  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 sublanguage is empty, we will determine the minimal
sets of job deadlines that need to be relaxed.
