Mathematical Models of Project Management for Investors


By Prof Vladimir I. Voropaev, PhD


Yan D. Gelrud, PhD 



The mathematical models, which are intended for managing project activities at all stages with the participation of one of the major stakeholders – the investor of the project, are considered in the article. The use of these models is aimed at the raising of the effectiveness of the investor’s activity; it provides the implementation of corresponding competencies and the achievement of their goals on different conditions of the project’s implementation.

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


There was an attempt in [1] to structure the peculiarities of the main interested parties (stakeholders) and develop the mathematical model of project management based on those peculiarities. The examples of such models are made for an investor, a customer, a project team, principal performers, vendors and regulating authorities.

We have mentioned that the choice of PM methods and tools for each of the interested party is largely defined by the choice of the interested party to be managed and the conditions of this. Interested parties differ from each other by various expectations, roles, measures of responsibility and actions. This is caused by their different goals in the project, different success criteria and the performance measurement, various values and performance strategies. These differences significantly affect the project problem statement, the methods used, the instruments and technologies of PM tasks’ solution oriented towards their specific needs [9]. Nevertheless, different variants of problem statement may appear when modeling the activity of a particular interested party due to the different conditions of project implementation. Besides, the methods of objects implementation of taking optimal decisions have the good deal of variance as well.

The article proposes the mathematical models intended for managing project activity at all stages having one of the interested parties, project investor involved. For every suggested alternative the specific conditions which the given model is adequate to are considered, and at the same time, the methods of finding solution, which could also be multivariate, are proposed and analyzed. The use of these models is aimed at increasing the efficiency of investor’s activity; it ensures the implementation of relevant competences and the attainment of the set objectives under various conditions of the project environment.


To read entire paper (click here)

About the Authors 


Author, Professor, International PM Expert

Founder, Former President, Chair – SOVNET

Former Vice President – IPMA

Full Member, RussianAcademy 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]

yan-gelrudflag-russiaYan D. Gelrud

South Ural StateUniversity

Chelyabinsk, Russia

Mr. Yan Gelrud was born in 1947 in  Birobidjan (KhabarovskTerritory). 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 SouthUralStateUniversity. 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]