Project Management Journal

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

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.