Abstract: The problem of scheduling a large-scale set of activities is a key issue in project management. There is a variety of project scheduling techniques developed to handle different aspects of the problem, ranging from the classical Critical Path Method and the Program Evaluation and Review Technique marked the beginning of the active research in the area in 1950s, to more recent methods of idempotent algebra. This algebra, which deals with vector semimodules over idempotent semirings, finds expanding application as a promising modeling and solution tool in applied mathematics, computer science, and operations research. The progress in the area is mainly due to the fact that many complicated problems that are actually nonlinear in the ordinary sense become linear and so more tractable when translated into the language of the algebra.
We describe a computational approach to project scheduling problems, which offers a useful way to represent different types of precedence relationships among activities in a project as linear vector equations and inequalities written in terms of an idempotent semiring. As a result, many issues in project scheduling reduce to solving computational problems in the idempotent algebra setting, like linear equations and the eigenvalue-eigenvector problem. We start with a brief introduction to idempotent algebra including main definitions, notation, and basic results that underlie subsequent applications. Furthermore, actual problems in project scheduling are considered. We show how to formulate the problems in terms of idempotent algebra, and present related algebraic solutions. To illustrate the application of the results, numerical examples are given.

Brief Biography of the Speaker:
Nikolai Krivulin received a university degree in applied mathematics and operations research in 1983 from St. Petersburg State University. He got his Ph.D. degree in 1990 and D.Sc. degree in 2010 both in applied mathematics from the same university. In 1983 he joined the Computer Center at St. Petersburg State University as a system software engineer, and in 1985 started his Ph.D. study. In 1987 he joined the Faculty of Mathematics and Mechanics at this university as an Assistant Professor, and became an Associate Professor there in 1990. From 1999 to 2002 he was the head of the Department of Information Management at the Graduate School of Management of the same university.
He is currently an Associate Professor of the Department of Statistical Modelling at St. Petersburg State University. His research interests include theory and applications of idempotent algebra, modelling and performance evaluation of queueing systems, methods of optimization, computational statistics and computer simulation. Nikolai Krivulin is an author and coauthor of more than 70 publications including papers published in reviewed journals and conference proceedings, books chapters, textbooks, and a monograph. He is a grantee of national and international foundations, including the Russian Foundation for Basic Research, the Russian Foundation for Humanities Research, the NATO Science Foundation, the USIA and Eurasia Foundation (USA), and the Royal Society (UK). He was a member of program and organizing committees of international conferences on mathematics, computer sciences, and information technology. He is a member of St. Petersburg Mathematical Society, AMS, and SIAM.