Network planning and resource optimization of a project in conditions of fuzzy group expert assessment of the duration of work

This article presents an algorithm for calculating time parameters and resource optimization of a network graph, the lengths of which are estimated by an expert group in the form of fuzzy triangular numbers. To account for the variation in expert assessments, the examination results are first summarized as fuzzy interval-digit numbers and then converted into fuzzy triangular numbers based on the risk factor of the decision maker. The use of fuzzy interval-valued numbers allows not only to take into account the uncertainty of expert opinions regarding the duration of work, but also the differences in expert opinion when forming the membership function of fuzzy triangular numbers. The network planning algorithm is based on the classical algorithm for finding the critical path using special methods for calculating the early and late times of events when setting the duration of work in the form of fuzzy triangular numbers. Instead of taking the maximum and minimum operations when finding the early and late times of events, a probabilistic comparison of fuzzy numbers is used. Based on the calculated fuzzy triangular estimates of the early and late completion of events, fuzzy estimates of the early and late moments of the start and completion of each job and the probability of each job being completed at each time are calculated. The probabilities obtained allow us to estimate the resource availability of the project at any given time. The paper also proposes a mathematical model for optimizing the resource availability of a project due to shifts in the beginning of each work within the early and late start.

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