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A MILP model for an extended version of the Flexible Job Shop Schedulingproblem is proposed. The extension allows the precedences between operations ofa job to be given by an arbitrary directed acyclic graph rather than a linearorder. The goal is the minimization of the makespan. Theoretical and practicaladvantages of the proposed model are discussed. Numerical experiments show theperformance of a commercial exact solver when applied to the proposed model.The new model is also compared with a simple extension of the model describedby \"Ozg\"uven, \"Ozbakir, and Yavuz (Mathematical models for job-shopscheduling problems with routing and process plan flexibility, AppliedMathematical Modelling, 34:1539--1548, 2010), using instances from theliterature and instances inspired by real data from the printing industry.

A MILP model for an extended version of the Flexible Job Shop Problem