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Int. J. Production Economics 112 (2008) 700– 713
Choosing a project risk-handling strategy: An analytical model
Miao Fan
a
, Neng-Pai Lin
b,
, Chwen Sheu
c
a
Department of Marketing and Logistics Management, Chihlee Institute of Technology, Taiwan
b
Graduate Institute of Health Care Organization Administration, National Taiwan University, Taipei, Taiwan
c
Department of Management, Kansas State University, Manhattan, KS 66506, USA
Received 1 September 2006; accepted 1 June 2007
Available online 10 July 2007
Abstract
Project risk management includes the process of risk identification, analysis, and handling (response). Risk handling/
response is the choice of a proper strategy to reduce the likelihood of the occurrence of risk events and/or the magnitude of
their negative impact. Research on risk handling is mostly opinion- or case-based and, as such, it offers scant guidelines for
making the decision. Managers often choose a risk-handling strategy based on their experience or preference toward risk,
with no consideration of project characteristics (e.g., project size, slack, or technical complexity) and the associated
financial implications. This study assumes that the choice of the risk-handling strategy should be aligned with unique
project characteristics. This study constructed a conceptual framework that defines the relationship between risk-handling
strategy and relevant project characteristics. A conceptual model was developed to describe the quantitative relationships
among all variables. Accordingly, optimization analysis is performed to derive a minimum-cost risk-handling strategy for a
particular risk event. The findings provide insights into how various project characteristics and risk situation affect the
choice of a risk-handling strategy.
r2007 Elsevier B.V. All rights reserved.
Keywords: Project management; Risk management; Conceptual modeling; Decision making
1. Introduction
A project is defined as a series of related activities
with a well-defined set of desired end results. Project
management is defined as planning, directing, and
controlling resources to achieve specific goals and
objectives. Most projects are not deterministic since
they are subject to risk and uncertainties due to
external factors, technical complexity, shifting
objectives/scopes, and poor management. The
purpose of risk management is to identify risky
situations and develop strategies to reduce the
probability of occurrence and/or the negative
impact of risky events. In practice, project risk
management includes the process of risk identifica-
tion, analysis, and handling (Gray and Larson,
2005). Risk identification requires recognizing and
documenting the associated risk. Risk analysis
examines each identified risk issue, refines the
description of the risk, and assesses the associated
impact. Finally, risk handling/response identifies,
evaluates, selects, and implements strategies (e.g.,
insurance, negotiation, reserve, etc.) in order to
ARTICLE IN PRESS
www.elsevier.com/locate/ijpe
0925-5273/$ - see front matter r2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.ijpe.2007.06.006
Corresponding author.
E-mail addresses: mfan2505@yahoo.com.tw (M. Fan),
nengpai@mail2000.com.tw (N.-P. Lin),csheu@ksu.edu
(C. Sheu).
reduce the likelihood of occurrence of risk events
and/or lower the negative impact of those risks to
an acceptable level. The risk-handling process
includes the documentation of which actions should
be taken, when they should be taken, who is
responsible, and the associated handling costs.
In general, among the three risk-management
functions, risk identification and analysis specify
and predict the likelihood and the adverse impact of
the risks, while risk handling/response is the phase
when management could take actions to reduce the
probability and/or magnitude of risks. In other
words, risk handling plays a proactive role in
mitigating the negative impact of project risks
(Kerzner, 2006;Miller and Lessard, 2001). Risk
handling is achieved by hiring experienced project
managers, providing up-front safety training, ac-
quisition of additional information, contracting for
missing skills, minimizing project scope changes,
etc. In the past, research concentrated more on risk
identification and analysis due to their relevance to
traditional financial and decision analysis. Despite
its importance, risk handling has not received due
attention in project risk research. Miller and
Lessard (2001) and Royer (2000) contended that
the risk-handling decision is frequently made with-
out considering project risk characteristics and
environment, which causes irrational management
behavior toward managing project risks. This study
develops an analytical model that defines the
mathematical relationship between project risk
parameters and risk event-handling cost. The model
should enable managers, at the planning stage of a
project, to select a minimum-cost risk-handling
strategy for a particular risk event. The next section
reviews previous studies pertinent to risk handling.
2. Literature review
The literature in project risk handling is limited to
opinion-based discussion and case studies that
illustrate the applications of various handling
strategies. For instance, Anderson (1969) discussed
the use of several strategies in reducing risk
associated with national defense projects. Baillie
(1980) reviewed a number of practical strategies to
reduce the risks and uncertainties inherent in R&D
projects. DSMC (1986) reviewed examples of risk
handling in weapon development projects, and Tsai
(1992) interviewed management in weapon devel-
opment projects and proposed seven risk-handling
strategies. Becker et al. (1999) surveyed more than
one hundred companies in the oil and gas industry
on the use of various risk-response techniques;
however, they did not explain their rationale for
selecting particular risk-handling techniques. In
order to define risk-response strategies, Royer
(2000) discussed the use of brainstorming sessions
with clients, project teams, and experts. Finally, the
Project Management Body of Knowledge (Project
Management Institute, 2004) provided a compre-
hensive review of various risk-handling strategies.
Overall, these studies reviewed and suggested
various risk-handling strategies in different types
of projects. However, there is no discussion of the
dimensions and characteristics of projects that are
critical to the choice of handling strategy. It is not
clear what variables impact the effectiveness of
various handling strategies in different projects, be
they R&D, construction, or new product develop-
ment. More specifically, decisions aimed toward
aligning handling strategy with unique project
characteristics, risks, and external environment have
not been addressed.
