A Procedure for Application of Critical Path Method with Fuzzy Sets and Fuzzy Operations

Abstract

Critical Path Method (CPM), which is used to schedule construction activitiesdepending to each other with network relationships, is deterministic in regards of the certaindurations assigned to activities for its execution and the results it produces in certain values.Unfortunately, construction activities are performed under uncertain conditions. Project riskscause variation in activity durations and in turn, the entire network is affected from uncertainty. In this context, activity durations are represented by fuzzy sets and CPM network calculations are performed by fuzzy operations through a new procedure developed in this study. In construction projects, the duration of an activity can not be proposed certainly inadvance. The predictions like "this activity can be completed most probably between 7 and 10days but perhaps it takes 15 days maximum and 5 days minimum depending on theconditions" are frequently made. Fuzzy numbers enable modeling such kind of uncertain predictions mathematically. Since the activity durations are represented by fuzzy numbers and network calculations are performed by fuzzy operations, the activity early/late start/finishtimes and the project completion time are calculated as fuzzy numbers by the proposed procedure. An example CPM application with fuzzy sets is also presented in the paper. The findings show that CPM is applicable with fuzzy sets and the developed procedure operates well for modeling the uncertainty in CPM calculations.