Modeling the project management tasks under the risk and uncertainty conditions with a cyclic alternative network model


By L.I. Averbach, V.I. Voropayev, J.D. Gelrud 

Chelyabinsk & Moscow, Russia

New York, USA

The high degree of complexity of making the implementation plans of a large number of works by many participants in the project, taking into account a wide range of resources used, the need for systematic monitoring of their implementation and adjustments often require effective methods for solving this complex class of problems.

This paper addresses the problem of project planning and control, as a set of interrelated activities, taking into account the risk and uncertainty of the conditions for their performance.

Endowed with similar characteristics are different types of projects in different areas of activity:

  • expansion, modernization, and diversification of production
  • construction of buildings and structures
  • design and manufacture of a new product sample
  • preventive maintenance of complex equipment
  • installation and commissioning of computer network, or other complex and diversified equipment
  • research and design
  • construction and repair of ships
  • manufacture and assembly of a large single product, etc

The main reason that such projects are often late in completion and lack control is the fact that these projects include many different random effects. This reflects in random duration of work, the structure of the model with random parameters unknown in advance, etc.

However, project managers tend to avoid “probabilistic” terminology and try to control complex, highly uncertain projects based only on deterministic models and methods, which causes systematic errors in estimating the parameters of the project, particularly, the time of its execution, which in most cases is cut short. This allows us to conclude that the development of sound models and stochastic project management is a relevant and important theoretical and applied task. [1]

Besides, the mathematical models are very diverse both in terms of their adequacy to the described processes and the complexity of perception and results. This is an important point because as it is rightly pointed out in [2]: “The manager would rather not resolve the issue than have models of which he does not have a clue.”

The development of modern project management methods began in the late 1950s with the advent of the first articles on network modeling [3], which introduced the so-called traditional (or classic) network models. At the heart of the first models in project management that used network (PERT, CPM) was the “critical path method» – a powerful but basically very simple method of analyzing the planning and scheduling work distribution for complex projects. This method makes it possible to determine a/ which tasks are “critical” in their impact on the overall duration of the project calendar and b/ how to make up the best schedule of all activities in the project in order to achieve the target date at minimal cost.

By the end of 1960s V.I. Voropayev and his team had worked out the generalized network models (GNM) [4], which present an opportunity to apply a wide range of technological dependencies.

These models make allow reflecting such relationships between the activities of a project as the combination of performance and sustainability, considering the variable intensity of their implementation, and reflecting the model dependence and restrictions of types “no earlier than” and “no later” for the project as a whole, individual activities and, most importantly, for the parts of the activities. Generalized network models make modeling technological processes more accurate while managing a complex project than the traditional network, and they can significantly decrease detailing the description of the simulated object without losing the value and reliability of information. This makes it possible to “serve” the various hierarchically structured categories: the organizational structure of the project management, the process structure, the structure of resources, the unit of time (year, month, week, day, and hour), etc. Such models are of particular importance in making decisions on optimization plans with various criteria relating to the use of resources and compliance with specific technological and organizational requirements. It is imperative that the time interval between the given pairs of activities not exceed the predetermined value. For example, such requirements include the continuity of carrying out the work on the project, the continuity or limit between tasks, the absolute limiting of the terms of some jobs, etc.


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About the Authors

flag-russialev-averbakhLev I. Averbakh, PhD

New York, USA

Lev Averbakh was born in Chelyabinsk, Russia in 1937. In 1959 he graduated with Master Degree in Industrial Construction from Chelyabinsk Polytechnical Institute (currently  South-Ural State University). Later, he worked as CEO of a large construction company and as senior project manager overseeing reconstruction of the largest in Russia Tractor Factory located in the city of Chelyabinsk. In 1968 Lev completed his term as a research fellow in Novosibirsk State University in the area of Economical Cybernetic, and received a PhD in Economics. In the early seventies Lev created and managed a company that was working on development of automatic control systems and management information systems, also  he functioned as chief engineer of these systems.  Since 1987 Lev had been working as a professor and had been teaching following subjects: Fundamentals of Management; Economic Analysis of Investment Projects; Mathematical Methods of decision-making; Financial mathematics; Economic Theory; and Securities Market and Trading. Lev has published about 50 research papers and has made numerous conference presentations.  In 2001 he moved to the USA and continued his scientific research in cooperation with Russian colleges. 

flag-russiayan-gelrudYan D. Gelrud, PhD

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]

flag-russiavladamir-voropajev-bioVladimir Voropajev, PhD 

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]