In practice, the choice of a specific risk-handling
strategy is contingent on the risk situation and the
project characteristics (Ala-Risku and Karakkai-
nen, 2006;Kwak and Stoddard, 2004;Miller and
Lessard, 2001;Royer, 2000;Lefley, 1997;Bromiley
and Curley, 1992). For example, management may
purchase insurance to buffer against earthquakes,
since the occurrence of the risk event cannot be
‘‘controlled’’ and the potential damage could be
financially disastrous. In another type of situation,
managers may choose to conduct a market survey
when additional information might be valuable in
reducing the probability of the occurrence of risk
events. Only a few studies have attempted to match
handling strategy with specific risk situation. March
and Shapira (1987) and Wehrung et al. (1988)
observed several risk situations (e.g., new product
development, overseas market development, pro-
duction facilities shutdown, and major customer
complaints) in the industry and found that the
choice of a risk-handling strategy was primarily
associated with the management’s attitude toward
risks and uncertainties. There was no consideration
of unique project characteristics and external
environment. Flanagan and Norman (1993) devel-
oped a framework for deciding on a risk-handling
strategy based on the likelihood of occurrence and
severity of the risks. Miller and Lessard (2001) used
the extent of control over risks to determine the
strategy of mitigating project risks. Fan et al.
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M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713 701
(2001), based on case studies of construction
projects, suggested that the choice of a risk-handling
strategy depended on the extent to which managers
were able to affect the probability of the occurrences
of risk events. However, it is not clear how manage-
ment should align risk-handling strategy with
unique risk situations and project characteristics.
In summary, previous studies discussed applica-
tions of various risk-handling strategies but offered
scant guidelines for choosing a strategy that
matches the characteristics of projects and risks.
Many managers often make risk-handling decisions
based on personal attitudes and preference toward
risk, which frequently results in irrational behavior
patterns (Royer, 2000). Jaafari (2001) suggested that
managers should improve risk handling by applying
a more holistic approach to evaluating risk-hand-
ling decisions and developing quantitative models
for integrating and evaluating risk-handling vari-
ables. This study develops an analytical model and
guidelines that may help managers assess the
effectiveness of various risk-handling strategies in
minimizing damages associated with risk events.
While the final choice of strategy may involve
managers’ attitudes toward risk, the model provides
managers a tool to aid in understanding the
financial implications of their decisions. The follow-
ing section develops a conceptual framework for
risk-handling decisions including relevant para-
meters of the decision. Two risk-handling cost
models are established to prescribe the theoretical
relationships among those parameters. Optimiza-
tion analysis of the cost models is then performed to
investigate the pattern of selecting risk-handling
strategies given specific project environment and
characteristics. Finally, the guidelines for making
risk-handling decisions are developed and future
research is suggested.
3. Model development
3.1. Problem definition
This study followed previous studies (Royer,
2000;Wehrung et al., 1988) and classified all risk-
handling techniques into two categories: risk pre-
vention and risk adaptation. Note the unit of
analysis in this project is ‘‘risk event’’, and both
techniques require taking actions to mitigate ex-
pected loss from risk events. Risk prevention refers
to actions taken in the planning stage to reduce the
probability of occurrence of risk events by acquiring
additional information, improving communication
with clients, hiring experienced project managers,
choosing more reliable contractors, etc. For exam-
ple, conducting a market survey could provide more
information on new product development and
thereby reduce the probability of product failure.
In contrast, an adaptation strategy refers to actions
implemented in the execution stage. The buffer and
reserve required by this strategy are usually planned
and prepared for through the project budget and
schedule so that managers can reduce the damage/
loss resulting from risk events. In contrast to risk
prevention, risk adaptation aims at alleviating and
reducing negative impacts resulting from the occur-
rence of risks. Examples of this strategy include the
purchase of insurance to cover for monetary losses,
the preparation of a budget reserve, searching for
backup suppliers, etc. Under this classification
scheme, the research question is defined as follows:
Given specific project characteristics and risk
situation, should risk prevention, risk adapta-
tion, or the combination of these two risk-
handling strategies be applied to minimize the
expected loss associated with a particular risk
event?
A conceptual framework is developed next to
identify relevant parameters and their relationships
with risk-handling decisions.
3.2. Conceptual framework
Assume that the probability of the occurrence of
event Eprior to risk handling is P
1
, and this
probability is reduced to P
2
(the posterior prob-
ability) after risk handling, P
2
pP
1
. Let L
1
be the
initial total loss from the occurrence of the event,
and this loss is reduced to L
2
after risk handling,
L
2
pL
1
. The expected loss (R
1
) prior to risk
handling is P
1
L
1
.Shapira (1998) argued that
managers implement risk handling when the current
risk level (R
1
) is not acceptable. The purpose of
project risk handling then is to reduce the level of
risk or expected loss from R
1
to an acceptable level
R
2
, where R
2
oR
1
and R
2
¼P
2
L
2
.(Table 1
provides the definition of all parameters used in
this study.)
Since risk prevention attempts to reduce the
probability of the occurrence of risk events, its
implementation results in P
2
oP
1
and L
2
¼L
1
. Risk
adaptation, on the other hand, alleviates losses from
the occurrence of risk events, and the implementa-
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M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713702
tion of a risk-adaptation strategy results in P
2
¼P
1
and L
2
oL
1
.Fig. 1 displays two isoquants, R
1
and
R
2
. Each curve represents numerous combinations
of probability (P) and loss (L) that would produce
the same level of expected loss (R¼PL). For
example, combinations of various P
2
and L
2
on R
2
(or AC) curve derive the acceptable risk level R
2
.
Theoretically, managers could use alternative risk-
handling options to reduce the expected loss from
the current level of R
1
(represented by point Y)to
an acceptable level R
2
. For example, managers
could choose a risk-adaptation strategy (indicated
by the path YA) to reduce the expected loss from the
original level Y(P
1
,L
1
)toA(P
1
,L
2
). The probability
of the occurrence of project risks remains the same,
while the magnitude of loss reduces due to the
action taken. Alternatively, managers could take the
risk-prevention option (path YC) to reduce the
likelihood of the occurrence of the risk event to the
new level C(P
2
,L
1
). Finally, the third risk-handling
option can be the combination of both risk-
prevention and adaptation strategies (path YB)to
reduce the expected loss from Yto B(P
b
,L
b
), where
P
2
pP
b
pP
1
,L
2
pL
b
pL
1
. In short, there are three
types of risk-handling strategies, YA,YC, and YB.
