Application of Fuzzy theory to project scheduling with critical path method

In this paper, we analyze the project scheduling problem using fuzzy theory. The crisp activity durations are modeled as triangular fuzzy sets. Fuzzy forward pass was carried out to determine fuzzy activity earliest start, fuzzy event earliest time and fuzzy activity earliest finish times. In order to overcome the occurrence of negative fuzzy numbers which occurs in fuzzy backward pass using fuzzy subtraction, we apply a modified fuzzy backward pass technique which uses a recursive relation to obtain the fuzzy event latest; fuzzy activity latest start and fuzzy activity latest finish times. Through numerical examples, we determine the criticality of the project activities and hence the critical path(s). The results obtained using the present method is compared with those obtained using other methods used in literature.