Performance Evaluation of a Multi Product Production System using Timed Event Graph and Max- Plus Algebra

Abstract

The production systems used in the modern industry are usually composed of integrated and complex processing equipment having automated material handling and advanced computer networks for information transfer. Mathematical models are essential for understanding various events which are occurring in production systems. In this paper, max-plus algebra have been applied to model a complex production system known as multi product production system (MPPS) with different routing policies and its usefulness to describe and analyze such systems has been presented. An algorithm known as MPA-algorithm is proposed for analytical model building in max-plus algebra from the timed event graph (TEG) model. The basic criterion used for performance evaluation of the modeled system is cycle time, which is evaluated by using Karp’s theorem from graph theory. Other performance measures of the MPPS are also evaluated from the max-plus model by treating MPPS as a flow-shop system