C. R. 1995. Weighing risk and uncertainty,
Psychological Review 102(2): 269-283. doi: 10.1037/0033-295X.102.2.269
Tversky, A.; Kahneman, D. 1992. Advances in prospect theory:
Cumulative representation of uncertainty, Journal of Risk Uncertainty
5(4): 297-323. doi:10.1007/BF00122574
Wakker, P.; Deneffe, D. 1996. Eliciting von Neumann-Morgenstern
utilities when probabilities are distorted or unknown, Management
Science 42(8): 1131-1150. doi:10.1287/mnsc.42.8.1131
Wang, T.-C.; Chang, T.-H. 2007. Forecasting the probability of
successful knowledge management by consistent fuzzy preference
relations, Expert Systems with Applications 32(3): 801-813.
doi:10.1016/j.eswa.2006.01.021
Wanous, M.; Boussabaine, A. H.; Lewis, L. 2000. To bid or not to
bid: a parametric solution, Construction Management and Economics 18(4):
457-466. doi:10.1080/01446190050024879
Wanous, M.; Boussabaine, A. H.; Lewis, J. 2003. A neural network
bid/no bid model: the case for contractors in Syria, Construction
Management and Economics 21(7): 737-744. doi:
10.1080/0144619032000093323
Wu, G.; Gonzalez, R. 1996. Curvature of the probability weighting
function, Management Science 42(12): 1676-1690. doi:
10.1287/mnsc.42.12.1676
Xu, Z. S.; Da, Q. L. 2002. The uncertain OWA operator,
International Journal of Intelligent Systems 17(6): 569-575.
doi:10.1002/int.10038
Xu, Z.; Da, Q. 2005. A least deviation method to obtain a priority
vector of a fuzzy preference relation, European Journal of Operational
Research 164(1): 206-216. doi:10.1016/j.ejor.2003.11.013
Min-Yuan Cheng (1), Chia-Chi Hsiang (2), Hsing-Chih Tsai (3),
Hoang-Linh Do (4)
Department of Construction Engineering, National Taiwan University
of Science and Technology, Keelung Rd., Taipei, Taiwan, R. O. C. 106
E-mails: (1)
[email protected]; (2)
[email protected]
(corresponding author);
(3)
[email protected]; (4)
[email protected]
Received 08 Oct. 2009; accepted 26 Nov. 2010
Min-Yuan CHENG. Professor in Department of Construction Engineering
at National Taiwan University of Science and Technology (NTUST), Taiwan.
He is a Board of Directors member of International Association for
Automation and Robotics in Construction (IAARC). His research interests
include geographic information system, construction automation and
e-business, management information system, business process
reengineering, artificial intelligence, knowledge management, and their
applications.
Chia-Chi HSIANG. Lecturer in Department of Civil Engineering at
Chung Yuan Christian University (CYCU), Taiwan. He is a Ph.D. candidate
in Department of Construction Engineering at National Taiwan University
of Science and Technology, Taiwan. His research interests include
prospect theory, fuzzy theory, game theory, construction management, and
bidding strategy.
Hsing-Chih TSAI. Assistant professor at National Taiwan University
of Science and Technology, Taiwan. His research interests include
computational mechanics, swarm intelligence, construction management,
RFID Application, high-order neural networks, and soft programming
engineering.
Hoang-Linh DO. He received his master's degree in Department
of Construction Engineering, National Taiwan University of Science and
Technology in 2008. His research interests include prospect theory,
fuzzy theory, and bidding strategy.
