Abstract
An analysis of the project network in which each activity duration time is represented by fuzzy number is discussed. The main methods used in previous approaches are classified into some groups with respect to the calculation of maximum of fuzzy numbers, i.e.the composite method and the comparison method and so on. Each method has some advantages while it has serious disadvantages. In this paper, introducing the concept of α-level set of fuzzy numbers and the fuzzy maximum operator, we propose an efficient method for determining the fuzzy project completion time and the degree of criticality for each activity in the project network. We point out the computational difficulty and the contradiction involved in the conventional definition of the degree of criticality, and improve the definition from the practical point of view. Furthermore, providing labels which consist of the set of preceding node and the fuzzy earliest node time, critical activities and paths can be identified without the backward pass. We can overcome the some drawbacks of the previous approaches. The Proposed method consists of two procedures called Algorithm 1 and 2. In Algorithm 1, we determine the project completion time represented as an interval and identify entire activities which degree of criticality are greater than a given threshold α. In Algorithm 2, we determine the degree of criticality for each activity by repeating Algorithm 1 with the threshold α increased gradually. Non-critical activities are eliminated in the network after each iterative procedure in Algorithm 2. Therefore the computing time is progressively shortened. Finally, a numerical illustration is shown.
