Schedule algebra: A progress report

The following paper is the first part of a summary of the schedule algebraic method and its applications to date. It covers the origin and motivation of the schedule algebraic technique, the current status of the algebra as a mathematical system, and a brief outline of the theory of scheduling which the algebra is used to support. Part II of the Progress Report will be published at a later time. It will review applications of the algebra to practical problems and experience gained in the use of the algebra to schedule on-going production systems.