Stochastic Time–Cost Optimization Model Incorporating Fuzzy Sets Theory and Nonreplaceable Front

Abstract

In a real construction project, the duration and cost of each activity could change dynamically as a result of many uncertain variables, such as weather, resource availability, productivity, etc. Managers/planners must take these uncertainties into account and provide an optimal balance of time and cost based on their own experience and knowledge. In this paper, fuzzy sets theory is applied to model the managers’ behavior in predicting time and cost pertinent to a specific option within an activity. Genetic algorithms are used as a searching mechanism to establish the optimal time–cost profiles under different risk levels. In addition, the nonreplaceable front concept is proposed to assist managers in recognizing promising solutions from numerous candidates on the Pareto front. Economic analysis skills, such as the utility theory and opportunity cost, are integrated into the new model to mimic the decision making process of human experts. A simple case study is used for testing the new model developed. In comparison with the previous models, the new model provides managers with greater flexibility to analyze their decisions in a more realistic manner. The results also indicate that greater robustness may be achieved by taking some risks. This research is relevant to both industry practitioners and researchers. By incorporating the concept of fuzzy sets, managers can represent the range of possible time–cost values as well as their associated degree of belief. The model presented in this paper can, therefore, support decision makers in analyzing their time–cost optimization decision in a more flexible and realistic manner. Many novel ideas have also been incorporated in this paper to benefit the research community. Examples of these include the use of fuzzy sets theory, nonreplaceable front concept, utility theory, opportunity cost, etc. With suitable modifications, these concepts can be applied to model to other similar optimization problems in construction.