Flexible Flow Shop Pattern

IntentA set of jobs is to be processed on a set of machines. There is a fixed number of stages and each job needs to be processed in each of the stages exactly once in a predetermined order, which is the same for all jobs. In each stage there are some number of identical machines that can process the job at this stage. Each machine can only ever process one job at a time.
MotivationFlexible flow shop machine environments regularly occur in manufacturing.
ApplicabilityNecessary conditions: Elementary Scheduling Problem
Sufficient conditions: The necessary conditions and let j_1 \in J_E be a job in the event log. For all j_2 \in J_E and all m\in M_E:
(a) Every job j_2 is processed on every machine at most once, so for all h, i \in \{1, \dots, |ops^p(j_2)|\} such that h \neq i: \texttt{\#}_{\mbox{machine}}(op^p_h(j_2)) \neq  \texttt{\#}_{\mbox{machine}} (op^p_i(j_2)).
(b) Every job j_2 consists of the same number of operations, so |ops^p(j_2)| = |ops^p(j_1)|.
(c) Each machine belongs to exactly one stage and the order through the stages is the same for all jobs, so for all i_1, i_2 \in \{1, \dots, |ops^p(j_2)|\} where i_1 \neq i_2 we have
\texttt{\#}_{\mbox{machine}}(op^p_{i_1}(j_1)) \neq \texttt{\#}_{\mbox{machine}}(op^p_{i_2}(j_2)).
ParticipantsA set of jobs consisting of operations, and a set of machines partitioned into stages.
CollaborationsThe machines are partitioned into stages. Each job has to be processed on one machine of each stage exactly once in a predetermined order of the stages, which is the same across all jobs.
DiagramGantt chart showing four jobs being processed in three stages, where machines 1 and 2 belong to stage 1, machine 3 belongs to stage 2 and machines 4 and 5 belong to stage 3.
ConsequencesEach operation belongs to a fixed and pedermined stage and can be processed on any of the (identical) machines belonging to this stage. Each job visits each stage exactly once and the order in which stages are visited by jobs is the same for all jobs.
Modelling variants(1) OPL for Cplex CP Download
(2) MiniZinc
ForcesElementary Scheduling Pattern
EnablesFlow Shop Pattern, Permutation Pattern, 1-Blocking Pattern
Compatible withNo Wait Pattern, Machine Setup Pattern, Distinguishable Resources Pattern, Indistinguishable Resources Pattern