Immaculada Ribas Vila

A note on the paper ‘Demonstrating Johnson’s algorithm via resource constrained scheduling’

In this paper, we demonstrate that the relation between two jobs defined by min{ai, bj} ≤ min{bi, aj}, used in Johnson’s theorem, is not transitive. However, both the theorem and Johnson’s algorithm are correct.

A New Constructive Heuristic for the Fm|block|ΣT

This paper deals with the blocking flow shop problem and proposes new constructive procedures for the total tardiness minimization of jobs. The heuristic has three-phases to build the sequence; the first phase selects the first job to be scheduled, the second phase arranges the remaining jobs and the third phase uses the insertion procedure of NEH to improve the sequence. The proposed procedures evaluate the tardiness associated to the sequence obtained before and after the third phase in order to keep the best of both because the insertion phase can worsen the result. The computational evaluation of these procedures against the benchmark constructive procedures from the literature reveals their good performance.