Scheduling and Control Modeling of HVLV Systems Using Max-Plus Algebra

Abstract

The High-Variety, Low-Volume (HVLV) scheduling problem is one of the most arduous and combinatorial optimization problems. This paper presents an analytical scheduling model using a tropical algebra called (max,+) algebra. The aim is to find an allocation for each operation and to define the sequence of operations on each machine, so that the resulting schedule has a minimal completion time and the due dates of the different jobs (products) are met such that a Just-In-Time (JIT) production will be satisfied. To generate feasible schedules, decision variables are introduced in the model. The algebraic model developed in this work describes the discontinuous operations aspect of HVLV systems as Discrete Event Dynamic Systems (DEDS). It is non-linear in the sense of (max,+) algebra. The focus of this research concerns the development of a static scheduling approach for deterministic and not-decision-free HVLV manufacturing systems. Firstly, using (max, +) algebra, a direct generation of event-timing equations for deterministic and not-decision free HVLV systems is obtained. Then, a non-linear optimization problem in (max, +) algebra is solved. Finally, the validity of the proposed approach is illustrated by simulation examples.

Affiliations

University of Savoie

Domaine Universitaire, BP 80439

74944 Annecy le Vieux

France

Contributors

Imed Nasri

Georges Habchi

Reda Boukezzoula

Conference

Publication date: September 2011

Publication date (Print): September 2011

Pages: 1-9

ID: 10.14236/ewic/VECOS2011.5

Copyright statement: © Imed Nasri et al. Published by BCS Learning and Development Ltd. Fifth International Workshop on Verification and Evaluation of Computer and Communication Systems (VECoS 2011), Tunis, Tunisia

License:

This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Conference name: Fifth International Workshop on Verification and Evaluation of Computer and Communication Systems (VECoS 2011)

Conference acronym: VECOS

Conference number: 5

Conference location: Tunis, Tunisia

Conference date: 15-16 September 2011

Conference sponsor: Electronic Workshops in Computing (eWiC)

Conference theme: Verification and Evaluation of Computer and Communication Systems (VECoS 2011)

Product

Product Information: 1477-9358 BCS Learning & Development

Self URI (article page): https://www.scienceopen.com/hosted-document?doi=10.14236/ewic/VECOS2011.5

Self URI (journal page): https://ewic.bcs.org/

Categories

Series title: Electronic Workshops in Computing