Research Article On Determining the Critical Path of Activity Network with Normalized Heptagonal Fuzzy Data Hamiden Abd El-Wahed Khalifa , 1,2 Majed G. Alharbi , 3 and Pavan Kumar 4 1 Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt 2 Mathematics Department, College of Science and Arts, Al-Badaya, Qassim University, Buraydah, Saudi Arabia 3 Mathematics Mathematics, College of Science and Arts, Methnab, Qassim University, Saudi Arabia 4 Mathematics Division, School of Advanced Sciences & Languages, VIT Bhopal University, Sehore-466114, MP, India Correspondence should be addressed to Pavan Kumar; pavankmaths@gmail.com Received 5 December 2020; Accepted 18 June 2021; Published 5 July 2021 Academic Editor: Giovanni Pau Copyright © 2021 Hamiden Abd El-Wahed Khalifa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. 1. Introduction The critical path method (CPM) is one of the most important concepts in network analysis. It is used as method for solving the complications of a project by preparing the networks and to determine the earliest date an activity can start and the ear- liest date can be finished. Also, it is an algorithm for schedul- ing a set of project activities. In addition, it is commonly used in conjunction with the program evaluation and review tech- nique (PERT). A technique for project planning that was developed known as critical path method (CPM) was devel- oped in 1950 by DuPont and was first used in missile- defense construction projects. When applying CPM, there are several steps that can be summarized as follows: (i) Define the required tasks and put them down in a sequenced list (ii) Create a flowchart or other diagram showing each task in relation to the others (iii) Identify the critical and noncritical relationships among tasks (iv) Locate or devise alternatives for the most critical paths CPM was emerged to support and serve as an alternative to Gantt chart. Studies and researches enumerate the possible causes of the breach to include inadequate knowledge and experience of the technique and lack of adoption of reluc- tance to adopt a new technological innovation as well as cost of operations [1]. Aliyu [2] clarified the effectiveness of the CPM in planning, scheduling, organizing, coordinating, managing, and controlling of project time and cost, where this study concludes that the CPM is not difficult to apply, and when applied, it improves interdepartmental communi- cations, gives clear definition of responsibilities, and mini- mizes the occurrence of crisis management. Agyei [3] defined the trade-off by crashing the activities using linear programming technique and concluded with an acceptable Hindawi Wireless Communications and Mobile Computing Volume 2021, Article ID 6699403, 14 pages https://doi.org/10.1155/2021/6699403