Table 1. Key influencing factors of bid/no bid decision
Category No. Inferential Factor
Client 1 Reputation of client
2 Relationship with client
3 Financial capability of the client
4 Client requirements
5 Fostering good relationship with regular clients
Other 6 Proportions to be subcontracted
7 Reputation of other consultants
8 Relationship with other consultants
Project 9 Nature of project
10 Project size
11 Project period
12 Project complexity
13 Project location
Resources 14 Experience for similar project
15 Professional demands of the contract
16 Physical resources necessary to carry out project
17 Availability of qualified/experienced staff
18 Financial resources necessary to carry out project
Tender 19 Time available for tender preparation
20 Cost of bidding
21 Tender conditions
22 Tendering method
23 Adequacy of tender information
24 Current workload in bid preparation
Contract 25 Type of contract
26 Contractual conditions
Company 27 Compliance with business strategy
28 Current work load
29 Availability of other projects
30 Promoting reputation
31 Operational capacity
Competitors 32 Number of competitors
33 Competence of the expected competitors
34 Degree of competition
35 Perceived chances of being successful
Financial 36 Client budget
37 Financial situation
38 Expected profitability
39 Expected cash flow
40 Confidence in the cost estimate
41 Projected break-even point for the contract
Culture 42 Local customs
Market 43 Market conditions
Risk 44 Expected risk
Category No. Literatures
1 2 3 4 5 6 7 8 9 10
Client 1 * * * * * *
2 * * * * * *
3 * * *
4 * *
5 *
Other 6 * * *
7 * *
8 * * *
Project 9 * * * * * * *
10 * * * * *
11 * * * *
12 * * * * *
13 * * * * * *
Resources 14 * * * * * *
15 * *
16 *
17 * * * * *
18 *
Tender 19 * * * * * *
20 * * *
21 * * *
22 * * *
23 * * * *
24 *
Contract 25 * * *
26 * * * * * *
Company 27 * *
28 * * * * *
29 * * * * * *
30 * *
31 * *
Competitors 32 * * * * *
33 * *
34 *
35 * *
Financial 36 * *
37 * * * *
38 * * * * *
39 * * *
40 * *
41 *
Culture 42 * *
Market 43 * * * * *
Risk 44 * * * * *
Questionnaire survey
Category No.
Average Factor
Score
Client 1
2 6.55 [BF.sub.6]
3
4
5
Other 6
7
8
Project 9
10 7.10 [BF.sub.3]
11
12 6.25 [BF.sub.7]
13
Resources 14 7.15 [BF.sub.2]
15
16
17 5.85 [BF.sub.8]
18
Tender 19
20
21
22
23
24
Contract 25
26 6.75 [BF.sub.4]
Company 27
28 6.70 [BF.sub.5]
29
30
31
Competitors 32 5.25 [BF.sub.9]
33
34
35
Financial 36
37
38 7.20 [BF.sub.1]
39
40
41
Culture 42
Market 43
Risk 44 5.10 [BF.sub.10]
Note: Literature (1) Cook (1985); (2) Skitmore (1985); (3) Marsh
(1989); (4) Cooke (1992); (5) Shash (1993); (6) Odusote and
Fellows (1992); (7) Wanous et al. (2000); (8) Chua and Li (2000);
(9) Han and Diekmann (2001); (10) Lewis (2003)
Table 2. Key influencing factors for markup scale decision
Category Inferential factor Factor
Project Project size [MF.sub.5]
Resources Experience in similar project [MF.sub.6]
Company Need for work [MF.sub.i]
Current workload [MF.sub.3]
Competitors Number of competitors [MF.sub.4]
Financial Expected profitability [MF.sub.8]
Market Overall economy [MF.sub.7]
Risk Expected risk [MF.sub.2]
Table 3. Case study data
Item Case 1 Case 2
Owner Housing and Urban Hanoi city people's
