Abstract
In this research work, an approach to determine the critical path of activity network with normalized heptagonal fuzzy data is proposed. In the proposed model, we attempt to develop a method for solving litigation problems by experts when they share the same information but differ in their opinions. The concepts for a critical path method (CPM) optimization with two kinds of data are as follows: those are to be optimistic and those considered being pessimistic. A numerical example is given for the illustration of the proposed approach and gain more insights. Based on the findings of the proposed work, we observe that the floating times with optimistic data are always smaller than or equal to the corresponding floating times for the pessimistic data.
Highlights
The critical path method (CPM) is one of the most important concepts in network analysis
This section introduces some of basic concepts and results related to fuzzy numbers, heptagonal fuzzy numbers, and their arithmetic operations and the associated ordinary number corresponding to the heptagonal fuzzy number
In the illustrative example, four experts established the data, but in a nonacademic example, this number depends on many factors: available experts, kind of operation, cost of operation, and so on
Summary
The critical path method (CPM) is one of the most important concepts in network analysis. Chen [15] studied the project network and further investigated the critical paths under the assumption of fuzzy activity times. Shankar et al [18] derived a solution method, which is based on analytical concept They applied this method to determine the critical paths, where the critical paths were considered in a fuzzy project network by Liang [19]. [20] developed a solution procedure for the determination of total float time as well as the critical path They considered the fuzzy uncertainty in their project network model. Radhakrishnan and Saikeerthana [33] applied the interval concepts to solve the CPM, and they performed the evaluation review technique in project network to determine the critical path and the project duration of the network.
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