A Max-Plus Algebra Approach to Study Time Disturbance Propagation within a Robustness Improvement Context

Industry 4.0 aims to ensure the future competitiveness of the manufacturing industry, where one of the major challenges faced by its implementation is the manufacturing/production system robustness (that is, able to perform in the presence of noise), as they may not be able to absorb input disruptions without bending or breaking. In this paper we propose to use the Max-Plus algebra approach to study the propagation of manufacturing disturbances (i.e., processing time variations), presenting a case study and performing a sensitivity analysis, with the idea of understanding under which conditions disturbance propagation takes place. Findings show that the impact propagation depends on where the variation source is located within the manufacturing system. Two are the main original contributions of this paper: the use of Max-Plus algebra to study the impact propagation of processing time variations and a four-step methodology to derive the equations representing the deterministic manufacturing system.

[1]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[2]  Jaime A. Camelio,et al.  Modeling Variation Propagation of Multi-Station Assembly Systems With Compliant Parts , 2003 .

[3]  Olga Gluchshenko,et al.  Performance based approach to investigate resilience and robustness of an ATM System , 2013 .

[4]  Felicjan Rydzak,et al.  - 1-A Concept of Resilience in Production Systems , 2006 .

[5]  Hamid Ullah,et al.  Petri net versus queuing theory for evaluation of FMS , 2011 .

[6]  Judit Mesterné Monostori,et al.  Robustness- and Complexity-oriented Characterization of Supply Networks’ Structures , 2016 .

[7]  Boris V. Sokolov,et al.  Control and system-theoretic identification of the supply chain dynamics domain for planning, analysis and adaptation of performance under uncertainty , 2013, Eur. J. Oper. Res..

[8]  A. Imaev,et al.  Hierarchial modeling of manufacturing systems using max-plus algebra , 2008, 2008 American Control Conference.

[9]  Angappa Gunasekaran,et al.  Building the “Triple R” in global manufacturing , 2017 .

[10]  Christian Schröder.  The Challenges of Industry 4 . 0 for Small and Medium-sized Enterprises , 2016 .

[11]  J. Fiksel.  Sustainability and Resilience: Toward a Systems Approach , 2006, IEEE Engineering Management Review.

[12]  Yu Ding,et al.  Process-oriented tolerancing for multi-station assembly systems , 2005 .

[13]  C. Leake.  Synchronization and Linearity: An Algebra for Discrete Event Systems , 1994 .

[14]  Nadia Bhuiyan,et al.  Production, Manufacturing and Logistics Entropy as a measure of operational flexibility , 2005 .

[15]  Ning Zhang,et al.  An optimization model for green supply chain management by using a big data analytic approach , 2017 .

[16]  Lindu Zhao,et al.  Research on measuring method of supply chain resilience based on biological cell elasticity theory , 2011, 2011 IEEE International Conference on Industrial Engineering and Engineering Management.

[17]  Jitesh H. Panchal,et al.  Towards the Design of Complex Evolving Networks with High Robustness and Resilience , 2013, CSER.

[18]  Stephan M. Wagner,et al.  DO PERCEPTIONS BECOME REALITY? THE MODERATING ROLE OF SUPPLY CHAIN RESILIENCY ON DISRUPTION OCCURRENCE , 2010 .

[19]  Boris V. Sokolov,et al.  A Dynamic Approach to Multi-stage Job Shop Scheduling in an Industry 4.0-Based Flexible Assembly System , 2017, APMS.

[20]  Haitao Zhang,et al.  Dynamic Analysis of Production Network from Perspective of Order Flows , 2016 .

[21]  Robert P. Judd,et al.  Block diagram-based modeling of manufacturing systems using , 2009, 2009 American Control Conference.

[22]  Hoda A. ElMaraghy,et al.  Max-plus Modeling of Manufacturing Flow Lines☆ , 2014 .

[23]  B. De Schutter,et al.  Max-plus algebra and max-plus linear discrete event systems: An introduction , 2008 .

[24]  James C. Chen,et al.  Supply chain management with lean production and RFID application: A case study , 2013, Expert Syst. Appl..

[25]  Nagesh N. Murthy,et al.  Achieving supply chain agility through IT integration and flexibility , 2008 .

[26]  Mohamed Mohamed Naim,et al.  A control engineering approach to the assessment of supply chain resilience , 2012 .

[27]  Kevin Otto,et al.  SYSTEM-LEVEL ROBUSTNESS THROUGH INTEGRATED MODELING , 1999 .

