Mathematical Models of Management for a Manager and His Project Management Team

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By Vladimir I. Voropayev, PhD,


Yan D. Gelrud, PhD,



This paper dwells on the complex of the interconnected mathematical models intended for project management activities with the participation of one of the main interested parties – a manager and his project management team. The use of such models aims at increasing efficiency of their activity, and ensures that relevant competences and the desired objectives achievement under various conditions of modalities for the project implementation are put into effect.

KEY WORDS: stakeholder, mathematical models of project management, competence of project management.


This work continues a cycle of articles devoted to creation of a complex of interconnected mathematical models, intended for management of design activity with participation of different interested parties. In [1] there was an attempt to structure the features of the main interested parties (stakeholders) and with these in mind to construct a complex of the interconnected mathematical models of project management. Isolated examples of such models are constructed for investor, customer, project team, main contractors, suppliers and regulators.

Ibid. we noted that various interested parties in the project are notable for different expectations, roles, measures of responsibility and management activities. These distinctions significantly influence project terms of reference, the methods used, tools and techniques of management problem solving, focused on their specific requirements. In [2-5] more detailed models for the investor, the customer, the supplier and regulators are constructed.

In the present article the offered mathematical models of management for the major interested party – the head and his team of management, are intended to calculate  all the technical and economic parameters of the project, to form a set of options of its realization for the subsequent choosing the most effective from them. The use of these models is aimed at the effectiveness increase of the project team’s activity, provides the realization of its corresponding competences and the achievement of goals at project implementation.

The complex multi-purpose project which description is made by means of network modeling is thus considered, and at that the traditional determined as well as probabilistic, alternative and stochastic models can be used. The description of similar network models and the methods of calculation of the main indicators of the project (early and late terms of the beginning and completion of tasks, probabilities of performance of the main stages and all project as a whole and so forth) can be found in [6,7] and several other publications provided in these articles. It is supposed that the realization of the project can be enabled by N options.

For each option the project team calculates their temporary, resource and financial performance, ecological and social characteristics. Actual examples of similar projects will be given in the following articles of the cycle.


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About the Authors 

flag-russiaVLADIMIR-VOROPAJEVDr Vladimir Voropajev 

Author, Professor, International PM Expert

Founder, Former President, Chair – SOVNET

Former Vice President – IPMA

Full Member, Russian Academy of Natural Sciences

Moscow, Russia

Professor Vladimir Voropajev, PhD. is Founder and former President and Chairman of the Board of the Russian Association of Project Management, SOVNET. Dr. Voropajev is professor of Project Management at the State University of Management, Moscow, Russia.  He is also Head of the Program and Project Management Faculty for the Russian State Academy’s Program for Professional Retraining and Professional Skill Development for Executives and Specialists in Investment Fields.

He is a full member of the Russian Academy of Natural Sciences on Information Science and Cybernetics, and of the International Academy of Investments and Economy in Construction. From 1991 to 2001, he was Vice-president and a member of the Executive Board of the International Project Management Association (IPMA), the global federation of national PM associations based in Zurich, Switzerland. He is the First Assessor for several IPMA certification bodies. In 2005 he was awarded IPMA Honorary Fellowship Award. He is also an honorary Fellow of the Indian Project Management Association and a past member of the Global Project Management Forum Steering Committee.

During his 40 years of engineering, scientific, teaching and consulting activities, he has published over 250 scientific research works including 7 monographs and 5 textbooks about the organization and planning of construction, information systems, and project management.  Vladimir serves on the editorial boards of several international project management journals, is a frequent participant in PM conferences worldwide, and provides ongoing counsel and support to PM professional leaders in Azerbaijan, Kazakhstan, Ukraine, Yugoslavia and several other countries.  Professor Voropajev can be reached at [email protected]

flag-russiaYakov-GelrudYan D. Gelrud

Professor, South Ural State University

Chelyabinsk, Russia

Mr. Yan Gelrud was born in 1947 in Birobidjan (Khabarovsk Territory). In 1965 he finished a school of mathematics and physics at Novosibirsk. In 1970 he graduated from the mathematical faculty of university at Novosibirsk on “Mathematics” speciality. From 1970 to 1991 Yakov was working in the Research Institute of automated control systems as a head of mathematical division. He took part in creation and adoption of more than 100 automated control systems in different branches of industry.

From 1991 to 1997 Mr. Gelrud was doing business, being director general of “URAL-ASCО-SERVICE”.  Since the 1st of September 1997 till now he works as a professor of the “Enterprise and management” department in South Ural State University. He teaches a multitude of disciplines, such as “Mathematics”, “Theory of probability and mathematical statistics”, “Econometrics”, “Economic and mathematical methods”, “Mathematical methods of decision-making”, “Bases of decision-making methodology”, “Economical evaluation of investments”, “Mathematical methods and models of project management”, “Studies of managerial systems.”

Yan Gelrud has more than 100 publications and speeches on seminars and conferences of different level. His monograph “Project management in conditions of risk and uncertainty” was published recently.  He can be contacted at [email protected]