Applying fuzzy method for measuring criticality in project network

Program evaluation and review technique (PERT) is widely used as a tool for managing large-scale projects. In the traditional PERT model, the durations of activities (tasks) are either represented as crisp numbers or drawn from the beta distribution to estimate the task durations such as pessimistic, most likely and optimistic times. However, the operation time for each activity is usually difficult to define and estimate precisely in a real situation. The aim of this paper is to present an analytical method for measuring the criticality in a project network with fuzzy activity times. Triangular fuzzy numbers are used to express the operation times for all activities in a project network. A new model that combines fuzzy set theory with the PERT technique is proposed to determine the critical degrees of activities (tasks) and paths. In the proposed model, a possibility index is defined to identify the likelihood of meeting a specified required time for a project network. At the end of the paper, an example is presented to compare with those obtained using the proposed method as well as other methods. The comparisons reveal that the method proposed in this paper is more effective in determining the activity criticalities and finding the critical path.