[28]  Alexandre Dolgui,et al.  Supply Chain Design With Disruption Considerations: Review of Research Streams on the Ripple Effect in the Supply Chain , 2015 .

[29]  Jiafu Wan,et al.  Implementing Smart Factory of Industrie 4.0: An Outlook , 2016, Int. J. Distributed Sens. Networks.

[30]  W. Marsden.  I and J , 2012 .

[31]  Abdulrahman Saad Salah-Eldin Seleim,et al.  Modeling and Performance Analysis of Manufacturing Systems Using Max-Plus Algebra , 2016 .

[32]  Rajesh S. Ransing,et al.  Risk based uncertainty quantification to improve robustness of manufacturing operations , 2016, Comput. Ind. Eng..

[33]  H. Nagai,et al.  On the Max-Plus Linear representation for event-varying systems with buffer and order constraints , 2007, 2007 IEEE International Conference on Industrial Engineering and Engineering Management.

[34]  Olga Gluchshenko,et al.  Definitions of Disturbance, Resilience and Robustness in ATM Context , 2012 .

[35]  Joseph Fiksel,et al.  Designing resilient, sustainable systems. , 2003, Environmental science & technology.

[36]  Prabath Chaminda Abeysiriwardana,et al.  A Model for Web-Intelligence Index to Evaluate the Web Intelligence Capacity of Government Web Sites of Sri Lanka , 2015, ArXiv.

[37]  Jay Lee,et al.  Self-maintenance and engineering immune systems: Towards smarter machines and manufacturing systems , 2011, Annu. Rev. Control..

[38]  Edward W. Kamen,et al.  Direct generation of event-timing equations for generalized flow shop systems , 1995, Optics East.

[39]  Virgilio Cruz-Machado,et al.  A mapping framework for assessing Supply Chain resilience , 2012 .

[40]  Jörg Raisch,et al.  Modelling and Performance Evaluation of DES - A Max-Plus Algebra Toolbox for Matlab , 2018, ICINCO.

[41]  Laurent Hardouin,et al.  Models combination in (max, +) algebra for the implementation of a simulation and analysis software , 2003, Kybernetika.

[42]  Randall P. Sadowski,et al.  Simulation with Arena , 1998 .

[43]  Leyuan Shi,et al.  Maintaining constant WIP-regulation dynamics in production networks with autonomous work systems , 2009 .

[44]  Nabil Absi,et al.  Impacts of Industry 4.0 on the Specific Case of Mass Customization Through Modeling and Simulation Approach , 2018 .

[45]  Keely L. Croxton,et al.  ENSURING SUPPLY CHAIN RESILIENCE: DEVELOPMENT OF A CONCEPTUAL FRAMEWORK , 2010 .

[46]  Gisela Lanza,et al.  An Approach towards Improving the Robustness of Production Systems , 2014 .

[47]  Konja Knüppel,et al.  Target-Based Evaluation of Disturbances in Production Systems , 2014 .

[48]  Ignacio E. Grossmann,et al.  Design of Resilient Supply Chains with Risk of Facility Disruptions , 2014 .

[49]  Luc Bongaerts,et al.  Disturbance measurement in manufacturing production systems , 1998 .

[50]  Tammy E. Beck,et al.  Developing a capacity for organizational resilience through strategic human resource management , 2011, Human Resource Management Review.

[51]  Liang Tang,et al.  Robustness of assembly supply chain networks by considering risk propagation and cascading failure , 2016 .

[52]  Darek Ceglarek,et al.  Transfer Function of Assembly Process with Compliant Non-ideal Parts☆ , 2014 .

[53]  Valentas Gružauskas,et al.  Big Data Concept in the Food Supply Chain: Small Markets Case , 2016 .

[54]  He Yanfeng.  Resilient supply chain system coordinating: Mechanism designing for emergence produced , 2011, MSIE 2011.

[55]  Mantas Vilkas,et al.  Managing Capabilities for Supply Chain Resilience Through it Integration , 2017 .

[56]  Paulo Leitão,et al.  Predictive disturbance management in manufacturing control systems , 2004 .

[57]  Neil Genzlinger.  A. and Q , 2006 .

[58]  Samuel Asante Gyamerah,et al.  Max-plus Algebra and Application to Matrix Operations , 2016 .

[59]  Alessandro Abate,et al.  Formal Verification of Stochastic Max-Plus-Linear Systems , 2016, IEEE Transactions on Automatic Control.