Scheduling with disjunctive constraints

The job shop scheduling problem consists of determining a sequence of jobs to be processed on each of the available machines such that the schedule time is minimized. The parts are processed in accordance with a prespecified technological ordering and the required processing times of the operations pertaining to each job are known. In this paper the authors study the job shop scheduling problem in two ways, namely, integer programming and graph theory. A computational program based on graph theory was developed and tested. This program allows us to solve efficiently several examples, despite the non-polynomial nature of the problem studied.