Study on partial flexible job-shop scheduling problem under tooling constraints: complexity and related problems
Étude sur le problème d'ordonnancement de job-shop flexible avec contraintes de tooling: complexité et problèmes reliés
Résumé
We introduce a new problem, which is an extension of the classical job shop with tooling constraints. We study it from 3 different aspects: scheduling, matrix visualization and vertex ordering in hypergraphs. We prove the equivalence of the different formulations of the problem and use them to prove several of its NP-Hard and polynomial subcases. This problem allows to find more elegant (and arguably shorter) proofs for several combinatorial problems. Including "Can a matrix can be made triangular by permuting rows and columns?", weak k-visit and a generalization of Johnson's argument for the two-machines flowshop.
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