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Jurnal Matematika UNAND
Published by Universitas Andalas
ISSN : 2303291X     EISSN : 27219410     DOI : -
Core Subject : Science, Education,
Computer Science & IT Mathematics
Fokus dan Lingkup dari Jurnal Matematika FMIPA Unand meliputi topik-topik dalam Matematika sebagai berikut : Analisis dan Geometri Aljabar Matematika Terapan Matematika Kombinatorika Statistika dan Teori Peluang.
Arjuna Subject : -
Articles 858 Documents
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BILANGAN R-M-H UNTUK GRAF LINTASAN P_4 DAN GRAF RODA W_n DENGAN n>=3 Multasya, Nadya Citra; SYAFWAN, MAHDHIVAN; SY, SYAFRIZAL
Jurnal Matematika UNAND Vol. 12 No. 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.135-143.2023

Abstract

Diberikan dua graf G dan H serta bilangan asli j>=2. Bilangan Ramsey multipartit himpunan (R-M-H) M_j(G,H) adalah suatu bilangan bulat positif terkecil t sedemikian sehingga untuk sebarang faktorisasi K_(txj) = F_1 + F_2 senantiasa F_1 memuat subgraf G atau F_2 memuat subgraf H. Pada artikel ini akan ditentukan M_3(P_4,W_n) dimana P_4 adalah suatu graf lintasan yang terdiri dari 4 simpul dan W_n adalah suatu graf roda yang terdiri dari n+1 simpul dengan n>=3.
ANALISIS KESTABILAN MODEL MATEMATIKA AKSI DEMONSTRASI MAHASISWA DI SUMATERA BARAT Putri, Yolanda; RINCE PUTRI, ARRIVAL; LESTARI, RIRI
Jurnal Matematika UNAND Vol. 12 No. 3 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.3.213-221.2023

Abstract

Aksi demonstrasi atau unjuk rasa merupakan salah satu fenomena di dunia nyata yang sering terjadi dan melibatkan berbagai kalangan, baik mahasiswa, buruh, maupun anggota suatu organisasi. Khususnya di Sumatera Barat, pada tanggal 23 dan 25 September 2019 telah terjadi demonstrasi polemik RUU di gedung DPRD Sumatera Barat yang melibatkan ribuan mahasiswa, aparat kepolisian, dan anggota DPRD Tingkat I.Pada penelitian ini dibahas model matematika aksi demonstrasi mahasiswa. Model ini merujuk pada model Richardson. Model dianalisis kestabilannya melalui analisis kestabilan titik ekuilibrium. Kestabilan titik ekuilibrium ditentukan dari nilai eigen matriks koefisien yang diperoleh. Hasil analitik dikonfirmasi dengan hasil numerik. Parameter model yang digunakan pada simulasi numerik diperoleh dari data yang diolah berdasarkan kuisioner yang diambil dari responden. Berdasarkan hasil yang diperoleh dapat disimpulkan bahwa aksi demonstrasi yang terjadi berlangsung anarkis. Hal ini sesuai dengan kenyataan yang terjadi di lapangan bahwa aksi demonstrasi yang terjadi pada kasus demonstrasi polemik RUU di gedung DPRD Sumatera Barat tanggal 25 September 2019 merupakan demonstrasi anarkis. 
Comparison Between SARIMA Model and Artificial Neural Network On Forecasting Foreign Tourist in Batam City Rasyid, Fadila; DEVIANTO, DODI; RAHMI HG, IZZATI
Jurnal Matematika UNAND Vol. 12 No. 3 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.3.282-290.2023

