Scheduling general production systems using schedule algebra

Abstract

The objective of this work is to demonstrate the use of schedule algebra to define and solve problems to generate and evaluate production schedules and, in the process, to describe a recently completed computer program, SCHEDULER I, which solves this problem for a wide class of products and production systems. The problem formulation requires that the program user describe each system output in terms of its constituent tasks and state, for each task, all restraints which will or may affect either the time it is performed or the choice of a particular facility to perform it. The user must also specify the numbers and types of facilities which are available to perform the tasks and all restraints affecting these availabilities. The problem is, given restraints of the preceding character, to determine when each task starts and ends, the specific facility which performs it, how long the task had to wait for the facility to become available (or, if the facility was previously idle, how long it was idle) and how long the task's scheduled start could be postponed without automatically forcing the postponement of the scheduled start of any other task. Novel features of the problem formulation permit the user to specify, with considerable latitude, the decision rules to be used in selecting tasks to be started on a vacated facility, to freely dovetail successive tasks to produce a same output and successive tasks performed by a same facility, and to change the capacity of the production system at any point in time. The program automatically readjusts the time‐phasing of a task if its processing must be interrupted in order to reduce the capacity of the production system.