Job-shop scheduling using automated reasoning: A case study of the car-sequencing problem

Abstract

The ‘job-shop scheduling problem’ is known to be NP-complete. The version of interest in this paper concerns an assembly line designed to produce various cars, each of which requires a (possibly different) set of options. The combinatorics of the problem preclude seeking a maximal solution. Nevertheless, because of the underlying economic considerations, an approach that yields a ‘good’ sequence of cars, given the specific required options for each, would be most valuable. In this paper, we focus on an environment for seeking, studying, and evaluating approaches for yielding good sequences. The environment we discuss relies on the automated reasoning program ITP. Automated reasoning programs of this type offer a wide variety of ways to reason, strategies for controlling the reasoning, and auxiliary procedures that contribute to the effective study of problems of this kind. We view the study presented in this paper as a prototype of what can be accomplished with the assistance of an automated reasoning program.