Improved critical path method with trapezoidal fuzzy activity durations

The critical path method is an essential tool for project planning, control, and scheduling. But when it is applied to analyze the critical path of project networks with fuzzy activity durations, two key issues need to be settled properly: sorting fuzzy numbers and avoiding the fuzzy subtraction operation to generate negative, infeasible solutions. In view of this, this study proposes an improved fuzzy critical path method. The primary contributions this research makes to the body of knowledge are as follows: an integrated vector similarity algorithm is used to resolve the sorting problem of fuzzy durations, while the improved standard algorithm for fuzzy subtraction is to circumvent the negative, infeasible solutions generated in fuzzy subtraction operation; moreover, this method analyzes and depicts the change of critical path under the fuzzy state of activity duration, which fills the knowledge gaps. The empirical analysis indicates that the inference and computation of this method are relatively objective and easy to implement, the effectiveness and practicability of which are further verified in practice.