Advances and Applications in Discrete Mathematics

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COMPARATIVE ANALYSIS WITH THE PERT METHOD: TIMES CERTAIN VS UNCERTAIN

Authors

  • YOUGBARE Wendpanga Jacob
  • SORY Boureima
  • ZONGO Moumouni

Keywords:

PERT method, fuzzy set, fuzzy number, uncertain job duration, central scheduling problem.

DOI:

https://doi.org/10.17654/0974165824008

Abstract

Purpose. This study consists in providing mathematical tools for monitoring the construction work of a school building in Banfora, Burkina Faso.

Methods. PERT/CPM, probabilistic PERT and fuzzy PERT were used to resolve the operational planning issue. Job durations were obtained from optimistic, likely, pessimistic estimates of these durations. The beta distribution was considered for the stochastic case and the random job durations were considered independent. For the fuzzy case, the fuzzy job durations were considered non-interactive.

Results. With PERT, the results allowed to have the minimum total duration of the project, the critical path, the critical tasks, the total margins and free margins of tasks.

With probabilistic PERT, probability calculations allowed for 90%, 95% and 99% confidence intervals and the probability of meeting the minimum total duration of 30.5%.

With fuzzy PERT, the calculations allowed to have the fuzzy number corresponding to the minimum total duration.

Conclusion. The results obtained show that the three approaches are complementary in a problem of operational planning and monitoring of works such as the case of building construction.

Received: May 18, 2023;
Accepted: July 4, 2023

References

Gotha, Les problèmes d’ordonnancement, RAIRO, Recherche opérationnelle 27(1) (1993), 77-150.

M. Mazlum and A. F. Güneri, CPM, PERT and project management with fuzzy logic technique and implementation on a business, Procedia - Social and Behavioral Sciences 210 (2015), 348-357.

C.-T. Chen and S.-F. Huang, Applying fuzzy method for measuring criticality in project network, Inform. Sci. 177(12) (2007), 2448-2458.

Stefan Chanas and J. Kamburowski, The use of fuzzy variables in PERT, Fuzzy Sets and Systems 5(1) (1981), 11-19.

F. A. Lootsma, Stochastic and fuzzy PERT, European J. Oper. Res. 43(2) (1989), 174-183.

D. Dubois and H. Prade, Operations on fuzzy numbers, Internat. J. Systems Sci. 9 (1978), 613-626.

J. C. Figueroa-García, G. Hernández-Pérez and J. S. Ramos-Cuesta, Uncertain project network analysis with fuzzy-PERT and interval Type-2 fuzzy activity durations, Heliyon 9(4) (2023), e14833.

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Published

2024-02-19

Issue

Vol. 41 No. 2 (2024)

Section

Articles

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Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

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How to Cite

COMPARATIVE ANALYSIS WITH THE PERT METHOD: TIMES CERTAIN VS UNCERTAIN. (2024). Advances and Applications in Discrete Mathematics, 41(2), 115-134. https://doi.org/10.17654/0974165824008

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