Abstract

Batam City is one of the tourist attractions in Indonesia with the number of foreign tourist arrivals increasing every year. As one of the impacts of increasing the number of foreign tourist visits, the provincial government must improve the existing facilities in the tourism area, both in quality and quantity. In order for these facilities to be adequate to serve foreign tourists visiting Batam City in the future, it is estimated that the number of tourist visits to Batam City in the future is expected. This study aims to model foreign tourist arrivals using the SARIMA method and Neural Networks and compare the accuracy of the two methods with Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). The best SARIMA model for data on the number of foreign tourist arrivals to Batam City is SARIMA (2, 1, 0)(1, 1, 0)12 with MSE = 2,672,774,359 and MAPE = 21,4487%. The Neural Network Model is ˆy = max(0, 0.03208266 + 0.48310924V1 +...+ 0.46732363V8) with MSE = 171.279.990 and MAPE = 7.1404%. Thus, modeling with Artificial Neural Networks in these cases provides a better model than SARIMA in modeling data on the number of tourist visits to Batam City.
GREY MARKOV (1,1) MODEL FOR FORECASTING THE PERCENTAGE OF THE POPULATION THAT EXPERIENCED HEALTH COMPLAINTS IN INDONESIA Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri
Jurnal Matematika UNAND Vol. 12 No. 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.108-120.2023

Abstract

In mathematics, in addition to the time series model, Autoregressive, Moving Average, or Autoregressive Moving Average, the Grey-Markov (1,1) model can be employed for forecasting. One of the gains of this model is that it may cover a minimum quantity of data, which is beneficial in situations when the amount of data that is available is restricted but is not excessively vast. This model works well with data that does not exhibit a great deal of variability. The Grey model was further developed into the Grey-Markov model by including the idea of a Markov chain into the original model. In this particular investigation, the processes consist of first forming a sequence using a 1-Accumulated Generating Operation (1-AGO), then forming a sequence using an MGO, and finally predicting using an AGO. The procedure that came before it is actually a modeling procedure for the Grey model. In addition, in order to model Grey- Markov(1,1), it is necessary to initially compute the relative inaccuracy of the forecast that came before it. The following step is to partition the outcome of the relative error into numerous states, one for each interval of the relative error. After that, each error is categorized based on a state that has been specified in advance. The state that is defined within the class is used as the basis for making predictions. The percentage of the population in Indonesia that reports having health difficulties on a yearly basis was chosen as the case study for this research because it is relevant to the topic at hand. The data came from the Central Statistics Agency in the United Kingdom. The period covered by the data is from 1996 to 2021. The purpose of this research is to investigate the structure of the Grey-Markov Model (1,1) and provide a forecast regarding the proportion of the general population that will be affected by health issues in the year 2022. According to the findings of this research project, the forecast of the proportion of the population in Indonesia that suffered health complaints in 2022 produced predictive data that was 30.36%, with a very good accuracy value of 2.43%.
AN ANALYSIS OF CLUSTER TIMES SERIES FOR THE NUMBER OF COVID-19 CASES IN WEST JAVA Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul
Jurnal Matematika UNAND Vol. 12 No. 3 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.3.203-212.2023

