A MILP model for an extended version of the Flexible Job Shop Scheduling problem is proposed. The extension allows the precedences between operations of a job to be given by an arbitrary directed acyclic graph rather than a linear order. The goal is the minimization of the makespan. Theoretical and practical advantages of the proposed model are discussed. Numerical experiments show the performance of a commercial exact solver when applied to the proposed model. The new model is also compared with a simple extension of the model described by \"Ozg\"uven, \"Ozbakir, and Yavuz (Mathematical models for job-shop scheduling problems with routing and process plan flexibility, Applied Mathematical Modelling, 34:1539--1548, 2010), using instances from the literature and instances inspired by real data from the printing industry.
@article{arxiv.1401.3654,
title = {A MILP model for an extended version of the Flexible Job Shop Problem},
author = {Ernesto G. Birgin and Paulo Feofiloff and Cristina G. Fernandes and Everton L. de Melo and Marcio T. I. Oshiro and Débora P. Ronconi},
journal= {arXiv preprint arXiv:1401.3654},
year = {2014}
}