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Study of a NP-hard cyclic scheduling problem: The recurrent job-shop. (English) Zbl 0801.90061
Summary: This paper tackles a cyclic scheduling problem with disjunctive resources called the recurrent job-shop. It is aimed to show structural properties of feasible schedules on which efficient algorithms could be based. The problem is proven to be NP-hard and is formulated as a mixed linear program. We prove that any feasible solution is associated with a valuation called a conservative height on the graph of constraints. Computing the critical circuit provides the best solution associated with a given conservative height. Bounds on the feasible heights and on the throughput based on these properties are then stated. Finally we propose a branch-and-bound enumeration procedure and two heuristics solving the problem. We report numerical experiments.

MSC:
90B35 Deterministic scheduling theory in operations research
90C60 Abstract computational complexity for mathematical programming problems
Software:
PESPLib
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