Flow Shop Pattern

Intent

A set of jobs is to be processed on a set of machines. Each job is to be processed on each of the machines exactly once in a predetermined order and the order is the same for all jobs.

Motivation

Flow shop machine environments regularly occur for example in car manufacturing and we can leverage the fixed machine order to make the constraint model more efficient.

Applicability

Necessary conditions: Job Shop Pattern and Flexible Flow Shop Pattern
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 $j_2$ consists of exactly $|M|$ operations, so $|ops^p(j_2)| = |M_E|$ .
(b) The route of every job through the machines must be the same, so for all $i \in \{1, \dots, |ops^p(j_2)|\}$ we have
$\texttt{\#}_{\mbox{machine}}(op^p_{i}(j_2)) = \texttt{\#}_{\mbox{machine}}(op^p_{i}(j_1))$ .

Participants

A set of jobs consisting of operations, and a set of machines.

Collaborations

Each job has to be processed on each of the machines exactly once in a predetermined order, which is the same across all jobs.

Diagram

Gantt chart showing four jobs being processed on three machines:

Consequences

The machine on which each operation is to be processed is predetermined and fixed. Each job visits each machine exactly once and the order in which machines are visited by jobs is the same for all jobs.

Modelling variants

(1) OPL for Cplex CP Download
(2) MiniZinc Download

Forces

Elementary Scheduling Pattern, Job Shop Pattern, Flexible Flow Shop Pattern

Enables

Permutation Pattern, 1-Blocking Pattern

Compatible with

No Wait Pattern, Machine Setup Pattern, Distinguishable Resources Pattern, Indistinguishable Resources Pattern