Fuzzy-based MOGA approach to stochastic time–cost trade-off problem

In construction projects, time and cost are manageable objectives with significant interdependencies for which sets of trade-offs may exist. This study presents a new approach for the solution of time–cost trade off problems in an uncertain environment. Fuzzy numbers are used to address the uncertainties in the activities execution times and costs. Fuzzy sets theory is then explicitly embedded into the optimization procedure. A multi-objective genetic algorithm is specially tailored to solve the discontinuous and multi-objective fuzzy time- cost model with relatively large search space. The proposed approach identifies the best set of implementation options defined by the sets of non-dominated solutions Accepted risk level and optimism of the decision maker are addressed using α-cut approach and optimism index (β) respectively. To illustrate the application and performance of the model, two case examples are presented, for which separate Pareto fronts are developed. The fuzzy presentation of the non-dominated solution helps the project manager to apply his own level of risk acceptance and degree of optimism in decision making process. Different risk acceptance level and/or optimism leads to different scheduling and sets of Pareto solutions from which the project manager may select his preferred options.