Developing a Mathematical Model for Scheduling and Determining Success Probability of Research Projects Considering Complex-Fuzzy Networks

Abstract

In project management context, time management is one of the most important factors affecting project success. This paper proposes a new method to solve research project scheduling problems (RPSP) containing Fuzzy Graphical Evaluation and Review Technique (FGERT) networks. Through the deliverables of this method, a proper estimation of project completion time (PCT) and success probability can be achieved. So algorithms were developed to cover all features of the problem based on three main parameters "duration, occurrence probability, and success probability." These developed algorithms were known as PR-FGERT (Parallel and Reversible-Fuzzy GERT networks). The main provided framework includes simplifying the network of project and taking regular steps to determine PCT and success probability. Simplifications include (1) equivalent making of parallel and series branches in fuzzy network considering the concepts of probabilistic nodes, (2) equivalent making of delay or reversible-to-itself branches and impact of changing the parameters of time and probability based on removing related branches, (3) equivalent making of simple and complex loops, and (4) an algorithm that was provided to resolve no-loop fuzzy network, after equivalent making. Finally, the performance of models was compared with existing methods. The results showed proper and real performance of models in comparison with existing methods.Journal of Applied Mathematics methods, that is, CPM (Critical Path Method) and PERT (Program Evaluation and Review Technique), were introduced and developed [6].Project management, in particular, project planning, is a critical factor in the success or failure of new product development (NPD) [7] and research and development (R&D) projects [8]. Limited facilities of CPM and PERT methods for modeling of projects having complex and uncertain networks [6] caused the great scientists such as Pritsker and Whitehouse [9] and Pritsker and Happ [10] to introduce the probability GERT (Graphical Evaluation and Review Technique) which is a method consisted of flow graph theory, moment generation functions, and PERT to solve problems with probability activities. Pritsker [11] developed GERT method and used it for different nodes and introduced use of simulation in that method. Of course it is pointed out that Pritsker and Whitehouse [9] used Maison's role which had been introduced in graph theory to solve probability networks. The pointed out probability methods are all based on probable distributions such as Beta ( ) or normal distribution which are used for estimation of project activities period. Thus, to use probable distributions, random samples, repeatability, and statistical deduction will be required.When fuzzy theory was introduced and developed by Zadeh [12], scientists' and researchers' attention in the field of network and science engineering was gradually caught by the issue that they will be able to solve the problem of uncertainty in problems and also expressed problems by a fuzzy approach. Thus, for the first time...

Development of a fuzzy GERT-model for investigating common software vulnerabilities

“…The results in Table 7 showed the commensurability of probabilistic and temporal indicators obtained using the improved algorithm of equivalent transformation with the values obtained from implementing known Gavareshki and Hashemin reference algorithms [10,15]. At the same time, the improved algorithm, unlike the reference algorithms, covers a wider range of logical operations and equivalent transformations.…”

“…To carry out simplifying equivalent transformations of the GERT network for investigating software vulnerabilities, the main ideas from scientific research [15] were used. At the same time, we shall improve the algorithm of simplifying equivalent transformations by taking into consideration the three evaluated parameters of software vulnerability research: the study time t ij , the probability of the beginning of the analysis (starting analysis) , , i j p and the probability of successful study completion (useful conclusion) , .…”

Using Stochastic Decision Networks to Assess Costs and Completion Times of Refurbishment Work in Construction

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Modification of the PERT method for project time evaluation taking into account unexpected delays

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