Algebraic solutions to scheduling problems in project management

An approach to schedule development in project management is proposed based on models and methods of idempotent algebra. The approach offers a way to represent various types of precedence relationships among activities in projects as linear vector equations 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 problem. The solutions to the problems are given in a compact vector form that provides the basis for the development of efficient computation procedures and related software applications.