Resource allocation as a basis for optimizing the network model of a project

This article presents a project optimization procedure in the form of a network graph. The idea of optimization is to make all paths from the initial event to the final one critical by transferring resources from non-critical work with a non-zero free reserve to critical work of some critical path. Assuming that the dependence of the duration of work on the resources allocated for its execution is linear, formulas for new work durations and a new critical time are obtained. The reallocation of resources reduces the duration of some work, but makes the project more stressful. To evaluate a project with new work durations, a stress coefficient was introduced for each work as the intensity of use of the generalized project resource per unit of time. In the process of optimization, these characteristics behave differently, therefore, a generalized characteristic of the project intensity is introduced based on the aggregation of particular characteristics of work using the "fuzzy majority" principle. Note that well-known weighted averages can be used to aggregate partial estimates, while, for example, the method of paired comparisons can be used to determine the weights. The article provides an illustrative example demonstrating the operation of the proposed approach.

1. Gel'rud Ya.D., Loginovskii O.V. Upravlenie proektami: metody, modeli, sistemy. Chelyabinsk: Izdatel'skii tsentr YuUrGU; 2015. 331 p. (In Russ.).

2. Setevye modeli v upravlenii. Moscow: Egves; 2011. 442 p. (In Russ.).

3. Zukhovitskii S.I., Radchik I.A. Matematicheskie metody setevogo planirovaniya. Moscow: Nauka; 1965. 296 p. (In Russ.).

4. Golenko-Ginzburg D.I. Stokhasticheskie setevye modeli planirovaniya i upravleniya razrabotkami. Voronezh: Nauchnaya kniga; 2010. 283 p. (In Russ.).

5. Ledenev M.Yu., Sergienko M.A. An Algorithm for Calculating Fuzzy and Interval Estimations of the Time Parameters of Network Model of a Project. International Research Journal. 2021;(6-1):118–128. (In Russ.). https://doi.org/10.23670/IRJ.2021.108.6.019

6. Ledeneva T.M., Dermanew D.A. Fuzzy Model of the Project with Duration Works in the Form of a Generalized Gaussian Numbers. Proceedings of Voronezh State University. Series: Systems Analysis and Information Technologies. 2015;(2):72–81. (In Russ.).

7. Shashkin A.I., Shiryaev M.M. Job Scheduling Based on Fuzzy Input Data. Bulletin of Samara State University. Natural Science Series. 2008;(3):208–216. (In Russ.).

8. Glushkov A.Yu., Dorofeev D.V., Moiseev S.I., Perevalova O.S. Optimizatsionnaya matematicheskaya model' pereraspredeleniya resursov v upravlenii proektami. In: Sistemnoe modelirovanie sotsial'no-ekonomicheskikh protsessov: trudy 43-oi Mezhdunarodnoi nauchnoi shkoly-seminara, 13–18 October 2020, Voronezh, Russia. Voronezh: Istoki; 2020. P. 422–426. (In Russ.).

9. Beliakov G., Sola H.B., Calvo T. A Practical Guide to Averaging Functions. Cham: Springer; 2016. 352 p. https://doi.org/10.1007/978-3-319-24753-3

10. Ledeneva T.M., Levkina I.N. Review of Main Classes of Order Weighted Aggregation Operators. Proceedings of Voronezh State University. Series: Systems Analysis and Information Technologies. 2022;(1):5–31. (In Russ.). https://doi.org/10.17308/sait.2022.1/9198