|
Software systems and computational methods
Reference:
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
// Software systems and computational methods.
2015. ¹ 1.
P. 69-78.
URL: https://en.nbpublish.com/library_read_article.php?id=66222
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
Abstract:
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
This article can be downloaded freely in PDF format for reading. Download article
This article written in Russian. You can find original text of the article here
.
References
1. Klimenko A.B., Trotsenko R.V. Reshenie zadachi optimizatsii resursov i planirovaniya vychisleniy s ispol'zovaniem parallel'noy imitatsii otzhiga // Programmnye sistemy i vychislitel'nye metody.-2014.-3.-C. 282-290. DOI: 10.7256/2305-6061.2014.3.13419.
2. Grakova N.V. Postroenie semanticheskoy modeli upravleniya proektami // Kibernetika i programmirovanie.-2012.-1.-C. 7-15. URL: http://www.e-notabene.ru/kp/article_13857.html
3. L. S. Kirina Etapy upravleniya nalogovymi riskami v nalogovom konsul'tirovanii // Nalogi i nalogooblozhenie.-2012.-5.-C. 46-54.
4. Labkovskaya R.Ya., Kozlov A.S., Pirozhnikova O.I., Korobeynikov A.G. Modelirovanie dinamiki chuvstvitel'nykh elementov gerkonov sistem upravleniya // Kibernetika i programmirovanie.-2014.-5.-C. 70-77. DOI: 10.7256/2306-4196.2014.5.13309. URL: http://www.e-notabene.ru/kp/article_13309.html
5. Wise M.E. The incomplete beta-function as a contour integral and a quickly conversing series for its inverse // Biometrika. 1950. V. 37. P. 208-218.
6. Krylov V.I., Bobkov V.V., Monastyrskiy P.I. Nachala teorii vychislitel'nykh metodov. Interpolirovanie i integrirovanie. Minsk, Nauka i tekhnika, 1983. – 287s.
7. Verzhbitskiy V.M. Osnovy chislennykh metodov. M.: Vyssh. shk., 2005. – 840s.
8. Mal'tsev A.I. Algoritmy i rekursivnye funktsii. – M., Nauka, Gl. red. fiz.-mat. lit. 1986. – 368 s.
9. Pirogov A.M., Oleynikova S.A. Ob odnom podkhode k otsenke dlitel'nosti proekta v zadachakh setevogo planirovaniya i upravleniya// Informatsionnye tekhnologii v vychislitel'noy tekhnike i svyazi: Materialy II Mezhd. konf. Vypusk II.-Voronezh, Mezhdunarodnyy institut komp'yuternykh tekhnologiy, 2013. – s. 57-69.
10. Kobzar' A.I. Prikladnaya matematicheskaya statistika. Dlya inzhenerov i nauchnykh rabotnikov. – M.: Fizmatlit, 2006. – 816 s.
11. Oleynikova S.A. Chislennaya otsenka vremeni obsluzhivaniya v zadachakh setevogo planirovaniya i upravleniya// Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta. 2009. T. 5. ¹ 3. S. 111-114.
12. Oleynikova S.A. Vychislitel'nyy eksperiment dlya analiza zakona raspredeleniya sluchaynoy velichiny, opisyvayushchey dlitel'nost' proekta v zadachakh setevogo planirovaniya i upravleniya// Ekonomika i menedzhment sistem upravleniya, 2013. T.9. ¹ 3. s. 90-96.
13. WILLIAMS, T. M. (1995) What are PERT estimates? J. Oper. Res. Soc., 46, 1498–1504.
14. Oleynikova S.A. Otsenka kriticheskogo vremeni v zadachakh upravleniya proektami// Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta. 2011. T. 7. ¹ 2. S. 106-109.
15. Oleynikova S.A. Kriticheskiy analiz metoda PERT resheniya zadachi upravleniya proektami so sluchaynoy dlitel'nost'yu vypolneniya rabot// Sistemy upravleniya i informatsionnye tekhnologii. ¹ 1(51), 2013. – s. 20-24. Kobzar' A.I. Prikladnaya matematicheskaya statistika. Dlya inzhenerov i nauchnykh rabotnikov. – M.: Fizmatlit, 2006. – 816 s.
16. Venttsel' E.S. Teoriya veroyatnostey. – M. Fizmatlit, 1962. – 564s.
17. Oleynikova S.A. Matematicheskaya model' i optimizatsionnaya zadacha sostavleniya raspisaniya dlya mul'tiproektnoy sistemy s vremennymi i resursnymi ogranicheniyami i kriteriem ravnomernoy zagruzki// Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta. 2013. T. 9. ¹ 6-3. S. 58-61.
18. Novakova N.E., Goryachev A.V., Goryachev A.A., Vasil'ev A.A., Monakhov A.V. Sistema upravleniya proektami v avtomatizirovannom proektirovanii // Kibernetika i programmirovanie.-2013.-4.-C. 1-13. DOI: 10.7256/2306-4196.2013.4.8301. URL: http://www.e-notabene.ru/kp/article_8301.html
19. Komartsova L.G., Lavrenkov Yu.N., Antipova O.V. Kompleksnyy podkhod k issledovaniyu slozhnykh sistem // Programmnye sistemy i vychislitel'nye metody.-2013.-4.-C. 330-334. DOI: 10.7256/2305-6061.2013.4.10551.
|
Eng
© 1998 – 2024 Nota Bene. Publishing Technologies. NB-Media Ltd.