All three strategies reduce the expected loss to R
2
,
but their implementation requires different financial
resources and, thus, various levels of total costs.
Therefore, the risk-handling decision can be framed
as follows: What risk-handling strategy should
managers choose in order to reduce the expected loss
to an acceptable level at the lowest implementation
cost?
Fig. 2 is the conceptual framework that illustrates
the relationships among several key parameters in
the decision of risk handling. This conceptual
framework was developed based on the observation
from several large-scale construction projects (Fan
et al., 2006). Large-scale construction projects are
usually involved in enormous budgets over lengthy
schedules, and they typically consist of various risk
events including natural disasters, technical difficul-
ties, insufficient information, politics, etc. For the
purpose of this study, it is necessary to include risk
events with a wide range of controllability and
multiple events with the same level of controllability
across projects. The field study of those construc-
tion projects was also used as the base for
developing a mathematical model for risk handling
in this study. In this conceptual framework, risk-
handling strategy is defined as the means and
actions taken to reduce the level of risk. In practice,
the strategy that managers choose can be risk
prevention, risk adaptation, or a combination
of these two. This study assumes that the choice
of strategy is determined by three parameters:
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Table 1
Description of parameters
P
1
prior probability of the occurrence of the risk event
L
1
monetary loss from the risk event
R
1
expected monetary loss from the risk event ¼P
1
L
1
P
2
posterior probability of the occurrence of the risk event
L
2
monetary loss from the risk event with risk-handling
strategy
R
2
posterior expected monetary loss from the risk
event ¼P
2
L
2
kunit risk prevention cost
oproportion of uncertainty that cannot be reduced/
controlled under current technology or information,
0pop1
1ocontrollability of project risk
bamount of project slack, bX0
runit opportunity cost or interest rate, 0prp1
sunit crash cost, sX0
A
CY (R1=P1xL1)
B
Lb
P1
Loss (L)
L1
P2
L2
R2=P1xL2
R2=P2xL1
R1
PbProbability (P)
R2
Fig. 1. Risk-handling strategies: prevention, adaptation, and
mixed.
Controllability
of
Risk Event
Project
Characteristics
Risk
Handling
Costs
Risk
Handling
Strategy
Fig. 2. The conceptual framework.
M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713 703
controllability of project risk, risk-handling costs,
and project characteristics.
First, controllability of risk event refers to the
likelihood of changing the probability distribution
of the occurrence of the event (Miller and Lessard,
2001). This factor is used to define the nature of the
risk situation. A low degree of controllability is
often associated with risk events such as natural
disasters (e.g., hurricane and earthquake) or eco-
nomic conditions (e.g., fluctuations of inflation and
exchange rates), where little can be done to change
the probability of occurrence. In contrast, risk
events with a high degree of controllability are
often associated with technical, scheduling, and
budget problems, which are easier (but not necessa-
rily less expensive) to resolve compared with natural
disasters. For example, the risk of receiving a late
delivery of components can be reduced by a careful
selection of reliable suppliers. Therefore, the level of
controllability of project risk could affect the choice
of a risk-handling strategy (Gray and Larson, 2005;
Miller and Lessard, 2001). Intuitively, managers
would adopt a risk-prevention strategy for a project
with high levels of controllability, while a risk-
adaptation strategy is more appropriate for a
project with low levels of controllability. Table 2
lists some combinations of level of controllability
and probable choice of risk-handling strategy based
on observations from several major construction
projects and the literature (Fan et al., 2001;Jaafari,
2001;Miller and Lessard, 2001). Many of those
handling strategies can be adopted as contractual
agreements but the choice of a specific strategy in
relation to project characteristics could be challen-
ging. While the choice is clear in the two extreme
levels of controllability, the choice becomes less
obvious for those risk events involving a medium
range of controllability. Specifically, managers can
choose either one of the two strategies or the
combination to handle risk when the level of
controllability is neither extremely high nor low. It
is likely that the costs required to handle risk events
would ultimately determine the choice of a specific
handling strategy in a ‘‘non-extreme’’ situation.
Project characteristics include project size, tech-
nological complexity, level of schedule slack, and
external economic and political factors. Those
characteristics could affect the cost of different
actions and, in turn, affect the choice of handling
strategy. For example, collecting information and
surveying the reliability of contractors improve the
selection decision and is a possible option to reduce
the likelihood of late completion, but the cost of a
survey is likely to be higher in a more technically
complicated project. In addition, a project with
more slack time is more capable of buffering against
schedule delay due to risk events. Politics also plays
a major role in project risk (Al-Tabtabai and Alex,
2000). A nuclear plant construction project is likely
to involve government regulations and environmen-
ARTICLE IN PRESS
Table 2
Project risk controllability and risk-handling strategy
Risk event Controllability Specific risk-handling actions Type of risk-
handling strategy
Acts of God: earthquake, flood,
hurricane, etc.
Low Purchase insurance coverage Risk adaptation
Fluctuations of exchange rate Low Prepare contingency fund Risk adaptation
Occurrence of inflation Low Prepare reserve Risk adaptation
Acquisition of land that involves
relocating residents
Medium Provide residents with substantial
subsidies
Risk adaptation
Failure of on-time completion by
subcontractors
Medium Perform more strict subcontractor
selection
Select a second contractor
Risk prevention
Risk adaptation
Alternation of project specifications/
scope
Medium Enhance control and communication
Set up contingency plan and provide
design flexibility
Risk prevention
Risk adaptation
Underground barriers High Conduct more thorough underground
investigation
Risk prevention
Integration of entire mass transportation
systems
High Subcontract to one single bidder Risk prevention
M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713704
tal policies, which require more communication
among various parties and, therefore, results in
higher risk-handling costs. In general, depending on
the characteristics of a project, a specific risk-
handling strategy involves different amounts of
handling costs.
Risk-handling cost is defined as the expenses
incurred in implementing a selected strategy that
would reduce risks to an acceptable level. This study
assumes that handling costs are a function of the
controllability of risk and project characteristics.
