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.

Masalah Nilai Eigen Atas Aljabar Max-Plus Pada Sistem Produksi Bulu Mata

“…Penelitian sebelumnya menunjukkan bahwa nilai eigen atas aljabarmax-plus sudah digunakan pada produksi shuttlecock T3 (Permana et al, 2020), produksi gelas (Pramesthi, 2017) dan penjadwalan laboratorium (Hasanah & Putrawangsa, 2015). Pada penelitian ini, pembahasan digunakan pada produksi bulu mata yang meliputi nilai eigen serta vektor eigen yang bersesuaian atas aljabar max-plus, pembentukan model max-plus dari sistem produksi bulu mata, masalah eigen pada sistem produksi bulu mata dan periodesasi waktu proses produksi bulu mata.…”

“…Beberapa penelitian terdahulu yang berkaitan dengan kajian teori nilai eigen atas aljabar max-plus dibahahasanahs pada Tunisa, dkk (2016) dan Musthofa & Binatari (2013). Selanjutnya, beberapa penelitian terdahulu yang berkaitan dengan penggunaan nilai eigen aljabar max-plus antara lain pada produksi shuttlecock T3 (Permana et al, 2020), produksi gelas (Pramesthi, 2017) dan penjadwalan laboratorium (Hasanah & Putrawangsa, 2015).…”

Input-Output Analysis on Pia Saronde Production Process Scheduling with Invariant Max-Plus Linear System

“…The implementation of max-plus algebra also to study time disturbance propagation within a robustness improvement context [11]. Another implementation was in creating a production schedule for a Kok brand by [12]. It was also applied to modeling motion and control of lower limb exoskeleton [13].…”

Application of System Max-Plus Linear Equations on Serial Manufacturing Machine With Storage Unit

“…A DES is the name of the classification of manmade system problems involving limited resources and users [1], [2]. Max-plus Algebra can be used to apply algebraically several of the DES [3]. This article discusses the application of max-plus algebra which focuses on one example of DES, namely the production system.…”

“…The basic understanding and operation of max-plus algebra and matrix operations for max-plus algebra that used in this article refers to [9]- [11]. This article also describes the eigenvalues and eigenvectors in max-plus algebra referring to [3], [4], [12], [13]. Next, to determine the eigenvalues and eigenvectors of the matrix of max-plus algebra, an algorithm is taken from the article [5], [14].…”