Max-Plus Algebra as a Tool for the Modelling and Performance Analysis of Manufacturing Systems

• Main Author: Jarosław Stańczyk
• Format: Article
• Language: English
• Published: Wrocław University of Science and Technology 2018-01-01
• Series: Operations Research and Decisions
• Online Access: http://orduser.pwr.wroc.pl/DownloadFile.aspx?aid=1336

This contribution discusses the usefulness of (max, +) algebra as a mathematical framework for a class of manufacturing systems. This class can be described as dynamic and asynchronous, where the state transitions are initiated by events that occur at discrete instants of time. An event corresponds to the start or the end of an activity. Such systems are known as discrete event systems (DES). An overview of the concepts of modelling and analysis using the (max, +) algebra approach to DES has been given. Also, examples of manufacturing systems have been provided to illustrate the potential of this approach. The type of production process used, such as serial line, assembly line, etc., influences the modelling of different basic manufacturing systems. We have also presented the impact of the capacity of interoperable buffers. Based on an analytical model, effectiveness and performance indexes have been evaluated. (original abstract)