Fig. 2 shows that controllability affects the selection
of handling strategy in two ways. Low controll-
ability implies higher handling costs but for a risk
event with high controllability it may still be too
expensive to prevent its occurrence. Moreover,
extremely high or low controllability usually implies
the application of a prevention or adaptation
strategy (see Table 2). Consequently, given a
particular risk event, a risk-handling strategy, be it
prevention, adaptation, or mixed, is chosen based
on the controllability of the event as well as the
associated handling cost. Specifically, managers
favor a handling strategy with a lower implementa-
tion cost, and the decision is also made considering
the level of controllability.
Note that utility theory would suggest that
managers will take the output of the model in Fig.
2and make their final decision by incorporating the
decision-maker’s attitude toward risk (Holloway,
1979). In other words, managers will compare the
cost of the cheapest handling strategy (the output of
this model) with the reduction of expected loss. In a
situation where the cost outweighs the benefit, a risk
taker will choose not to take any action, while a risk
averter may still choose to implement a handling
strategy. The remainder of this section pro-
vides mathematical definitions of project character-
istics, controllability, and handling costs. Accord-
ingly, this study develops a mathematical model
that would determine a minimum-cost handling
strategy.
3.3. Risk-handling cost model
Since a risk-handling strategy involves the possi-
ble application of risk prevention and/or risk
adaptation, the total risk event-handling cost (TC)
is, therefore, the sum of the two types of cost,
risk-prevention cost (C
P
) and risk-adaptation
cost (C
L
).
3.3.1. Risk-prevention cost (C
p
) function
Recall that the purpose of risk handling is to
reduce the level of risk or expected loss from R
1
to
R
2
, where R
2
oR
1
and R
2
¼P
2
L
2
. The imple-
mentation of a risk-prevention strategy results in
P
2
oP
1
and L
2
¼L
1
. Prevention cost (C
p
)isa
function of P
2
with the following properties and
assumptions:
C
p
increases with the decrease of P
2
. It costs to
reduce the probability of the occurrence of a risk
event.
When P
2
¼P
1
,C
p
¼0. No handling cost is
incurred when the prior probability is equal to
the posterior probability.
MC
p
represents the marginal prevention cost, or
the slope of C
p
.MC
p
is negative due to the
inverse relationship between C
p
and P
2
.AsP
2
approaches a small value (the posterior prob-
ability of occurrence of the event becomes
extremely small), the marginal cost becomes
extremely large, or MC
p
approaches N. In other
words, it becomes more expensive to reduce the
probability of occurrence further when the
probability is already low.
krepresents unit prevention cost where k40. kis
a measure of the difficulty or complexity of
reducing risks by either obtaining additional
information or overcoming technical and politi-
cal obstacles. For a given P
1
and P
2
, a larger kis
related to a larger C
p
and a smaller MC
p
(or
larger absolute value of MC
p
).
C
p
is also related to the level of controllability of
project risks, 1o, where ois the proportion of
uncertainty that cannot be reduced/controlled using
current technology or information and 0pop1.
Fig. 3 illustrates the concept of 1oand o. The
ARTICLE IN PRESS
P1 = prior probability of the occurrence of the risk event.
P2 = posterior probability of the occurrence of the risk event.
0P1
Uncertain &
Uncontrollable
Uncertain but can be removed with
risk handling strategy
P2
1 – = the level of controllability of the risk event
Fig. 3. Level of controllability, P
1
¼prior probability of the
occurrence of the risk event. P
2
¼posterior probability of the
occurrence of the risk event. 1o¼the level of controllability of
the risk event.
M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713 705
proportion P
1
ois the amount of project un-
certainty that can be feasibly removed, while P
2
o
represents the amount of uncertainty that is
technically removable but is not removed with a
specific handling strategy. A large value of oimplies
a low degree of controllability and, thus, a high
value of MC
p
. Overall, MC
p
can be defined as a
function of P
2
,o, and k:
MCp¼k
ðP2oÞ. (1)
The risk-prevention cost, C
p
, then is the integral
of MC
p
from P
1
to P
2
,or
Cp¼ZP2
P1
MCpdP2¼ZP2
P1
k
ðP2oÞdP2¼kln P1o
P2o
.
(2)
3.3.2. Risk-adaptation cost (C
L
) function
A risk-adaptation strategy intends to reduce loss
resulting from risks. There are two types of loss,
monetary loss (m) and schedule delay loss (t). In the
case of monetary loss, the purpose of risk adapta-
tion is to maintain a ‘‘buffer’’ to absorb the whole
or partial loss associated with risk events. The
buffer approach is similar to the concept of
‘‘organizational slack’’ with the purpose of increas-
ing the effectiveness of adapting to external
environmental uncertainties (Bourgeois, 1981;Gray
and Larson, 2005). The risk-adaptation cost is
treated as the opportunity cost associated with the
provision of such a buffer. For instance, when
insurance is used as a risk-adaptation strategy, the
associated premium is the adaptation cost, and the
insurance coverage is the buffer prepared to deal
with the potential loss. Alternatively, we can
establish a management reserve to reduce the
impact of risk events (Gray and Larson, 2005).
The literature suggests a linear relationship between
the opportunity cost and the amount of potential
loss, and rate of investment can be used as the
estimation of C
L
(Baumol, 1977).
In the case of loss due to schedule delay, the
adaptation cost is estimated based on the concept of
slack (b)(Stigler, 1961;de Vonder et al., 2005).
Depending on the amount of slack in the project,
the cost of establishing a time buffer varies. This
concept is similar to project compression where the
unit crash cost increases as the degree of crash
intensifies (Kerzner, 2006). In other words, the
handling (crash) cost increases exponentially with a
decrease in slack. The risk-adaptation cost (C
L
) has
the following properties and assumptions:
(1) C
L
increases with the decrease of L
2
.
(2) When L
2
¼L
1
,C
L
¼0.
(3) In the case of monetary loss, the marginal
adaptation cost (MC
L
) is a constant r, the rate
of return on investment or insurance premium.
