Application of Max-Plus Algebra for Scheduling the Alethaskin Body Lotion Production System
Winarni (a*)- Umul Kalsum Septiani (a)- Kartika Nugraheni (a)

(a) Institut Teknologi Kalimantan
Jalan Soekarno-Hatta KM 15 Karang Joang Balikpapan 76127, East Kalimantan, Indonesia
*winarni[at]lecturer.itk.ac.id

Abstract

Companies must plan and determine a good production system to be able to meet market demand. CV Dermalis Group is a cosmetic manufacturing company. The main product is Alethaskin body lotion. There are two variants of Alethaskin body lotion, namely Infused Body Night Serum with AHA and Gluthation (night lotion) and Booster Perfect Brightening Day Lotion with Repairing and UV Filter (day lotion). The problem that often occurs in Alethashin^s body lotion production is irregular production because there is no proper production schedule. Therefore, in this study, the Alethaskin body lotion production system was scheduled using the max-plus algebraic model. The existing production system was arranged in the form of a production flow diagram and graph. Then, the max-plus algebraic model for the production schedule is constructed. The model that had been constructed was analyzed to determine the eigenvalues and eigenvectors using the power algorithm with Scilab and the max-plus algebra toolbox, to obtain a periodic production system, after that the production schedule is arranged. Based on the research results, the eigenvalue is 285, which means that the period between one production to the next is 285 minutes. Furthermore, a good initial condition was obtained to start production, in the P1 to P10 process, starting respectively at 1, 1, 17, 20, 53, 61, 91, 99, 188, and 224 minutes. Alethaskin body lotion production schedule is periodically carried out for 24 hours of work with a shift system. It can be produced in five batches for 24 hours.

Keywords: cosmetics- graph- max-lus algebra- production system- scheduling

Topic: MATHEMATICS AND STATISTICS