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Oleynikova S.A. Recursive numerical method for the experimental evaluation of the distribution law of the duration of the project in network planning and management tasks

Published in journal "Software systems and computational methods", 2015-1 in rubric "Mathematical models and computer simulation experiment", pages 69-78.

Resume: In this paper a problem of network planning and management with a random duration of individual operations is considered. The subject of the study is the law of distribution of the random variable which describes duration of the project. The aim is to estimate such law. The urgency of this problem is related to the need to improve the accuracy of the known existing assessments which do not take into account the specifics of the distribution law of separate works determining the project. The main difficulty of the practical solution of this problem is the need to calculate the multiple definite integral, wherein the number of individual integrals not known in advance and determined by the number of works that make up the critical path of the project. As a result, the numerical method based on recursion is proposed, which allows to numerically estimate the desired distribution law. Scientific novelty of the results is in obtaining estimates of the distribution law of the duration of the project that improves positional accuracy over the existing analogues. Without loss of generality developed a recursive algorithm can be used for a wide class of problems in which the unknown distribution of the sum of random variables with known distributions of the individual terms.

Keywords: project management, the sum of beta-values, beta-distribution, distribution law, duration of the project, probabilistic and temporal characteristics, mathematical model of risks, PERT, recursion, numerical method

DOI: 10.7256/2305-6061.2015.1.14674

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