Formal Methods in Manufacturing

2	Modelling Manufacturing Systems in a Dioid Framework Thomas Brunsch, Laurent Hardouin and Jörg Raisch

CONTENTS

2.1 Motivational Example

2.2 Timed Event Graphs

2.3.1 Ordered Sets

2.3.2 Idempotent Semirings

2.3.3 Natural Order in Idempotent Sesmirings

2.3.4 Mappings in Idempotent Semirings

2.3.6 Fixed Point Equations

2.3.7 Dual Residuation

2.3.7.1 Dual Multiplication

2.3.8 Idempotent Semirings of Formal Power Series

2.3.8.1 Quotient Dioids

2.5 Modelling Manufacturing Systems with Dioids

2.5.1 Input-Output Behaviour of Manufacturing Systems

2.5.2 Modelling Time Window Constraints

2.5.3 Modelling Reentrant Operations

2.5.4 Checking Constraint Feasibility

References

2.1 MOTIVATIONAL EXAMPLE

A small manufacturing process is considered, where ...