Study of a NP-hard cyclic scheduling problem: The recurrent job-shop

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 algorighms could be based. The problem is proven to be NP-hard and is formalized as a mixed linear program. The paper proves 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 the paper proposes a branch and bound enumeration procedure and two heuristics solving the problem. It reports numerical experiments.