Generating scheduling constraints for discrete event dynamic systems

In most scheduling literature, constraints are seemingly generated in an ad-hoc manner using intuitive arguments. This could result in overlooking some constraints or including unnecessary constraints. Schruben (2000) has shown how the dynamics of some discrete event systems can be modeled as the solutions of optimization programs. In this paper, we use this idea to generate mathematical programming models systematically for scheduling resources in discrete event dynamic systems. Two examples are presented: a multiple server queue and a semiconductor manufacturing cluster tool. An interesting result was that the mathematical structure of the scheduling program generated from a simulation of a cluster tool found in the literature leads to a different, more concise and illuminating cluster tool simulation model that would have been difficult to discover otherwise. The corresponding optimal scheduling problem is surprising in that it does not include explicit representation of the resource that is actually being scheduled!.