Abstract
Consider n jobs ( J 1,…, J n ) and m machines ( M 1,…, M m ). The route by which a job passes through the machines is either M 1 → M 2 → … → M m or M m → M m−1 → … M 1, i.e. reversible-shop. It is proved that for three machines, the problem of minimizing the schedule length is NP-hard. Efficient algorithms are developed for the following special cases: three machines of which one or more are dominated; arbitrary number of machines where all operations have equal processing times; three machines, route-dependent reversible-shop where the second machine dominates the other two.
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