The risk-adaptation cost (C
L
) function is
CL¼rðL1L2Þ. (5)
(4) In the case of time delay loss, the marginal cost
of compressing a project schedule is lower when
there is more slack time in the project. Assuming
that sis the unit crash cost and that it increases
exponentially with the decrease of b(the amount
of slack), bX0. The marginal cost function is
MCL¼sebL2;s40. (6)
When L
2
¼0, MC
L
¼s, which indicates
that s, the absolute value of MC
L
, is the
marginal cost to absorb the last unit of possible
time delay. bis the amount of slack in the
project and the less er the slack the higher the
crash cost (sand |MC
L
|). Therefore, the
risk-adaptation cost function for time delay
loss can be defined as CL¼RL2
L1MCLdL2¼
RL2
L1seb‘dL2and
CL¼s
bebL2ebL1
. (7)
3.3.3. Risk-handling cost (TC)
Given any particular risk event, its risk-handling
cost (TC) includes risk-prevention and risk-adapta-
tion costs or TC(P
2
,L
2
)¼C
P
+C
L
. This study
assumes that risk events result in one of the two
losses, monetary or schedule. Therefore, with the
prevention cost function (Eq. (2)) and two adapta-
tion cost functions (Eqs. (5) and (7)), we generated
two TC functions as follows:
TC1¼kln P1o
P2o
þrðL1L2Þ, (8)
TC2¼kln P1o
P2o
þs
bebL2ebL1
. (9)
These two cost functions are then used to perform
an optimization analysis to identify the optimal
level of P
2
and the minimum-cost handling strategy
given the specific sets of risk situation (o), project
characteristics, and handling costs (k,r,s,b), and
the desired risk level (R
2
).
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M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713706
4. Optimization analysis
The primary purpose of this study is to identify
an optimal strategy to reduce project risk from the
current level R
1
to an acceptable R
2
with minimum
cost as indicated by the following model:
Min TCðP2;L2Þ
s:t:P2L2¼R2.
Let p¼P
2
,l¼L
2
,m¼R
2
/R
1
, and 0pmp1. The
above model can be rewritten as
Min TCðp;lÞ
s:t:pl ¼mR1
0pppP
1
;0plpL
1
;0pmp1.
Since l¼mR
1
/p,TC(p,l)¼TC (p,mR
1
/p).
Therefore, TC can be regarded as the function of
pand mP
1
pppP
1
. Mathematically, we can take the
first and second derivative of TC (p,mR
2
/p)tofind
the ‘‘optimal’’ acceptable risk level p* that would
minimize the risk event-handling cost in the
restricted domain [mP
1
,P
1
]. Note that p*is
associated with the optimal combination of para-
meters (o,r(or s), band k) that would provide the
lowest cost to reach R
2
. As illustrated in Fig. 1,we
can classify various risk-handling strategies into
three categories:
(1) Risk prevention (YC), where p*mP
1
.
(2) Risk adaptation (YA), where p*P
1
.
(3) Mixed strategy (YB), where mP
1
op*oP
1
.
The process and result of the cost optimization
analysis for those two cost functions (Eqs. (8) and
(9)) are presented in Appendix A. Table 3 sum-
marizes the findings of the analysis. In short, the
values of oand rR
2
/k(or sR
2
/kin the case of TC
2
)
determine the optimal pvalue (p*). A high rR
2
/k
value implies high opportunity cost (large r), large
project scale (R
2
), or a low prevention cost (small k).
When rR
2
/kis large, p* approaches the lower bound
of the solution domain mP
1
, implying the selection
of a prevention strategy. On the other hand, when
rR
2
/kis small, p* approaches the upper bound of
the solution range, P
1
,orp* ¼P
1
, which implies the
selection of an adaptation strategy. Nonetheless, the
effect of rR
2
/kon the location of p* is also affected
by the value of o. When ois extremely large
(extremely low controllability), p* always equals P
1
regardless of the value of rR
2
/k.Asodecreases, p*
shifts from the upper bound (P
1
) to the middle of
the domain (mP
1
op*oP
1
) and finally to the lower
bound (mP
1
). Such movement of p* implies switch-
ing from an adaptation to a mixed and then to a
prevention strategy. This result is consistent with
the previous observations presented in Table 2.
When ois not extremely large, rR
2
/khas greater
impact on the value of p*. A large rR
2
/kpushes p*
toward mP
1
(prevention), while a small rR
2
/kmoves
p* toward P
1
(adaptation). The remainder of this
section discusses the managerial implications of the
effects of oand rR
2
/kon p*, or the selection of a
project risk-handling strategy.
4.1. The value of controllability (1o)
When o(the level of uncertain and uncontrol-
lable proportion) has a large value (i.e., 1ois
small and the degree of controllability is low), its
effect on the choice of risk-handling strategy
dominates that of other parameters (r,s,k,R
2
).
For example, it is unlikely that managers are able to
do anything to reduce the probability of the
occurrence of acts of God. Therefore, the likely
strategy to be implemented is risk adaptation, such
as purchasing insurance coverage to reduce the
negative impact of risk events. As obegins to
ARTICLE IN PRESS
Table 3
Results of optimality analysis
Cost function Results
TC
1
(Monetary)
1. rR
2
/kp4o
The optimum solution locates at right extreme of
[mP
1
,P
1
], or P
1
, which implies the selection of a
risk-adaptation strategy.
2. rR
2
44ko
(a) When ois extremely large (extremely low
controllability), p*¼P
1
regardless of the
value of rR
2
/k, i.e., adaptation strategy is
chosen.
(b) As odecreases, p* can be found between mP
1
and P
1
but not at the two extremes, which
implies a mixed strategy. As odecreases even
more (controllability increases), rR
2
/kbegins
to have more impact on the value of p*. A
large rR
2
/kmoves p* toward mP
1
(prevention),
and a small rR
2
/kpushes p* toward P
1
(adaptation).
TC
2
(Time
delay)
1. When bapproaches 0, TC
2
TC
1
.
