Eigen Problem Over Max-Plus Algebra on Determination of the T3 Brand Shuttlecock Production Schedule

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. Max-plus algebra can be applied in the DES problem to change the system of nonlinear equations obtained into linear equations. Max-plus algebra is a set of real numbers  combined with  equipped with operations max  and plus ⊗ or can be denoted  with . An effective and efficient production process needs to pay attention scheduling steps well. The purpose of this research is to determine the Shuttlecock T3 production schedule using eigenvalue and eigenvector in max-plus algebra. The research method in this research is study of literature and observation. Literature study is carried out by studying references about max-plus algebra, especially material related to scheduling problems, while observation are carried out in the process of taking data of the Shuttlecock T3 production process in Surakarta. The linear equation system that is formed based on the results of the observation is then presented in the form  and . The periodic time and initial system production time are determined from the eigenvalue and eigenvector matrix  where . The results of the research showed that the production system run periodically every 249 minutes, then the best time for each processing unit to start working can be determined, as well as the Shuttlecock T3 production schedule according to the working hours more effective and efficient can be determined too.