Analysis of Different Fuzzy CPM Network Planning Procedures
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With great progress in fuzzy set theory and its success and compatibility in such dread applications, there has been also several efforts in using this theory in network planning methods such as PERT and CPM to make more realistic usage of them and better dealing with uncertainties that is intrinsic in estimating duration of activities. Although these efforts are essential and basic in operation research and specially its network planning branch, the problem, which appears in application of these methods especially in projects with great number of nodes and activities, is insufficiency of graphical methods. In this paper, using non-interactive fuzzy subtraction, an algorithm is proposed that reads fuzzy numbers as activity durations along with their initial and final node numbers; then constructs network and computes earliest expected time, latest allowable time, and slack time for each node. At the end, critical path, or paths for different a-cuts are calculated. Instead of classical descriptive methods, numeric methods are used and whenever the shape of the fuzzy number differs from initial shape (e.g. triangular), using defuzzification with center of gravity and refuzzification, the number is converted to its initial shape.
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