Job-shop scheduling models with set-up times

In this paper we consider the classical representation of job-shop scheduling problems in terms of disjunctive graphs. We derive a mixed integer-linear programming model that keeps track of the immediate precedence relation between operations. Finally, we show how this framework can be used to solve job-shop scheduling problems with sequence-dependent set-up times. Two cases are considered: the set-up operation required before processing a job on a machine may start as soon as the machine is available, or only if both job and machine are available.