2. When bis greater than a threshold value, p*
approaches upper bound P
1
.
M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713 707
decrease (project controllability increases), preven-
tion or a combination of the two strategies becomes
more probable. Various project characteristics (rR
2
/
kor sR
2
/k) are then assessed to determine a
minimum-cost risk-handling strategy.
4.2. The value of rR
2
/k (or sR
2
/k)
Note that the term rR
2
/k(or sR
2
/k) represents the
project characteristics in terms of project size,
complexity, financial, and project slack situations.
Table 4 summarizes the practical implications of
these parameters using examples from several
construction projects. First, kis the unit cost of
reducing the probability of the occurrence of risk
events, which is a surrogate of the difficulty of
reducing risks by obtaining additional information
or the complexity of overcoming technical obstacles.
A larger kvalue indicates a higher cost of risk
prevention, which encourages the selection of a risk-
adaptation strategy. Next, r(or s) represents the
cost of creating a monetary (or time) buffer for risk
uncertainty. A small value of r(or s) (e.g., insurance
premium, monetary reserve, and crashing cost) is
equivalent to a low adaptation cost. Finally, R
2
represents the acceptable expected loss by decision-
makers. Managers who are risk-seekers may be
willing to set a relatively high R
2
level, while risk-
averters will choose a lower R
2
level. Moreover, the
value of R
2
is likely to be associated with the size of
projects as well. The expected loss on large-scale
projects is high and managers would accept a larger
R
2
than on small projects. Thus, managers are more
inclined to choose a risk-prevention strategy to
reduce the damage of risk events when the project
scale and the expected loss are large.
Overall, a high rR
2
/kvalue implies a relatively
high adaptation cost and the preference of a
prevention strategy. When there is a high crashing
cost (large s), a high opportunity cost (large r), a
large project scale (R
2
), or a low prevention cost
(small k), rR
2
/kis large and risk prevention is a
more economical option. In contrast, a risk-
adaptation strategy is associated with low crashing
cost, low opportunity cost, small project scale, and
high prevention cost. Fig. 4 displays the general
pattern of risk-handling decisions with regard to the
values of rR
2
/kand o. A risk-prevention strategy is
chosen (see zone 1) with large values of rR
2
/kand
small o, which represents a combination of high
controllability, high crashing cost (large s), high
opportunity cost (large r), large project scale (R
2
),
or low prevention cost (small k). If controllability is
low, prevention cost is very high, and crashing and
opportunity costs are low (see zone 3), a risk-
adaptation strategy is selected. Moreover, when the
level of controllability is extremely low, the effect of
project characteristics becomes less significant, and
ARTICLE IN PRESS
Table 4
Parameters of project characteristics
Project characteristics Implications Parameter
1. High level of technological
complexity involved in the
project
Difficult to obtain
information
Large k
value
Difficult to handle
obstacles
encountered
2. High level of involvement by
various parties
Difficult to
communicate or
resolve conflicts
Large k
value
3. Weak technical background
or lack of expertise and
experience in project team
Difficult to deal with
unexpected events
Large k
value
4. Companies are undertaking
many similar projects
simultaneously
Tight financial
situation
Large r
value
5. Benign environment with
little political interference,
flexible regulations and
favorable economy
More project
execution flexibility
Low rand
svalues
More financial
resources and time
buffers
6. Tight project schedule Little time slack Large s
value
7. Large project scale High expected project
risk loss
Large R
2
value
Zone 3:
Risk Adaptation
Zone 1:
Risk Prevention
Zone 2:
Mixed
Strategy
High ←Controllability →Low
Project Characteristics
rR2/k
Fig. 4. Choice of risk-handling strategy (*zones can be defined
using Eqs. (A1) and (A2) in Appendix A).
M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713708
a risk-adaptation strategy is always preferred.
Managers are more likely to purchase insurance to
buffer potential loss against catastrophes such as
earthquakes and floods. Finally, in the situation
where the controllability of the project is not clear
(i.e., is not at either extreme; see zone 2), the mixed
strategy could be adopted to minimize the total
handling cost.
The result of the optimization analysis of TC
2
also indicates that an adaptation strategy is
preferred when there is a high level of slack (b)
available.
5. Numerical example
The purpose of this section is to exemplify how
the mathematical model (Eq. (8)) and the decision
model (Fig. 4) could enable managers with risk-
handling decision-making. As both the mathema-
tical and the decision models indicate, managers
need three parameters, R
2
,k, and r, to select an
optimal handling strategy. We use the ‘‘under-
ground barrier’’ risk event in Table 2 as an example
to illustrate the application of the proposed models.
Suppose the a priori probability of damaging
underground cables (P
1
) is 0.5, and the cost to
remove the barriers and compensate for the damage
is $100,000, the expected loss (R
1
) would be $50,000
or 0.5 $100,000. If managers intend to reduce the
expected loss by 50% to achieve a targeted level of
R
2
¼$25,000, the following three options are
available.
5.1. Prevention strategy (YC in Fig. 1)
Since P
2
¼P
1
0.5 ¼0.25 and L
2
¼L
1
, the total
risk-handling cost can be computed using Eq. (8).
TC ðpreventionÞ¼kln 0:50
0:25 0
þrð0Þ¼0:7k.
Note that the kvalue represents the cost of
obtaining additional information to reduce the level
of uncertainty, and it can be estimated indirectly in
practice. In this example, reducing the probability
of encountering underground barriers to 25% can
be achieved through gathering additional informa-
tion such as the map of the current underground
cable or water pipe network. The cost involved
would be the fee of acquiring the cable/pipe network
information from the city government and any
associated administration cost. In reality, gathering
such information would not be huge. Suppose the
cost is $500, then the total handling cost of the
prevention strategy would be 0.7($500) or $350.
5.2. Adaptation strategy (YA in Fig. 1)
With an adaptation strategy, P
2
¼P
1
¼0.5 and
L
2
is reduced from the original level (L
1
¼$100,000)
to $50,000 (or $25,000/0.5) in order to reach the
targeted R
2
level. Therefore, the total risk-handling
cost is
TC ðadaptationÞ¼klnð1Þþrð100;000 50;000Þ¼50;000r.