Abstract

The government may be able to develop more effective strategies for dealing with COVID-19 cases if it groups districts and cities according to the features of the number of Covid-19 cases being reported in each district or city. The data can be more easily summarized with the help of cluster analysis, which organizes items into groups according to the degree of similarity between members. Since it is possible to group more than one period together, the generation of clusters based on time series is a more efficient method than clusters that are created for each individual unit. Using a time series cluster hierarchical technique that has complete linkage, the purpose of this study is to categorize the number of instances of Covid-19 that have been found in West Java by district or city. The data that was used comes from monthly reports of Covid-19 instances compiled by West Java districts from 2020 to 2022. The Autocorrelation Function (ACF) distance cluster was utilized in this investigation to determine how closely cluster members are related to one another. According to the findings, there could be as many as seven separate clusters, each including a unique assortment of districts and cities. Cluster 3, which is comprised of three different cities and regencies, including Bandung City, West Bandung Regency, and Sumedang Regency, has an average number of cases that is 66, making it the cluster with the highest number of cases overall. A value of 0.2787590 is obtained for the silhouette coefficient as a result of the established grouping. This value suggests that the structure of the newly created cluster is quite fragile.The government may be able to develop more eective strategies fordealing with COVID-19 cases if it groups districts and cities according to the featuresof the number of Covid-19 cases being reported in each district or city. The data canbe more easily summarized with the help of cluster analysis, which organizes items intogroups according to the degree of similarity between members. Since it is possible togroup more than one period together, the generation of clusters based on time series isa more ecient method than clusters that are created for each individual unit. Using atime series cluster hierarchical technique that has complete linkage, the purpose of thisstudy is to categorize the number of instances of Covid-19 that have been found in WestJava by district or city. The data that was used comes from monthly reports of Covid-19 instances compiled by West Java districts from 2020 to 2022. The AutocorrelationFunction (ACF) distance cluster was utilized in this investigation to determine howclosely cluster members are related to one another. According to the ndings, there couldbe as many as seven separate clusters, each including a unique assortment of districtsand cities. Cluster 3, which is comprised of three dierent cities and regencies, includingBandung City, West Bandung Regency, and Sumedang Regency, has an average numberof cases that is 66, making it the cluster with the highest number of cases overall. Avalue of 0.2787590 is obtained for the silhouette coecient as a result of the establishedgrouping. This value suggests that the structure of the newly created cluster is quitefragile.
Aplikasi Goal Programming untuk Optimalisasi Jadwal Kerja Studi Kasus pada Laundry Zone Medianto, Muhammad Fadly Putra; BAHRI, SUSILA; LESTARI, RIRI
Jurnal Matematika UNAND Vol. 12 No. 3 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.3.194-202.2023

Abstract

Selama ini, pada Laundry Zone pekerja dijadwalkan bekerja 7 hari dalam seminggu dan hanya bekerja pada satu jadwal tertentu saja. Untuk kenyamanan karyawan, maka perlu dikonstruksi jadwal sehingga pekerja memiliki hari libur dalam seminggu dan dapat bekerja pada jadwal lain. Pada penilitian ini digunakan metode Goal Programming dan software LINGO 11.0 untuk menyusun jadwal yang optimal tersebut.
MODEL CAPITAL ASSET PRICING MODEL (CAPM) DALAM PEMBENTUKAN PORTOFOLIO OPTIMAL SAHAM JAKARTA ISLAMIC INDEX (JII) NASTHASYA, NOVALISA; Yozza, Hazmira; DEVIANTO, DODI
Jurnal Matematika UNAND Vol. 12 No. 4 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.4.299-308.2023

Abstract

Dalam berinvestasi saham, setiap investor ingin mendapatkan return yang tinggi dan risiko yang rendah. Salah satu cara untuk meminimalisir risiko adalah dengan membentuk portofolio optimal yang menguntungkan dari segi return dan risiko. Pada penelitian ini digunakan Capital Asset Pricing Model (CAPM) dalam membentuk portofolio optimal. Data yang digunakan adalah data saham dalam Jakarta Islamic Index (JII) periode Desember 2020-November 2021. Pemodelan menghasilkan 5 saham penyusun komposisi portofolio optimal. Return eskpektasi portofolio sebesar 0,015282 dan risiko portofolio sebesar 0,069750. Evaluasi kinerja portofolio optimal yang terbentuk diukur berdasarkan ukuran rasio Sharpe, Modigliani Square dan Treynor. Dari hasil penelitian didapat bahwa portofolio optimal yang dibentuk dengan Capital Asset Pricing Model (CAPM) layak untuk diinvestasikan.
PREMI ASURANSI PENDIDIKAN DENGAN MEMPERHITUNGKAN PENGARUH WAIVER OF PREMIUM DAN RETURN OF CASH VALUE Suherman, Sandi Nurhibatulloh; ZANBAR SOLEH, ACHMAD; NOVIYANTI, LIENDA; INDRAYATNA, FAJAR
Jurnal Matematika UNAND Vol. 12 No. 3 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.3.244-257.2023

