Date of Award


Publication Type

Master Thesis

Degree Name



Industrial and Manufacturing Systems Engineering

First Advisor

ElMaraghy, Hoda


ِDiscrete Event Dynamic System, Discrete Even Simulation, FlexSim, Line Balancing, Max-Plus Algebra, Modelling Manufacturing System




In today's dynamic environment, particularly the manufacturing sector, the necessity of being agile, and flexible is far greater than before. Decision makers should be equipped with effective tools, methods, and information to respond to the market's rapid changes. Modelling a manufacturing system provides unique insight into its behavior and allows simulating all crucial elements that have a role in the system performance. Max-Plus Algebra is a mathematical tool that can model a Discrete Event Dynamic System in the form of linear equations. Whereas Max-Plus Algebra was introduced after the 1980s, the number of studies regarding this tool and its applications is fewer than regarding Petri Nets, Automata, Markov process, Discrete Even Simulation and Queuing models. Consequently, Max-Plus Algebra needs to be applied and tested in many systems in order to explore hidden aspects of its function and capabilities. To work effectively; the production/assembly line should be balanced. Line balancing is one of the manufacturing functions that tries to divide work equally across the production flow. Car Headlight Manufacturing Line as a Discrete Manufacturing System is considered which is a combination of manufacturing and assembly lines composed of different stations. Seven system scenarios were modeled and analyzed using Max-Plus to balance the car headlights production line. Key Performance Indicators (KPIs) are used to compare the various scenarios including Cycle Time, Average Deliver Rate, Total Processing Lead Time, Stations' Utilization Rate, Idle Time, Efficiency, and Financial Analysis. FlexSim simulation software is used to validate the Max-Plus models results and its advantages and drawbacks compared with Max-Plus Algebra. This study is a unique application of Max-Plus Algebra in line balancing of a manufacturing system. Moreover, the problem size of the considered model is at least twice (12 stations) that of previous studies. In the matter of complexity, seven different scenarios are developed through the combination of parallel stations and buffers. Due to that the last scenario is included four parallel stations plus two buffers Based on the findings, the superiority of scenario 7 compared to other scenarios is proved due to its lowest system delivering first output time (14 seconds), best average delivery rate (24.5 seconds), shortest cycle time (736 seconds), shortest total processing lead time (11,534 seconds), least percentage of idle time (12%), lowest unit cost ($6.9), and highest efficiency (88%). However, Scenario 4 has the best utilization rate at 75%.