Development Corporation committee
(HUD)
Project Housing project Housing project
2 units--14 floors 1 unit--21 floor
and 21 floor
Total Floor area Total Floor area
21960 [m.sup.2] 19950 [m.sup.2]
Basement area Basement area
1588 [m.sup.2] 1800 [m.sup.2]
Location Hanoi city, Vietnam Hanoi city, Vietnam
Estimated cost Approx. US $17,954,000 Approx. US $4,228,000
Total duration 30 months 18 months
Bidding system Open competitive bid Open competitive bid
Fund Self, customer Self (government)
mobilization
fund, Agri Bank
Contract type Lump sum Lump sum
Payment methods Local currency (VND) Local currency (VND)
Timing of 2.5 months 2 months
payments
Prior project Common markup 3-6% Common markup 3-6%
markup scale The best case 20% gain The best case 20% gain
The worst case 15% loss The worst case 15% loss
Item Case 3
Owner Infrastructure
Development and
Construction Corporation
(LICOGI)
Project Housing project
2 units--14 floors
and 17 floor
Total Floor area
19558 [m.sup.2]
Basement area
1500 [m.sup.2]
Location HaiPhong city, Vietnam
Estimated cost Approx. US$9,735,000
Total duration 24 months
Bidding system Open competitive bid
Fund Self, government,
Viet Com Bank
Contract type Lump sum
Payment methods Local currency (VND)
Timing of 2 months
payments
Prior project Common markup 3-6%
markup scale The best case 20% gain
The worst case 15% loss
Table 4. Questionnaire sheet for importance of influencing
factors of evaluator 1
Intensity of importance
Factor Factor
[BF.sub.i] AM VM SM WM EQ WL SL VL AL [BF.sub.j]
[BF.sub.l] X [BF.sub.2]
[BF.sub.2] X [BF.sub.3]
[BF.sub.3] X [BF.sub.4]
[BF.sub.4] X [BF.sub.5]
[BF.sub.5] X [BF.sub.6]
[BF.sub.6] X [BF.sub.7]
[BF.sub.7] X [BF.sub.8]
[BF.sub.8] X [BF.sub.9]
[BF.sub.9] X
Table 5. Risk assessment by PDM on influencing factors of
Case 1
No Influencing factor [RS.sub.i]
0 25 50 75 100
1 Expected profitability X
2 Experience for similar project X
3 Project size X
4 Contractual conditions X
5 Current workload X
6 Relationship with client X
7 Project complexity X
8 Availability of qualified/ X
experienced staff
9 Number of competitors X
10 Expected risk X
Table 6. Evaluator 1's pair-wise comparison
MPR matrix for case 1 and markup scale 3%
Influencing MPR [B.sup.k]
factor
Win Lose
[MF.sub.l] Win 1 5
Lose 1/5 1
[MF.sub.2] Win 1 4
Lose 1/4 1
[MF.sub.3] Win 1 4
Lose 1/4 1
[MF.sub.4] Win 1 3
Lose 1/3 1
[MF.sub.5] Win 1 5
Lose 1/5 1
[MF.sub.6] Win 1 4
Lose 1/4 1
[MF.sub.7] Win 1 5
Lose 1/5 1
[MF.sub.8] Win 1 4
Lose 1/4 1
Table 7. CPT value for each markup scale of Case 1 and Case 3
Markup scale Probability
Markup Utility Value of Winning
Case scale M(n) U(M(n)) P(M(n))
1 3% 0.252 78%
4% 0.345 71%
5% 0.400 63%
7% 0.508 43%
10% 0.643 25%
3 3% 0.252 77%
4% 0.345 68%
5% 0.400 60%
7% 0.508 46%
10% 0.643 28%
Probability Prospect Decision
Markup Weight Value Markup
Case scale M(n) PW(M(n)) VCPT scale
1 3% 0.682 0.172
4% 0.611 0.211
5% 0.554 0.221 5%
7% 0.424 0.215
10% 0.330 0.212
3 3% 0.668 0.168
4% 0.590 0.203
5% 0.532 0.213 7%
7% 0.439 0.223
10% 0.345 0.222
Table 8. Profit and bid price for Case 1 and Case 3
Case Estimated Cost Decision Profit Bid price
(USD) Markup scale (USD) (USD)
1 17,954,000 5% 897,700 18,851,700
3 9,735,000 7% 681,450 10,416,450
