Resource-constrained construction project scheduling model for proﬁt maximization
considering cash ﬂow
, Chang-Jung Wang
Department of Construction Engineering, National Yunlin University of Science and Technology, No. 123, Section 3, University Road, Touliu, 640, Taiwan, ROC
Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology, No. 123, Section 3, University Road, Touliu, 640, Taiwan, ROC
Accepted 7 April 2008
Resource-constrained project scheduling
Regarding project scheduling problems, resource-constrained issue is generally considered essential for
contractors as a means. Researchers have thus devoted considerable efforts to investigating this issue over the
past decade. Furthermore, since adequate cash ﬂow management beneﬁts cost control and assists proﬁt
acquisition for contractors, numerous techniques have recently been developed for project scheduling in
situations involving cash ﬂow. However, most of these studies simpliﬁed resource utilization, and assumed that
cash out ﬂows are directly related to activities without considering resource usage. Fundamentally, resources
incur activities' costs, project cash ﬂow, which conforms to resource utilization. It is thus regarded as a main
issue in this study. This study establishes a resource-constrained project scheduling model based on constraint
programming, whose solution can be found by using combinatorial optimization algorithms. The proposed
model integrates the issues involving resource-constrained problems and cash ﬂow, and maximizes net project
cash ﬂow to optimize project proﬁt from the perspective of contractors. Model validation and two scenarios,
including multi-resource, resource combination selection, and various constraints such as resource limit, are
performed to demonstrate the model capability and applications. Contractors thus can evaluate appropriate
project schedules under associated constraints, and arrange activities and resources to maximize project proﬁt.
© 2008 Elsevier B.V. All rights reserved.
Numerous researches have examined scheduling problems in an
attempt to achieve optimization of project cost or total duration under
various constraints, such as in situations where resources are limited. One
of main issues related to project scheduling focuses on resource utilization
in a resource-constrained environment to arrange activities for project
objective attainment. Resource usage involves the implementation of
resource allocation, resource leveling, or time-cost trade-off to boost
project performance. Therefore, many studies have discussed ways of
enhancing resource utilization under speciﬁed constraints, such as
contract date or resource limit, and these studies have employed various
techniques for project duration or total cost minimization.
For project scheduling problems, resources are utilized in accor-
dance with activity requirement and implementation time, and
relevant cash ﬂow are generated in construction. That is, resource
usage for activity execution indicates contractors' expenses during
construction, and represents related cash out on project cash ﬂow. On
the other hand, since over 60% of construction contractor failures have
ﬁnancial causes , ﬁnancial aspects of project scheduling recently
have received considerable attention. Various ﬁnancial factors, such
as interest rate, payment condition, and credit limit, not only affect
project cash ﬂow, but also inﬂuence the amount and timing of resource
usage. Therefore, considering scheduling problems with resource
usage and cash ﬂow beneﬁts project objective such as proﬁt maximi-
zation by arranging resources and activities properly, and generates a
reliable cash ﬂow forecasting plan to avoid project ﬁnancial failure.
This study proposes a novel optimization model for solving con-
struction resource-constrained project scheduling problems consider-
ing cash ﬂow, by adopting Constraint Programming (CP) techniques.
The proposed model integrates resource constraints and cash ﬂow
management issues, and maximizes net cash ﬂow to optimize project
proﬁt from the contractors' perspective. Multi-resource usage and
resource combination selection are incorporated in the proposed
model, and cash ﬂow and related ﬁnancial factors are also involved.
Moreover, two scenarios with various resource limits and credit limits
are conducted and illustrated to demonstrate model applications.
2. Cash ﬂow to construction projects
Cash ﬂow consists of the ﬂows of cash into and out of a business
; typical cash out ﬂows on a construction project include interest,
material, labor cost, etc., and cash in ﬂows include various payments,
such as bonuses. Numerous approaches have been developed for
investigating cash ﬂow in construction. For example, Barbosa and
Automation in Construction 17 (2008) 966–974
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