Izvestiya of Saratov University.

Economics. Management. Law

ISSN 1994-2540 (Print)
ISSN 2542-1956 (Online)

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Kataev A. V., Kataeva T. M., Makarova E. L. Project Management: Mathematical Models of Optimal Executors’ Appointment for Project Works. Journal Izvestiya of Saratov University. Economics. Management. Law, 2016, vol. 16, iss. 3, pp. 294-299. DOI: 10.18500/1994-2540-2016-16-3-294-299

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005; 330.45

Project Management: Mathematical Models of Optimal Executors’ Appointment for Project Works

Kataev Alexey Vladimirovich, Southern Federal University
Kataeva Tatiana Mikhailovna, Southern Federal University
Makarova Elena Lvovna, Southern Federal University

Introduction. The majorityof projects implemented in the world community exceeds in duration and cost limits indicated on the planning phase, so they are not successfully executed. In our opinion, the main reason for this situation is the complexity of the optimal selection and appointment of executors to perform main project work, coupled with the lack of consideration for a number of important factors. Theoretical analysis. Theory and practice of project management and operations research proposed a number of optimization models for drafting work schedules taking into account their interrelationships, as well as the necessary resources. These models are usually referred to a class of extremely NP-hard, which explains some difficulties for their effective implementation into practice. Methodology. The basic problem of optimal selection and executors’ appointment for project work, which takes into account the topology of the network schedule, as well as the optimization criterion serving the duration of the project is researched. In researched model the limits on the total cost of all the work for the project are set, and it is determined that only one executor is involved for each job, which, if necessary, is able to perform a number of tasks. Results. During the research more significant limitations, which are implemented in the model and can significantly expand the scope and improve the efficiency of its use in practice, were developed by authors. The article provides a detailed description of the meaningful data limitations, as well as their correct formalization.

  1. Hayes S. Complex Project Management Global Perspectives and the Strategic Agenda to 2025. The task force report. ICCPM : Kingston, 2012. 64 p.
  2. Barkalov S. A., Voropayev V. I. et al. Matematicheskie osnovy upravleniia proektami [Mathematical Foundations of project management. Ed. by V. N. Burkov]. Moscow, 2005. 423 p.
  3. Zukhovitskiy S. I., Radchik I. A. Matematicheskie metody setevogo planirovaniia [Mathematical methods of network planning]. Moscow, 1965. 296 p.
  4. Balash V. A., Firsovа A. A., Chistopolskaya E. V. Spetsifi ka otsenki effektivnosti innovatsionnykh proektov s ispol’zovaniem portfel’nogo podkhoda [Specifi c of Evaluation of Innovative Projects Effectiveness Using Portfolio Approach]. Izv. Saratov Univ. (N.S.), Ser. Economics. Management. Law, 2012, vol. 12, iss. 2, pp. 73–77.
  5. Voropayev V. I., Gel’rud Ya. D. Matematicheskie modeli proyektnogo upravleniia dlia zainteresovannykh storon [Mathematical models for project management stakeholders]. Upravlenie proektami [Project management], 2012, no. 4 (32), pp. 258‒269.
  6. Lazarev A. A., Gafarov E. R. Teoriia raspisaniy. Zadachi i algoritmy [Theory schedules. The tasks and algorithms]. Мoscow, 2011. 222 p.
  7. Kolish R., Padman R. An Integrated Survey of Project Scheduling. Manuscripte aus den Institut fur Betriebswirtschaftslehre. Kiel, 1997.
  8. Katayev A. V. Virtual’nyie biznes-organizatsii [Virtual business organizations]. St. Petersburg, 2009. 120 p.
  9. Katayev A. V., Katayeva T. M. Optimizatsiia dlitel’nosti vypolneniia proekta za schet vybora ispolniteley rabot: matematicheskie modeli i metodicheskie priemy [Optimization of the project duration due to the choice of the executors’ work: mathematical models and methods]. Vestnik TMEI [Bulletin of the Taganrog institute of management and economy], 2015, no. 2 (22), рp. 100‒103.
  10. Kelley J. E., Walker M. R. Critical Path Planning and Scheduling: An Introduction. Mauchly Associates, Ambler, PA, 1959.
  11. Kelley J. E. Critical-Path Planning and Scheduling: Mathe matical Basis. Operat. Res., 1961, vol. 9, pp. 296‒320.
  12. Johnson, S.M. Optimal two- and three-stage production chedules with setup times included. Nav. Res. Log. Quart. 1954, vol. 1, no. 1, pp. 61‒68.
  13. Manne A. S. On the job-shop scheduling problem. Operat. Res., 1960, no. 2, pp. 219‒223.