SAJSET-01-2023-0015 Scheduling model of manufacturing systems using tropical algebra

Abstract

The production process is included in the Discrete Event System (DES). The DES independent variable generally depends on the event, so an event is influenced by the previous event. Tropical algebra can be used in the DES system to change the nonlinear system of equations to linear equations. Whereas Tropical Algebra was introduced after the 1980s, the number of studies regarding this tool and its applications is fewer than regarding Discrete Even Simulation and Queuing models. Consequently, tropical Algebra needs to be applied and tested in many systems in order to explore hidden aspects of its function and capabilities. The purpose of this study is to provide a scheduling model using tropical algebra, for a specific class of discrete event system which are specifically manufacturing systems. Such systems are called tropical linear discrete event systems. The methods used is constructing matrix equations from the system of equations, solving Eigen value and Eigen vectors to determine the schedule production and find starting time. The results of the research showed that the production system run periodically every 7 hours. Also the best time for each unit to start working was determined, as well as the production schedule base on daily working hours is obtained.