Decision Making in Controlled Cyclic Alternative Network Projects with Deterministic Branching Outcomes


By Vladimir I. Voropayev, PhD,

Yan D. Gelrud, PhD,


Dimitri Golenko-Ginzburg, PhD

Russia & Israel


We present a new controlled alternative network model which is more universal and unifies two formerly developed network models:

a)    The acyclic controlled alternative model (CAAN model [1,2]) is a branching network with two types of alternative events. The first one reflects stochastic (uncontrolled) branching of the development of the project. The alternative event of the second type is of deterministic nature, i.e., the project’s decision-maker chooses the outcome direction.

b)    The cyclic GERT type alternative model including loops and a variety of different logical relations [3]. The model includes only events of stochastic branching.

The problem of controlling a project boils down to choosing an optimal outcome direction at every decision-making node which is reached in the course of the project’s realization. This is carried out by applying a special algorithm, based on lexicographical scanning.

A numerical example is given and application areas are presented.

I.  Introduction

We present a newly developed controlled cyclic alternative network model (CCANM) which is a finite oriented cyclic graph  consisting of a set of nodes (events)  and arcs (activities) , , defined by the adjacency matrix , , where  defines a deterministic arc  and  determines an alternative event  which is connected with event  with probability , .

Besides events with stochastic alternative branching (call them henceforth ), certain nodes  are decision making events. Each of them presents a subset of deterministic outcomes leaving node  with probability equal to one. Only one of those branching arcs can be realized, and the choice of the outcome decision is the sole prerogative of the project’s manager. Call them , both .


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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]

yan-gelrudflag-russiaYan 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]

flag-isrealpmwj14-sep2013-Voropajev- GINSBURG AUTHOR IMAGE.jpgDimitri Golenko-Ginzburg, PhD

Professor Emeritus

Ben Gurion University of the Negev


Dimitri Golenko-Ginzburg is professor-emeritus and incumbent of the Rabbi Gunter Plaut Chair in Project Management, in the Industrial Engineering and Management Department of the Ben Gurion University of the Negev, Israel, as well as professor in Department of Industrial Engineering and Management, Academic College of Judea and Samaria, Israel. He was born in Moscow in 1932. He received his M.A. degree in Mathematics from the Moscow State University in 1958 and his Ph.D. degree in Applied Mathematics from the Moscow Physico-Technical Institute (Russia) in 1962. In Russia during the period 1958÷1985 he wrote 14 books and more than 200 articles. His professional experience includes 45 years of scientific research and academic teaching in leading academic institutions in the former USSR and, after repatriating in 1985, in Israel. His current research interests are in managing and planning under uncertainty, planning and control of network projects, and industrial scheduling. During the period 1985÷2004 he published more than 150 articles. His recent publications have appeared in Mathematics and Computers in Simulation, International Journal of Production Economics, Automation and Remote Control, Communications in Dependability and Quality Management, and Computer Modelling and New Technologies.

Голенко-Гинзбург Димитрий — доктор ф.-м. наук, профессор, заслуженный деятель и преподаватель факультетов организации производства и управления Университета им. Бен-Гуриона в Негеве и университетского центра “Ариэль” в Самарии. В 1958 г. получил степень кандидата наук по математике в МГУ, в 1962 г. — степень доктора наук по прикладной математике в Московском физико-техническом институте. В течение 45 лет занимался научной деятельностью и преподавал в ведущих высших учебных заведениях бывшего СССР и Израиля. В настоящее время проводит научные исследования в области управления и планирования при неопределенности, планирования и контроля сети проектов, а также календарного планирования в промышленности.

Автор 14 книг и более 350 статей, опубликованных в таких журналах, как Mathematics and Computers in Simulation, International Journal of Production Economics, Automation and Remote Control, Communications in Dependability and Quality Management и Computer Modeling and New Technologies.