Distinguishable Resources Pattern

Intent

When processing a number of operations, exactly one resource from a set of distinguishable resources needs to be present for each of the operations.

Motivation

In flow shop or (flexible) job shop problems it frequently occurs that workers process the jobs at different machines and the workers can move between machines. We also wish to distinguish between the workers (eg. because some workers may not be able to work on certain machines or there may be resource setup times).

Applicability

Necessary conditions: Scheduling Problem Pattern
Sufficient conditions: The necessary conditions and
(a) A resource is present at someoperation. There exists $j_1\in J_E$ and $i \in \{1, \dots, |ops^p(j_1)|\}$ , such that $\texttt{\#}_{\mbox{resource}}(op^p_i(j_1)) \neq \bot$ .
(b) Each resource can only process one operation at a time: Let $j_1\in J_E$ and $i \in \{1, \dots, |ops^p(j_1)|\}$ . Then for all $j_2 \in J_E$ and all $k \in \{1, \dots, |ops^p(j_2)|\}$ such that $\texttt{\#}_{\mbox{resource}}(op^p_k(j_2)) = \texttt{\#}_{\mbox{resource}}(op^p_i(j_1)) (\neq \bot)$ : $\texttt{\#}_{\mbox{start}}(op^p_k(j_2)) \geq \texttt{\#}_{\mbox{end}}(op^p_i(j_1))$ or $\texttt{\#}_{\mbox{end}}(op^p_k(j_2)) \leq \texttt{\#}_{\mbox{start}}(op^p_i(j_1))$ .

Participants

A set of operations to be processed and a set of distinguishable resources used to process them.

Collaborations

Exactly one resource must be assigned to each operation.

Diagram

Gantt chart showing three resources processing one job:

Consequences

If there is no need to distinguish between all of the resources, the indistinguishable resources pattern will usually yield a more efficient model.

Modelling variants

(1) OPL for Cplex CP with Job Shop Pattern Cplex modelling variant Download
(2) OPL for Cplex CP with Flexible Flow Shop Pattern Cplex modelling variant Download
(3) OPL for Cplex CP with Flow Shop Pattern Cplex modelling variant Download
(4) MiniZinc with Job Shop Pattern MiniZinc modelling variant Download
(5) MiniZinc with Flexible Flow Shop Pattern MiniZinc modelling variant Download
(6) MiniZinc with Flow Shop Pattern MiniZinc modelling variant Download

Forces

Elementary Scheduing Pattern

Enables

Resources Setup Pattern

Compatible with

Machine Setup Pattern, 1-Blocking Pattern, No Wait Pattern, Permutation Pattern