Issue: 2018/Vol.28/No.3, Pages 77-97
MAX-PLUS ALGEBRA AS A TOOL TO MODELLING AND PERFORMANCE ANALYSIS OF MANUFACTURING SYSTEMS
Jarosław Stańczyk
Cite as: J. Stańczyk. Max-plus algebra as a tool to modelling and performance analysis of manufacturing systems. Operations Research and Decisions 2018: 28(3), 77-97. DOI 10.5277/ord180306
Abstract
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 di screte 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.
Keywords: discrete event system, max-plus algebra, performance evaluation, manufacturing systems
Received: 9 October 2017 Accepted: 14 August 2018