Cyclic stochastic alternative network models for project management

FEATURED PAPER                                                           

By Vladimir I. Voropayev, PhD


Yan D. Gelrud, PhD



Project implementation process modelling is the main active methodological body of the Project Management discipline [1]. The efficiency of decisions made and the whole functioning of the PM system is determined by the adequacy of models for real processes and their meeting the requirements of project management tasks and goals.

The high degree of complexity and laboriousness of drawing up timing schedules for numerous activities performed by many project members using a great range of resources, strict requirements for the quality of plans, the need for regular control of their fulfillment and adjustment call for the proper methods of solving problems of such sophisticated nature.

Today world market of Project Management Software[11] presents products with network models and methods of scheduling based on the researches of the end of 50th- beginning of 70th [2],[7] with very limited possibilities. At the same time the current mathematical methods of modelling project processes (classical network models [2], generalised [3, 4, 5], probabilistic [6] and stochastic [7] network models) do not always appear adequate to the complex reality of the modelled process. It should be noted that it refers to each method taken separately and to some combinations of these methods.

This paper describes a new class of network models adequately reflecting the complex project realisation process that are used for stating and solving optimal management tasks for this project. This class of models is a synthesis of generalized network models (with their rich spectrum of means for equivalence conversion of  models [12,13] and describing the different logical and time interrelations between of project activities) with probabilistic and stochastic models to a considerable extent taking into account factors of risk and uncertainty  the implementation of a project involves. These models (further referred to as cyclic alternative network models – CANMs) are the flexible and adequate in the range of known tools for describing the process of managing and control over the development of a complex sophisticated project. CANMs offer all the advantages of generalised and stochastic models in comparison with traditional network models while at the same time involving just a slight complication of the language used for describing CANMs.

A general description of CANM category models was given in a number of works [8-10,14-17].

In the present paper a detailed mathematical description of CANM is given and supplied with the substantiation of the requisite conditions of consistency as well as problem statements and CANM time analysis algorithms.

Keywords: Classical network models; Generalised network models; Probabilistic network models; Stochastic  network models; Cyclic alternative network model.


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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]

flag-VLADIMIR-VOROPAJEVyan-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]