APPLICATION OF SYSTEM MAX-PLUS LINEAR EQUATIONS ON SERIAL MANUFACTURING MACHINE WITH STORAGE UNIT

The set  together with the operation maximum (max) denoted as  and addition (+) denoted as  is called max-plus algebra. Max-plus algebra may be used to apply algebraically a few programs of Discrete Event Systems (DES), certainly one of the examples in the production system. In this study, the application of max-plus algebra in a serial manufacturing machine with a storage unit is discussed. The results of this are the generalization system max-plus-linear equations on a production system that is, in addition, noted the max-plus-linear time-invariant system. From the max-plus-linear time-invariant system, it can be obtained the equation  which is then used to determine the beginning time of a production system so the manufacturing machine work periodically. The eigenvector and eigenvalue of the matrix  are then used to find the beginning time and the period time of the manufacturing machine. Furthermore, the time when the product leaves the manufacturing machine with the time while the raw material enters the manufacturing machine is given and vice versa are obtained from the max-plus-linear time-invariant system that is can be formed in the equation

Gold Price Fluctuation Forecasting Based on Newton and Lagrange Polynomial Interpolation

Gold is a highly valuable commodity and an investment opportunity for many people. However, thereare often significant fluctuations in gold prices that affect investment decisions. Various mathematicalforecasting methods have been developed to anticipate gold price fluctuations. This study uses historicaldaily data of gold prices during January-May 2023. The method used in this study is the Newton andLagrange polynomial interpolation method with several orders to analyze data and forecast gold pricefluctuations. The purpose of this study is to compare the performance and accuracy of the order levels ofthe Newton and Lagrange polynomial interpolation forecasting models. In this study, the test data pointsand orders are selected so that a range is formed that matches the amount of data available. The testorders used in this study include orders 2, 3, 5, 6, and 10. This study found that the 2nd order polynomialinterpolation method is more effective and accurate in forecasting gold price fluctuations compared tothe higher orders tested. This is indicated by the results of the calculation of MAE, RMSE, and MAPEvalues in 2nd order polynomial interpolation which are smaller than in 3rd, 5th, 6th, and 10th orderpolynomial interpolation. This suggests that a polynomial of 2nd order has been able to model andforecast gold price fluctuations well. However, it is important to remember that these conclusions arebased on the data and methods used in this study. Variability in forecasting results can occur dependingon the quality of the data, the time period used, and the interpolation method applied, among others.Therefore, further research and wider testing needs to be conducted to validate these conclusions

APLIKASI ALJABAR MAKS-PLUS PADA SISTEM PRODUKSI DENGAN SWITCHING, TIPE SERIAL, ASSEMBLY, SPLITTING, PARALLEL, DAN FLEXIBLE DENGAN AKTIVITAS BARISAN TERTENTU

ABSTRAK Andika Ellena Saufika Hakim Maharani, 2015. APLIKASI ALJABAR MAKS-PLUS PADA SISTEM PRODUKSI DENGAN SWITCHING , TIPE SERIAL, ASSEMBLY , SPLITTING , PARALLEL, DAN FLEXIBLE DENGAN AKTIVITAS BARISAN TERTENTU. Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Sebelas Maret. Aljabar maks-plus adalah himpunan Rmax = R ∪ {"} dilengkapi operasioperasi ⊕ dan ⊗ yang dinotasikan sebagai Rmax = (Rmax; ⊕; ⊗; "; e) dengan " = −∞, e = 0 dan R adalah himpunan bilangan real. Untuk semua a; b ∈ Rmax, didefinisikan a ⊕ b = max{a; b} dan a ⊗ b = a + b. Aljabar maks-plus dapat digunakan untuk mengaplikasikan secara aljabar beberapa aplikasi dari sistem kejadian diskrit (SKD), salah satunya adalah sistem produksi. Pada penelitian ini, dibahas aplikasi aljabar maks-plus pada suatu sistem produksi dengan switching, tipe serial, assembly, splitting, parallel, dan exible dengan aktivitas barisan tertentu. Hasil dari penelitian ini adalah persamaan linear yaitu x(k + 1) = ¯ A ⊗ x(k) yang kemudian digunakan untuk menentukan waktu mulai suatu sistem produksi agar sistem produksi berlangsung secara periodik. Hal ini dilakukan dengan menghitung nilai eigen dan vektor eigen dari matriks ¯ A. Waktu mulai dan periode sistem produksi diperoleh dengan menentukan vektor eigen dan nilai eigen dari matriks ¯ A. Kata kunci: aljabar maks-plus, sistem produksi, persamaan linear, nilai eigen, vektor eigen, periodi

The Defuzzification Methods Comparison of Mamdani Fuzzy Inference System in Predicting Tofu Production

One of the tofu-producing companies in Kupang City is Bintang Oesapa. With the Covid-19 pandemic,the factory needs to reconsider the amount of production by taking into account the unpredictability ofdemand and resources to minimize losses due to excessive accumulation or shortages of supplies. Indetermining the amount of production, Mamdani’s Fuzzy Inference System (FIS) can be used, whichis a method for the analysis of an uncertain system. This method has three stages in the process ofdecision making, namely fuzzification, inferencing and defuzzification. In the defuzzification stage,the FIS Mamdani has five methods, namely Centroid, Bisector, Mean of Maximum (MOM), Smallestof Maximum (SOM), and Largest of Maximum (LOM). This study discusses an application of FISMamdani with five defuzzification methods for determining daily tofu production. The purpose of thisstudy is to offer a solution by first comparing the five defuzzification methods in assessing the amount oftofu production at the Bintang Oesapa factory and then determining that which is most appropriate. Theinput variables used in this research are the amount of demand and the amount of available stock, whilethe amount of production is our variable of interest. The results showed that the best defuzzificationmethod was the MOM method with an accuracy level of 94.73% and a small error value, 5.27%. TheMOM defuzzification is expected to aid decision makers in determining the best amount of productionduring the pandemic