Automaton-based timed supervisory control for operational planning and scheduling under multiple job deadlines

In this paper we model an operational planning and scheduling problem under multiple job deadlines in a time-weighted automaton framework. We first present a method to determine whether all given job specifications and deadlines can be met by computing a supremal controllable job satisfaction sublanguage. When this supremal sublanguage is not empty, we compute one of its controllable sublanguages that ensures the minimum total job earliness by adding proper delays. When this supremal sublangauge is empty, we will determine the minimal sets of job deadlines that need to be relaxed.