PAPE
RS
ABSTRACT ■
A Study on Complexity and Uncertainty
Perception and Solution Strategies for
the Time/Cost Trade-Off Problem
Mathieu Wauters, Faculty of Economics and Business Administration, Ghent University,
Ghent, Belgium
Mario Vanhoucke, Faculty of Economics and Business Administration, Ghent University,
Ghent, Belgium
INTRODUCTION
Time/cost trade-offs in project scheduling find their roots in the Critical Path Method (CPM), which was developed at the duPont Company and at Remington Rand Univac (Kelley & Walker1959; Walker & Sawyer, 1959; Kelley, 1961). CPM is a project scheduling technique
used to analyze and represent the tasks involved in completing a given project.
Although this method does not explicitly take resource requirements into
account, it assumes that the cost of an activity is a function of its duration. As
the duration of an activity is decreased, its associated costs will rise, since more
resources will need to be allocated to that activity. Initial research efforts on the
time/cost trade-off problem focused on the continuous case and can be found
in standard texts, such as those from Elmaghraby (1977) and Moder, Phillips,
and Davis (1983). Several techniques were used to solve this type of problem
(Robinson, 1975; Hindelang & Muth, 1979; Phillips & Dessouky,1977; Meyer
& Shaffer, 1965). An overview of the literature up through the mid-1990s is
provided by De, Dunne, Ghosh, and Wells (1995); we will cover the contributions
related to the time/cost trade-off problem from the mid-1990s onward. The
Discrete Time/Cost Trade-off Problem (DTCTP), shown to be NP-hard by De,
Dunne, Ghosh, and Wells (1997), was solved precisely by Demeulemeester,
Elmaghraby, and Herroelen (1996). In this article, the authors present two
approaches based on dynamic programming for reaching the optimal solution
of the three objective functions of the DTCTP. Three possible variants of the
time/cost trade-off problem can be identified. The first variant—scheduling
project activities with the goal of minimizing the total project costs, while
meeting an imposed deadline—is known as the deadline problem (DTCTP-D).
The budget problem, which is the second variant, specifies a limit on the
budget (DTCTP-B), in which the objective is then to minimize the duration
of the project. Finally, the third variant deals with generating a complete and
efficient time/cost profile. Demeulemeester, De Reyck, Foubert, Herroelen,
and Vanhouke (1998) improved the computational results for solving the
DTCTP optimally; this is done using a branch-and-bound procedure, which
calculates lower bounds by convex piecewise linear underestimations of the
time/cost trade-off curves of the activities. This contribution is of special
relevance to this article because it will be used to provide an optimal solution
for the data instances of the computational experiment.
Over the last decade, two new research avenues on the time/cost trade-off
problem have been examined. The first new direction is the extension of the
(D)TCTP, whereas the second direction focuses on the inclusion of stochastic
Project Management Journal, Vol. 47, No. 4, 29–50
© 2016 by the Project Management Institute
Published online at www.pmi.org/PMJ
In this article, the Discrete Time/Cost Tradeoff
Problem (DTCTP) is revisited in light of a
student experiment. Two solution strategies
are distilled from the data of 444 participants
and are structured by means of five building blocks: focus, activity criticality, ranking,
intensity, and action. The impact of complexity and uncertainty on the cost objective is quantified in a large computational
experiment. Specific attention is allocated
to the influence of the actual and perceived
complexity and uncertainty and the cost
repercussions when reality and perception
do not coincide.
KEYWORDS: project scheduling game;
simulation; complexity; uncertainty