Articles
<![CDATA[APLIKASI METODE KHUN-TUCKER DALAM PENJUALAN OLI MOBIL (Studi Kasus : PT. Anugrah Mitra Dewata) ]]>
<![CDATA[Ni Made Asih]]>;
<![CDATA[I Nyoman Widana]]>
<![CDATA[ Jurnal Matematika Vol 2 No 1 (2012) ]]>
Publisher : <![CDATA[Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University ]]>
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DOI: 10.24843/JMAT.2012.v02.i01.p18
<![CDATA[Aplikasikan Metode Khun-Tucker dalam kasus penjualan oli mobil padaPT. Anugrah Mitra Dewata merupakan salah satu kasus optimasi bersyarat, untukmengetahui oli apa yang harus diproduksi oleh perusahaan, agar mencapai keuntunganmaksimal dan nilai-nilai ekstrim yang akan diperoleh, yang nantinya berperandalam menentukan tingkat keuntungan yang diperoleh perusahaan. Metode Khun-Tucker ini dapat dipergunakan untuk mencari solusi optimal dari suatu fungsi tanpamemandang sifat apakah linier atau nonlinier. Dalam proses pengerjaannya MetodeKhun-Tucker secara esensial melibatkan langkah-langkah yang sama seperti halnyaMerode Lagrange, yaitu: Membentuk Lagrangian untuk dapat menghitungtitik-titik kritisnya, mencari semua solusi (x; ), dan menghitung nilai f(x). Dalamproses pencarian semua solusi x dan nya dibantu dengan menggunakan programMATLAB. Hasil penelitian menunjukkan pada caturwulan I dengan memproduksioli SMO HP sebanyak 587 liter diperoleh keuntungan maksimal perusahaansebesar Rp 19.837.000 . Untuk caturwulan II dengan memproduksi oli SMO HPPLUS sebanyak 776 liter diperoleh keuntungan maksimal perusahaan sebesar Rp20.112.000. Untuk caturwulan III dengan memproduksi oli SMO HP sebanyak 470liter diperoleh keuntungan maksimal perusahaan sebesar Rp 20.029.000.]]>
<![CDATA[Analisis Premi dari Asuransi Pengangguran ]]>
<![CDATA[I Nyoman Widana]]>;
<![CDATA[Ketut Jayanegara]]>
<![CDATA[ Jurnal Matematika Vol 9 No 1 (2019) ]]>
Publisher : <![CDATA[Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University ]]>
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DOI: 10.24843/JMAT.2019.v09.i01.p111
<![CDATA[Unemployment insurance is designed to overcome some of the financial problems faced by workers who have been involuntarily terminated from their jobs. The benefit insurance is financed based on the contributory from an employer, employee or government in recent times, some developing countries have been establishing unemployment insurance. This research aims to analyze the unemployment insurance products in Indonesia. Especially to analyze the financial viability of the product. The method used is the equivalence premium principle. Based on data sourced from BPJS Ketenagakerjaan and a claim rate of 10%, it is found that a premium rate of 5% of insured wages would support a benefit level of 50% of the wages for 43 weeks. This premium rate would also support 70% of the wages for 32 weeks. Meanwhile, the premium rate of 1% of the participant wages would guarantee a benefit level of 50% for 6 weeks.]]>
<![CDATA[Evaluasi Premi Joint Life Pasangan Suami Istri Menggunakan Copula Frank ]]>
<![CDATA[I Nyoman Widana]]>;
<![CDATA[Ni Made Asih]]>
<![CDATA[ Jurnal Matematika Vol 8 No 1 (2018) ]]>
Publisher : <![CDATA[Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University ]]>
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DOI: 10.24843/JMAT.2018.v08.i01.p97
<![CDATA[This paper introduces the joint life satatus for married couples with independent and dependent mortality models. Using Frank copula and Indonesia Life Tables 2011, we evaluate the impact of dependent future lifetimes on the net single and level premium. The results show premium rates are reduced if models of dependent future lifetime are used compared to the models using an assumption of independence.]]>
<![CDATA[Pengaruh Tingkat Bunga Terhadap Biaya ]]>
<![CDATA[I Nyoman Widana]]>
<![CDATA[ Jurnal Matematika Vol 1 No 2 (2011) ]]>
Publisher : <![CDATA[Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University ]]>
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DOI: 10.24843/JMAT.2011.v01.i02.p12
<![CDATA[This article discusses the impact of interest rates on expense rates. An insuranceexpense is the difference calculated between Gross Premium and Net Premium. The calculationsindicate that the expense reduces when the interest rate increases.]]>
