Finding the Fuzzy Critical Path with Octagonal Fuzzy Numbers using Linear Programming model

A Binary Integer Linear Programing (BILP) model was used to find the Fuzzy Critical Path (FCP) of a fuzzy project network, when the lengths of all activities are represented as Octagonal Fuzzy Numbers (OFN). Although there are many methods to solve the fuzzy network problems, this paper presents the simplest method for the purpose of estimating the CP, especially, when every path activity is expressed by an OFN in the fuzzy network problems. The OFN of each activity converted to the crisp one using a modified ranking approach. A numerical example of a fuzzy network problem is given to illustrated the steps of the method were the OFN of each activity represented the time needed to complete implementation of that activity. The same example is solved by using CP Method (CPM). This is considered to be one of the leading standard methods of solving such problems. This paper presents a comparison of results of the two methods.