Owing to different resource utilization, activity duration might need to be adjusted and the project direct cost could also change accordingly. Moreover, activity duration is uncertain due to variations in the outside environment, such as weather, site congestion, productivity level, etc. A new optimal construction time–cost trade-off method is proposed in this paper, in which the effects of both uncertain activity duration and time–cost trade-off are taken into account. Fuzzy set theory is used to model the uncertainties of activity durations. A searching technique using genetic algorithms (GAs) is adopted to search for the optimal project time–cost trade-off profiles under different risk levels. The method provides an insight into the optimal balance of time and cost under different risk levels defined by decision makers.
Since the late 1950s, Critical-Path-Method (CPM) techniques have become widely recognized as valuable tools for the planning and scheduling of large projects. In a traditional CPM analysis, the major objective is to build up the feasible duration required to perform a specific project. However, in a real construction project, project activities must be scheduled under available resources, such as crew sizes, equipment and materials. The activity duration can be looked upon as a function of resource availability. Moreover, different resource combinations have their own costs. Ultimately, the scheduler needs to take account of the trade-off between project direct cost and duration. For example, using more productive equipment or hiring more workers may save time, but the project direct cost could increase. In general, the less expensive the resources used, the longer it takes to complete an activity. Finding the most cost effective way to complete a project within a specific completion time is desirable for schedule planners. Several mathematical and heuristic models have been generated to solve construction time–cost trade-off problems [4], [9], [20], [23] and [24]. These models mainly focused on deterministic situations. However, during project implementation, many uncertain variables dynamically affect activity duration, and the costs could also change accordingly. Examples of these variables are weather, space congestion, productivity level, etc. To solve problems of this kind, some systematic methods, such as PERT, PNET and Monte Carlo simulation, have been developed to deal with uncertainty in the project duration. Nevertheless, these non-deterministic scheduling methods seldom take account of time–cost trade-off. Therefore, combining the aforementioned concepts to develop a construction time–cost trade-off model under uncertainty would be beneficial to scheduling engineers in the forecast of a more realistic project duration and cost. Such a model could generate additional management information, such as the relationships between project duration and cost, level of sensitivity of an activity to specific uncertain variables, and the interactive effects of both factors. Based upon the information, project management can take appropriate timely action to provide the optimal balance of time and cost.
This paper adopts a new approach, employing genetic algorithms (GAs) and fuzzy set theory to develop a construction time–cost trade-off model under uncertainty. In this model, the activity duration is characterized by a fuzzy number. An acceptable risk level (i.e., α-cut level) is then defined as the minimum condition that can be accepted. Genetic algorithms are then used to search for the minimum project direct costs for a specific project duration within feasible project time spectrums. In other words, the focus of the model is to find time–cost trade-off curves based upon different risk levels defined by decision makers.
This paper addressed a GA-based fuzzy construction time–cost trade-off model that incorporates an efficient computational technique for time–cost trade-off and a more suitable way of modeling uncertainty in a network analysis. Compared with the traditional (crisp) construction time–cost trade-off approach, the GA-based fuzzy time–cost trade-off model proposed in this paper has several advantages. First, this paper adopts fuzzy set theory to develop a framework to perform construction time–cost trade-off in an uncertain environment, in which the fuzzy model can reflect the degree of uncertainty of the input data. Unlike traditional models which generally provide only an optimal time–cost trade-off curve, the fuzzy-based approach can address several possible time–cost trade-off curves, based upon the different α-cut values (i.e., decision maker's risk levels). Such solutions provide an insight into the trade-off between project time and cost under different risk levels defined by decision makers. Second, it is not necessary for the GA-based model to commit to any particular heuristic rules. Because of this, the GA-based model has more flexibility when solving complex construction time–cost trade-off problems. The deterministic time–cost trade-off model proposed by Feng [8] also showed this advantage of the GA-based approach. Although the GA-based model has the same imperfection as heuristic models: solutions from the GA-based and heuristic models do not commit to optimal solutions; from the application viewpoint, feasible or near-optimal solutions may provide sufficient enough information for engineering decision making. In the course of future research, clear guidelines on GA parameters, such as crossover rates, mutation rates and so on, will be of great use to practitioners. Moreover, the main aim of the time/cost trade-off model is to determine the shortest project duration that allows the contractor to complete the job with minimum total project cost. This paper was only concerned with direct costs. The main focus of the paper was to determine the impact of uncertain activity durations on project direct costs. The relationship between time and total project cost under an uncertain environment needs to be studied in future research.
