1-Blocking Pattern

Intent

When processing a number of jobs on machines under the Flexible Flow Shop Pattern or Flow Shop Pattern, there must at any time be at most one job queuing in front of a stage/machine, in other words the buffer between any two stages/machines has capacity 1.

Motivation

For example in car manufacturing, there may only be space for one car between two machines.

Applicability

Necessary conditions: Flexible Flow Shop Pattern
Sufficient conditions: The necessary conditions and for any two consecutive machines, the start time of a job at the second machine occurs before the end time of the next job at the first machine. In particular, for any $m \in M_E$ , and any $k \in \{1, \dots, |\mathfrak{ops}^p(m)|-1\}$ , let $j=\texttt{\#}_{\mbox{job}}(\mathfrak{op}^p_{k+1}(m))$ . For any $i \in \{2, \dots, |ops^p(j)|\}$ such that $\texttt{\#}_{\mbox{machine}}(op^p_i(j)) = m$ then
$\texttt{\#}_{\mbox{start}}(\mathfrak{op}^p_k(m)) \leq \texttt{\#}_{\mbox{end}}(op^p_{i-1}(j))$ .

Participants

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

Collaborations

In front of every stage/machine (except the initial stage/machine) at most one job is allowed to wait at any time.

Diagram

Gantt chart showing three jobs being processed on two machines with Buffers of capacity one between machines:

Consequences

This pattern implies the Permutation Pattern.

Modelling variants

Note: As the Permutation Pattern (for (Flexible) Flow Shop) is implied by the modelling variants of the 1-Blocking Pattern, there is no need to also include the Permutation Pattern modelling variant in the model
(1) OPL for Cplex CP with Flexible Flow Shop Pattern Cplex modelling variant Download
(2) OPL for Cplex CP with Flow Shop Pattern Cplex modelling variant Download
(3) MiniZinc with Flexible Flow Shop Pattern MiniZinc modelling variant Download
(4) MiniZinc with Flow Shop Pattern MiniZinc modelling variant Download

Forces

Scheduing Problem Pattern, Flexible Flow Shop Pattern, Permutation Pattern

Enables

Compatible with

Machine Setup Pattern, Distinguishable Resources Pattern, Indistinguishable Resources Pattern