Managers can provide contingent reserve or
purchase insurance to reduce the expected loss to
L
2
¼$50,000. The cost of both options is related to
the opportunity cost of the premium rate. While the
exact insurance fee may depend on the nature of the
construction and the technical complexity of opera-
tions, such information is available in reality. A rate
of 1% would result in the handling cost of
TC ¼50,000(0.01) or $500.
5.3. Mixed strategy (YB in Fig. 1)
Under this strategy, the manager can find various
combinations of P
2
and L
2
that would result in the
targeted level of R
2
, $25,000. Taking the pair of
P
2
¼0.4 and L
2
¼$62,500 as an example, we can
compute the upper bound of the handling cost
assuming that kand rremain the same.
TC ¼500 lnð0:5:=0:4Þþ0:01ð100;000 62;500Þ¼$485.
Consequently, the prevention strategy has the
lowest cost ($350) to achieve the lower level of
expected loss (R
2
¼$25,000).
Continuing with this numerical example, we can
further illustrate the practical relevance of the
decision model in Fig. 4 by analyzing the interac-
tions between R
2
,k, and r. If managers attempt to
achieve an even lower R
2
level such as #5000, then
the total cost for the three options with the same k
and rvalues are $1151 (prevention), $900 (adapta-
tion), and $1208 (mixed), respectively. Therefore,
adaptation becomes the most economical risk-
handling strategy. This finding is consistent with
the behavior of the decision model in Fig. 4, where
an adaptation strategy becomes more attractive
when R
2
becomes small. Alternatively, if it requires
both cable network information and further under-
ground investigation to reduce the probability of
damaging underground cable networks, the value of
ARTICLE IN PRESS
M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713 709
kincreases and both the cost model and the decision
model would indicate the preference of adaptation
strategy.
Finally, assuming that the construction project is
technically complex and the insurance fee or the
cost providing contingent reserve is high, the
opportunity cost could increase to 4%. Keeping
R
2
and kunchanged, the total cost of the three
handling strategies becomes $1151 (prevention),
$3600 (adaptation), and $3458 (mixed), respectively.
Therefore, the manager could select prevention as
the best risk-handling strategy, which is again
consistent with the suggestion from the decision
model in Fig. 4. What is worth noting is the
feasibility of estimating the values of those para-
meters in practice.
In summary, this numerical example is used to
demonstrate the practical relevance of the proposed
cost model and the decision model in Fig. 4. Note
that PMI (2004) also offers the following sugges-
tions for assessing risk-related parameters.
Risk can be assessed in interviews or meetings
with participants selected for their familiarity
with risk categories on the agenda. Project team
members and, perhaps, knowledgeable persons
from outside the project, are included. Expert
judgment is required, since there may be little
information on risks from the organization’s
database of past projects.’’ (Project Management
Body of Knowledge, 2004, p. 251)
Namely, if the parameters are not readily avail-
able, expert judgment can be a reliable source for
assessing their values.
6. Conclusions
Despite its importance to the success of project
management, risk management is rarely approached
with the same rigor as other project management
processes such as project scope and scheduling. The
lack of a systematic approach in making the risk-
handling decision has contributed to irrational
behavior patterns managers exhibit to fend off the
impact of project risks (Royer, 2000). It is suggested
that the development of quantitative models for
integrating and evaluating risk-handling variables is
necessary to improve risk handling and, therefore,
risk management (Stewart and Fortune, 1995).
This study establishes a conceptual framework
for risk-handling decisions, which defines relation-
ships among risk-handling strategy, project char-
acteristics (project size, slack, unit prevention cost),
and risk situation (level of risk controllability). We
developed a mathematical model of risk-handling
(prevention and adaptation) costs and performed an
optimality analysis to determine the minimum-cost
strategy. The primary purpose is to enable man-
agers, at the planning stage of a project, to quantify
relevant parameters, to rationalize and analyze
alternatives, and to select a particular risk-handling
strategy that could minimize handling cost for a
particular risk event. Theoretically, this study
contributes to the development of the conceptual
framework of risk-handling decisions (with identi-
fication of important project risk parameters), risk-
handling cost models, and the relationship between
the optimal handling strategy and project charac-
teristics and risk situation. Managerially, we pro-
vided guidelines for selecting a minimum-cost risk-
handling strategy that would reduce the risk of an
event to an acceptable level, given a set of project
characteristics and risk situation. No longer will
managers make a risk-handling decision based
simply on their attitude toward risks without
considering unique project characteristics, risk
situation, and cost implications. The following is a
summary of the guidelines developed:
(1) When the complexity of a project (defined as
ease of conducting internal and external com-
munication among parties, obtaining necessary
information, keeping project specifications/
scope intact, etc.) is low and the unit prevention
cost is low, a risk-prevention strategy is pre-
ferred.
(2) When the project team has strong management
skills (e.g., complete information network,
strong project experience and ability), the ability
to reduce the prior probability of risk is high.
Therefore, the unit prevention cost is likely to be
low, and a risk-prevention strategy gives lower
cost.
(3) For a specific risk event, the larger the project
scale, the more likely risk a prevention strategy
will be adopted to minimize total cost.
(4) When financial resources are sufficient and the
likelihood of increasing project budget is high,
the unit cost of monetary reserve is low, and
thus a risk-adaptation strategy is preferred.
(5) For projects with little slack and high pressure
for on-time completion, the unit cost of crash is
high, and a risk-prevention strategy is preferred.
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M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713710
A few issues may limit the generalization of the
results. First, all the project characteristics (R
2
,r,s,
and k) in the risk-handling cost models were
identified, analyzed, and discussed based on ob-
servations from a few major construction projects
and previous project management literature. While
the literature supported the selection of those
parameters in defining project characteristics, it is
not clear whether any other critical parameters were
missed in the analysis. Practitioners have suggested
managing different types of projects differently.
