Applying fuzzy sets and linear programming for measuring total duration in a project network with fuzzy activity duration

In the traditional CPM/PERT model, the durations of activities are either represented as crisp numbers or drawn from the beta distribution to estimate the task durations. 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 total duration of a project network with fuzzy activity times. The method is mainly based on the linear programming (LP) formulation and Zadeh's extension principle. In the last, an example illustrates that the proposed approach is able to find the membership function of the total duration time.