Fuzzy Critical Path Method Based on Lexicographic Ordering

The Critical Path Method (CPM) is useful for planning and control of complex projects. The CPM identifies the critical activities in the critical path of an activity network. The successful implementation of CPM requires the availability of clear determined time duration for each activity. However, in practical situations this requirement is usually hard to fulfil since many of activities will be executed for the first time. Hence, there is always uncertainty about the time durations of activities in the network planning. This has led to the development of fuzzy CPM. In this paper, we use a Lexicographic ordering method for ranking fuzzy numbers to a critical path method in a fuzzy project network, where the duration time of each activity is represented by a trapezoidal fuzzy number. The proposed method is compared with fuzzy CPM based on different ranking methods of fuzzy numbers. The comparison reveals that the method proposed in this paper is more effective in determining the activity criticalities and finding the critical path. This new method is simple in calculating fuzzy critical path than many methods proposed so far in literature.