Reversible-shop scheduling

Abstract

Abstract Consider n jobs (J1,…,Jn) and m machines (M1,…,Mm). The route by which a job passes through the machines is either M1 → M2 → … → Mm or Mm → Mm−1 → … M1, 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.