Mathematical Models of Project Management
For Interested Parties


By Vladimir I Voropajev and Yakov D Gelrud




Recently, in regulatory documents and in professional literature more and more attention has been drawn to project management particularities seen through the eyes of various stakeholders. Nonetheless, most sources, unfortunately, confine themselves to examining this, in our opinion, topical issue on content-descriptive level and this approach does not constructively clarify the problem, therefore there is still much to be solved and to be worked on within the subject matter. This makes it difficult to approach the problem from a practical side. The authors have attempted to structure the main features of different stakeholders and to build mathematical models of project management taking the aforementioned features into account. Such models have been built for investor, customer, project team, principal executors, suppliers and regulatory bodies. We hope that such approaches and problem definitions will be of interest to master and postgraduate students, and doctoral candidates will strive to continue research in this direction. The paper is meant to be problem-setting, open to discussion and is the work that must be continued.

This article describes a set of interrelated mathematical models intended for complex project management at all stages of its implementation with participation of various interested parties(project sponsor, investor, general contractor, etc.).  Using these models allows for an increase in the effectiveness of stakeholders’ activity, provides systems-thinking approach, integrity and adequacy of the decisions made.


According to the international research and professional organizations (e.g., see [30]), only 40% of carried-out projects in the world are completed in time and within budget. That means, about 60% of projects do not end successfully. Roughly the same pattern is observed with the accomplishment of complex and mega projects. Unfortunately ,projects in Russia experience the same problems. Thus, in practice, project management makes use of no more than half of its powerful intellectual capabilities. What is the reason? There is a set of factors that reduces the effectiveness of project management. However, we would like to highlight the most important of them and find ways to reduce their impact. Let us try to do so.

Project management is carried out at least at three levels:

  1. The higher echelons of government and business management – the level of strategic decision-making – the main stakeholders’ level.
  1. The executors’ level – project managers, project management team.
  1. Operational level – members of project management team, specialists from the offices.

Let us combine our view of the second and the third levels and let us examine the two levels of management. About 50% of project activity success depends on the first level. It is the place where all the resources are concentrated and the most important decisions are made. The executors’ level plays an important role, too. It does not allocate resources but it  acts up to the will of its employers, i.e. key executives.

At the same time, almost all of the entire global methodology and all the modern standards [1,2,3,13,14,15,16,21], focus mainly on the project manager’s ant project management team’s role and competence. The few exceptions are, perhaps, Japanese [16] and Australian [29, 30] approaches which pay considerable attention to the higher levels. Thus, in our opinion, one of the main causes of project management failure lies in the fact that the upper levels of management are weakly involved in this work while modern project management methodology and technology do not adequately take their interest into account. We need to change the usual project management paradigm: rather than using a “top-down” approach to management we should develop a “bottom-up” approach.

When implementing rather complex large-scale projects and multi-project activity various interested parties may take part in management with each party possibly having its own project management team lead by their own project manager having the appropriate authority and representing the interests of the particular interested party in the project.

As shown in the system model and the system methodology [2,6,7], the choice of project management methods and tools is largely determined by the choice of an interested party to be managed in particular case. Different interested parties in the project vary in expectations, roles, degrees of responsibility and adequate actions. This is because, despite the fact that in the project they are partners working towards a common goal, they may have different objectives in the project, different criteria for the success and estimations of the achievement of their goals, values and different strategies for achieving goals. These differences significantly affect the formulation of their project management tasks, methods, tools and management decision-making technology for different stakeholders focused on their specific needs.


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About the Authors


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]

Yakov Gelrud

South Ural State University

Chelyabinsk, Russia

Mr. Yakov 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.”

Yakov 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.