A New Approach to Computing Optimal Schedules for the Job-Shop Scheduling Problem

From a computational point of view, the job-shop scheduling problem is one of the most notoriously intractable NP-hard optimization problems. In spite of a great deal of substantive research, there are instances of even quite modest size for which it is beyond our current understanding to solve to optimality. We propose several new lower bounding procedures for this problem, and show how to incorporate them into a branch-and-bound procedure. Unlike almost all of the work done on this problem in the past thirty years, our enumerative procedure is not based on the disjunctive graph formulation, but is rather a time-oriented branching scheme. We show that our approach can solve most of the standard benchmark instances, and obtains the best known lower bounds on each.

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