<![CDATA[Model Matematika (Nonlinier) Populasi Anjing Rabies dengan Vaksinasi ]]>
<![CDATA[Ahmad Fitri]]>;
<![CDATA[Tjokorda Bagus Oka]]>;
<![CDATA[I Nyoman Widana]]>
<![CDATA[ Jurnal Matematika Vol 5 No 1 (2015) ]]>
Publisher : <![CDATA[Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University ]]>
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DOI: 10.24843/JMAT.2015.v05.i01.p52
<![CDATA[Rabies is a fatal infectious virus that can attack all mammals especially dogs. Infection happens when there is interaction between healthy dogs and rabies-infected dogs. In Bali, rabies was first found in late 2008. One of the solutions done by government to the problem is by giving vaccine to healtly dogs, so that they are not easily infected by the virus. Thus, a mathematical model is needed to analyze the development of dogs population in Bali. By using analysis of fixed point and stability on the model, the population of rabies-infected dog was affected by not only the percentage of vaccination but also the number of healthy dogs birth. Lastly, a numeric simulation by using Taylor’s seriesorder was conducted to illustrate and to strengthen the result of the analysis.]]>
<![CDATA[Aplikasi Algoritma Biseksi dan Newton-Raphson dalam Menaksir Nilai Volatilitas Implied ]]>
<![CDATA[Komang Dharmawan]]>;
<![CDATA[I Nyoman Widana]]>
<![CDATA[ Jurnal Matematika Vol 1 No 2 (2011) ]]>
Publisher : <![CDATA[Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University ]]>
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<![CDATA[Volatilitas adalah suatu besaran yang mengukuran seberapa jauh suatu harga sahambergerak dalam suatu periode tertentu dapat juga diartikan sebagai persentase simpanganbaku dari perubahan harga harian suatu saham. Menurut teori yang dikembangkan oleh Black-Scholes in 1973, semua harga opsi dengan ’underlying asset’ dan waktu jatuh tempo yang samatetapi memiliki nilai exercise yang berbeda akan memiliki nilai volatilitas implied yang sama.Model Black-Scholes dapat dipakai mengestimasi nilai volatilitas implied dari suatu sahamdengan mencari sulusi numerik dari persamaan invers dari model Black-Scholes. Makalah inimendemonstrasikan bagaimana menghitung nilai volatilitas implied suatu saham dengan mengasumsikanbahwa model Black-schole adalah benar dan suatu kontrak opsi dengan denganumur kontrak yang sama akan memiliki harga yang sama. Menggunakan data harga opsi SonyCorporation (SNE), Cisco Systems, Inc (CSCO), dan Canon, Inc (CNJ) diperoleh bahwa, ImpliedVolatility memberikan harga yang lebih murah dibandingkan dengan harga opsi darivolatilitas yang dihitung dari data historis. Selain itu, dari hasil iterasi yang diperoleh, metodeNewton-Raphson lebih cepat konvergen dibandingkan dengan metode Bisection.]]>
<![CDATA[Analisis Komponen Biaya Asuransi Jiwa Dwiguna (Endowment) ]]>
<![CDATA[Desak Nyoman Trisnawati]]>;
<![CDATA[I Nyoman Widana]]>;
<![CDATA[Ketut Jayanegara]]>
<![CDATA[ Jurnal Matematika Vol 4 No 1 (2014) ]]>
Publisher : <![CDATA[Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University ]]>
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DOI: 10.24843/JMAT.2014.v04.i01.p41
<![CDATA[Asuransi adalah suatu istilah penyediaan jasa yang bergerak dalam bidang pertanggungan atau perlindungan. Seseorang yang telah mengasuransikan dirinya akan menyetujui kontrak yang disebut dengan polis. Di Indonesia terdapat beberapa jenis asuransi jiwa, salah satunya adalah asuransi jiwa dwiguna. Asuransi jiwa dwiguna adalah asuransi jiwa yang kepada tertanggung akan diberikan sejumlah uang pada akhir asuransi sesuai dengan polis. Jika tertanggung meninggal selama masa asuransi atau setelah akhir asuransi, kepada tertanggung akan diberikan uang sebesar uang pertanggungan. Untuk memenuhi pertanggungan, akan dibayarkan sejumlah uang yang disebut dengan premi. Premi terdiri dari premi netto dan premi bruto, premi netto adalah premi yang perhitungannya hanya berdasarkan faktor mortalita, sedangkan premi bruto adalah gabungan dari premi netto dengan faktor-faktor lain seperti faktor biaya. Penelitian ini membahas tentang analisis komponen biaya pada asuransi jiwa dwiguna. Komponen dari biaya asuransi jiwa dwiguna ini adalah biaya penutupan awal, biaya pengumpulan premi dan biaya pemeliharaan.Semua perhitungan aktuaria menggunakan tabel CSO 1980 dengan bunga 9%. Dengan menerapkan metode Eliminasi Gauss Jordan besarnya komponen biaya dari asuransi jiwa dwiguna masing-masing, biaya penutupan awal sebesar dan , biaya pengumpulan premi sebesar 0,075 dan biaya pemeliharaan sebesar 2.]]>