While all cost models were developed without
assuming a specific type of project, the effects of
parameters in other types of projects, such as R&D,
need further study. Case studies in other industries
are necessary to confirm the significance of those
parameters to the decision of risk handling. Future
research must collect empirical data to confirm the
significance of those parameters and to verify the
proposed framework and the cost model.
Another limitation of this study is related to the
estimation of model parameters. The values for
most of the parameters in risk management are
derived from estimation (Project Management
Institute, 2004). Nonetheless, Pender (2001) and
Zahir et al. (2002) suggested that traditional use of
the probability theory is insufficient to estimate the
values of risk-management parameters, and the
theory of fuzzy set should be applied to produce the
estimation. In reality, quantifying the variable
controllability would not be a trivial task. We
suggest that the estimate of controllability be made
based on P
1
and P
2
, the prior and posterior
probability of the occurrence of the risk event.
Both P
1
and P
2
have been used in project risk-
management research, and the difference of those
two values would be an estimate of controllability.
Considering the importance of including the con-
cept of controllability as suggested by the literature,
future studies should investigate the estimation of
this variable.
Finally, it is worthy of note that the decision
framework in Fig. 2 can be extended by including
the comparison of the best cost of risk-handling
strategy and the reduction of reduced expected loss.
With such cost–benefit comparisons, the final risk-
handling decision will be made based on a
manager’s utility function, or the attitude toward
risk (Holloway, 1979). In this case, the proposed
framework in Fig. 2 and the cost analysis provide
valuable quantitative information for making the
risk-handling decision based on utility theory.
Appendix A. Optimization analysis
A.1. Optimization analysis for TC
1
Substitute l¼R
2
/pto Eq. (8) and
TC1 ¼kln P1o
P2o
þrðL1L2Þ.
To minimize the level of TC
1
within the close
domain [mP
1
,P
1
] we can take the derivative of TC
1
with respect to p.
dTC1¼k
poþrR2
p2¼kp2þrR2prR2o
p2ðpoÞ.
The determinate coefficient of kp2þrR2p
rR2ois rR
2
4ko. Given the value of rR
2
4ko,
TC
1
can be solved as
1. rR
2
4kop0 and dTC
1
p0. TC
1
is, therefore,
decreasing, and p* equals the upper bound of
[mP
1
,P
1
], or P
1
.
2. rR
2
4ko40-Solving for dTC
1
and p¼
rR2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rR2ðrR24koÞ
p=2k:Let p1¼rR2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rR2ðrR24koÞ
p=2kand p2¼rR2þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rR2ðrR24koÞ
p=2k.
Since d
2
TC
1
(p*
1
)X0 and d
2
TC
1
(p*
2
)p0, TC
1
is
convex at p*
1
and concave at p*
2
. Mathematically,
the minimum level of TC
1
is determined by the
relations among p*
1
,p*
2
,mP
1
, and P
1
. There are a
total of six possible relations: p*
1
XP
1
,mP
1
o-
p*
1
oP
1
pp*
2
,mP
1
op*
1
op*
2
pP
1
,p*
1
om-
P
1
oP
1
pp*
2
,p*
1
omP
1
op*
2
pP
1
,p*
1
op*
2
omP
1
p
P
1
.Fig. 5 displays the location of the optimal
solution in these six possible cases. In any case, the
optimal solution or the lowest TC
1
level is located
between the boundaries of p*
1
¼P
1
and p*
1
¼mP
1
.
(Note that p*
1
pp*
2
.) Since this study is interested in
investigating the effect of project characteristics
(defined by r(or s), R
2
, and k), P
1
and mP
1
are
rearranged as follows:
p1¼rR2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rR2ðrR24koÞ
p2k¼P1)rR2
k¼P2
1
P1o,
(A1)
p1¼rR2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rR2ðrR24koÞ
p2k¼mP1)rR2
k¼m2P2
1
mP1o.
(A2)
Using Eqs. (A1) and (A2), we can then generate
various combinations of rR
2
/kand o, given a
ARTICLE IN PRESS
M. Fan et al. / Int. J. Production Economics 112 (2008) 700–713 711
specific P
1
value. Accordingly, we can develop the
pattern of risk-handling strategy selection as dis-
played in Fig. 4, where rR
2
/kand oare treated as
vertical and horizontal axes, respectively.
A.2. Optimization analysis for TC
2
Substitute l¼R
2
/pto Eq. (9) and
TC2¼kln P1o
po
þs
bðebR2=pebL1Þ
dTC2¼k
poþsR2
p2ebR2=p.
We can simulate the values of parameters in TC
2
and derive the following findings.
1. When b0,
TC2¼lim
b!0kln P1o
po
þs
bðebR2=pebL1Þ
¼kln P1o
po
þlim
b!0
s
bðebR2=pebL1Þ
.
Since lim
b!0
s
bðebR2=pebL1Þ
¼sL
1R2
p
,
TC2¼kln P1o
po
þsL
1R2
p
.
Other than replacing rby s, this cost function
is the same as TC
1
in Section A.1 of Appendix A.
Therefore, the result of the optimality analysis
for TC
2
will be the same as TC
1
.
2. When b40, the optimal value approaches P
1
.
The implication is that adaptation strategy is
preferred when there is a high level of organiza-
tional slack available.
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ARTICLE IN PRESS
p2*
p1*
p2*
p1*
p1*
p2*
p1*
P1
P1
C6
C5
C4
C3
C2-2
C2-1
C1
P1≤p1*
(Optimal→P1)
p2*
p1*
p2*
p1*
p2*
p1*
p2*P1< p1* < P1≤p2*
(Optimal → between
P1 & P1)
P1< p1* < p2*≤P1
(Optimal → between
P1 & P1)
p1*< P1< P1≤p2*
(Optimal → P1)
p1*< P1<p2*≤P1
(Optimal → P1)
p1*< P1 < p2*≤P1
(Optimal→ P1)
p1*< p2*< P1≤P1
(Optimal → P1)
Fig. 5. Six possible locations of the optimal solution of TC
1
.
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