An algebraic approach to project schedule development under precedence constraints

TL;DR

This paper introduces an algebraic method using idempotent algebra to model and solve project scheduling problems with precedence constraints, enabling efficient computation and software development.

Contribution

It presents a novel algebraic framework for project scheduling that simplifies precedence relationships into linear equations within an idempotent algebra setting.

Findings

Representation of precedence constraints as linear vector equations

Reduction of scheduling issues to solving algebraic problems

Development of efficient computational procedures

Abstract

An approach to schedule development in project management is developed within the framework of idempotent algebra. The approach offers a way to represent 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, including linear equations and eigenvalue-eigenvector problems. 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.