<![CDATA[Model Matematika (Linier) Populasi Anjing Rabies dengan Vaksinasi ]]>
<![CDATA[Ahmad Fitri]]>;
<![CDATA[Tjokorda Bagus Oka]]>;
<![CDATA[I Nyoman Widana]]>
<![CDATA[ Jurnal Matematika Vol 4 No 2 (2014) ]]>
Publisher : <![CDATA[Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University ]]>
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DOI: 10.24843/JMAT.2014.v04.i02.p46
<![CDATA[Rabies is an infectious virus that can attack all mammals especially dogs. In Bali, rabies was found in late 2008. One of the solutions done by government for the problem is by giving vaccine to healtly dogs, so that they are not easily infected by the virus. Thus, a mathematical model is needed to analyze the development of dog population in Bali and to determine the limination of dogs birth population and the percentage limination of vaccination that can be possibly done so that the population of dogs infected by rabies becomes extinct. By using analysis of fixed point and stability on the model, the limination of dogs birth population and the percentage limitation of the vaccination was obtained. Lastly, a numeric simulation by using Taylor’s series order was conducted to illustrate and to strengthen the result of the analysis.]]>
<![CDATA[Perhitungan Iuran Normal Program Pensiun dengan Asumsi Suku Bunga Mengikuti Model Vasicek ]]>
<![CDATA[I Nyoman Widana]]>;
<![CDATA[Ni Made Asih]]>
<![CDATA[ Jurnal Matematika Vol 7 No 2 (2017) ]]>
Publisher : <![CDATA[Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University ]]>
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DOI: 10.24843/JMAT.2017.v07.i02.p85
<![CDATA[Labor has a very important role for national development. One way to optimize their productivity is to guarantee a certainty to earn income after retirement. Therefore the government and the private sector must have a program that can ensure the sustainability of this financial support. One option is a pension plan. The purpose of this study is to calculate the normal cost with the interest rate assumed to follow the Vasicek model and analyze the normal contribution of the pension program participants. Vasicek model is used to match with the actual conditions. The method used in this research is the Projected Unit Credit Method and the Entry Age Normal method. The data source of this research is lecturers of FMIPA Unud. In addition, secondary data is also used in the form of the interest rate of Bank Indonesia for the period of January 2006-December 2015. The results of this study indicate that the older the age of the participants, when starting the pension program, the greater the first year normal cost and the smaller the benefit which he or she will get. Then, normal cost with constant interest rate greater than normal cost with Vasicek interest rate. This occurs because the Vasicek model predicts interest between 4.8879%, up to 6.8384%. While constant interest is only 4.25%. In addition, using normal cost that proportional to salary, it is found that the older the age of the participants the greater the proportion of the salary for normal cost.]]>
<![CDATA[MODEL PENYERAPAN OBAT UNTUK INTERVAL DAN DOSIS BERBEDA ]]>
<![CDATA[I NYOMAN WIDANA]]>
<![CDATA[ Jurnal Matematika Vol 1 No 1 (2010) ]]>
Publisher : <![CDATA[Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University ]]>
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DOI: 10.24843/JMAT.2010.v01.i01.p07
<![CDATA[This article will discuss the accumulated quantity of the drug in the bloodstream of the twoadministered methods of the drug. The first method the drug is administered every 12 hours with adose of 12.5 mg, whereas for the second method the drug is administered every 24 hours with a dose of25 mg. The calculations show that the second method accumulates more drugs in the bloodstream thanthe first method.]]>
