Permutation Pattern

IntentA number of jobs are processed on machines under the Flexible Flow Shop Pattern or Flow Shop Pattern and further no job is allowed to overtake another job, so the order in which jobs are processed on the stages/machines is the same for all stages/machines.
MotivationIn the manufacturing of large items, for example in car manufacturing, there may not be space for jobs to overtake one another.
ApplicabilityNecessary conditions: Flexible Flow Shop Pattern
Sufficient conditions: The necessary conditions and the order in which jobs are processed on a machine is the same for all machines, so for all m_1, m_2 \in M_E and all k \in \{0, \dots, |J_E|\} we have \texttt{\#}_{\mbox{job}}(\mathfrak{op}^p_{k}(m_1)) = \texttt{\#}_{\mbox{job}}(\mathfrak{op}^p_{k}(m_2)).
ParticipantsA set of jobs consisting of operations, and a set of machines.
CollaborationsThe jobs appear on each machine in the same order.
DiagramGantt chart showing four jobs being processed on three machines:
ConsequencesThe machine on which each operation is to be processed is predetermined and fixed.
Modelling variants(1) OPL for Cplex CP with Flexible Flow Shop Pattern Cplex modelling variant Download
(2) MiniZinc with Flexible Flow Shop Pattern MiniZinc modelling variant Download
(3) OPL for Cplex CP with Flow Shop Pattern Cplex modelling variant Download
(4) MiniZinc with Flow Shop Pattern MiniZinc modelling variant Download
ForcesElementary Scheduling Pattern, Job Shop Pattern, Flow Shop Pattern
EnablesNo Wait Pattern, 1-Blocking Pattern
Compatible withMachine Setup Pattern, Distinguishable Resources Pattern, Indistinguishable Resources Pattern