Abstract

Asuransi pendidikan adalah kombinasi antara tabungan pendidikan dan asuransi jiwa berjangka. Asuransi Pendidikan melibatkan dua orang yaitu orang tua (Ayah/Ibu) sebagai tertanggung dan anak sebagai penerima beasiswa. Asuransi Pendidikan memberikan manfaat berupa (1) dana tabungan pendidikan yang akan diberikan dalam 4 periode waktu yaitu di akhir tahun polis saat anak berusia 5 tahun, 11 tahun, 14 tahun, dan 17 tahun, (2) manfaat proteksi jiwa apabila orang tua meninggal dunia dalam masa asuransi. Pada penelitian ini akan memperhitungkan pengaruh manfaat lain yaitu (3) waiver of premium yang merupakan polis bebas premi apabila orang tua meninggal dunia, namun manfaat tetap dibayarkan sesuai kesepakatan awal, dan (4) return of cash value apabila anak yang dibeasiswakan meninggal dunia. Penelitian ini menentukan besaran premi kotor tahunan didasarkan pada konsep fully-discrete dengan anuitas joint-life. Dengan penambahan manfaat waiver of premium dan return of cash value akan meningkatkan premi kotor menjadi lebih mahal, akan tetapi manfaat yang diberikan sesuai dengan kebutuhan pemegang polis.
KESTABILAN MODEL NICHOLSON-BAILEY Oktaviani, Mira; ZULAKMAL, ZULAKMAL; MUHAFZAN, MUHAFZAN
Jurnal Matematika UNAND Vol. 12 No. 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.144-152.2023

Abstract

Dalammakalahinidikajikestabilan Model Nicholson-Bailey yang mempelajaritentanginteraksiantarainangdanparasit. Model Nicholson-Bailey digambarkandalambentukpersamaanbeda non linierdiskrit. Darihasilanalisisdiperolehduatitiktetap yang kestabilannyaditentukanolehtingkatreproduksiinang. Sebagaihasilutamadarimakalahini, disajikan suatusyaratperludancukupuntukkestabilanasimtotikdarititiktetap model Nicholson-Bailey.
PERFORMA KLASIFIKASI DATA TIDAK SEIMBANG DENGAN PENDEKATAN MACHINE LEARNING (STUDI KASUS: DIABETES INDIAN PIMA) Aqsha, Masjidil; Sunusi, Nurtiti
Jurnal Matematika UNAND Vol. 12 No. 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.176-193.2023

Abstract

Diabetes merupakan suatu penyakit atau gangguan metabolisme kronis dengan multi etiologi yang ditandai dengan tingginya kadar gula darah disertai dengan gangguan metabolisme karbohidrat, lipid, dan protein sebagai akibat insufisiensi fungsi insulin. Faktor risiko diabetes berhubungan dengan status diabetes sesorang. Berbagai pendekatan machine learning menjadi alternatif dalam memprediksi status diabetes. Namun, dalam banyak kasus, data yang tersedia tidak cukup seimbang dalam kelas datanya. Adanya ketidakseimbangan data dapat menyebabkan hasil prediksi menjadi tidak akurat. Tujuan penelitian dalam paper ini adalah untuk mengatasi masalah ketidakseimbangan data dan membandingkan kinerja model dalam memprediksi status diabetes. Secara umum, metode seperti Synthetic Minority Over-sampling Technique (SMOTE) dan Adaptive Synthetic (ADASYN) dapat digunakan untuk menyeimbangkan data. Data Diabetes Indian Pima yang telah diseimbangkan kemudian diprediksi dengan metode machine learning seperti metode Bagging, Random Forest, dan XGBoost. Hasil penelitian menunjukkan bahwa performa model machine learning meningkat setelah menangani ketidakseimbangan data dan model terbaik adalah model XGBoost. 

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