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An Analytical Method for Finding Critical Path in a Fuzzy Project Network

Critical path method (CPM) techniques have become widely recognized as valuable tools for the planning and scheduling of large projects. The aim of this paper is to present an analytical method for measuring the criticality in a fuzzy project network , where the duration time of each activity is represented by a trapezoidal fuzzy number. In this paper, we use a new defuzzification formula for trapezoidal fuzzy number and apply to the float time (slack time) for each activity in the fuzzy project network to find the critical path. The defuzzification formula used for critical path can not be applied to the trapezoidal fuzzy number having equal elements because that trapezoidal fuzzy number is a crisp number. The proposed method can overcome the drawback of the existing fuzzy CPM method. We use examples to compare our proposed method with the existing method. The comparison reveal that the method proposed in this paper is more effective in determining the activity criticalities and finding the critical path.