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Unnes Journal of Mathematics
ISSN : 22526943     EISSN : 24605859     DOI : https://doi.org/10.15294/ujm
Core Subject : Education,
Unnes Journal of Mathematics (UJM) publishes research issues on mathematics and its apllication. The UJM processes manuscripts resulted from a research in mathematics and its application scope, which includes. The scopes include research in: 1. Algebra 2. Analysis 3. Discrete Mathematics and Graph Theory 3. Differential Equation 4. Geometry 5. Mathematics Computation, 6. Statistics.
Articles 11 Documents
Search results for , issue "Vol 7 No 2 (2018)" : 11 Documents clear
Optimization of Production Scheduling and Planning of Raw Materials Supply Using Markov Chains (A Case Study of Kinken Cake & Bakery Kutoarjo) Oktaviyani, Oktaviyani; Dwijanto, Dwijanto; Supriyono, Supriyono
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.13894

Abstract

Competition in the industry sector influences the companies to increase productivity in their production activities, such as production scheduling. Production scheduling consists of various aspects, those are amount of production, production costs, and the availability of raw materials production. The scope of operations research used in this study was Markov chains. The decision process was used in order to decide the amount of production demand, planning of raw material supply of Kinken products Cake & Bakery Kutoarjo. . The problem was how to use Markov chains in production scheduling and planning of bread raw materials, how was the optimal policy in planning raw materials supply by considering its scheduling production. This study aimed at finding out Markov chains steps to estimate the amount of products demand for the upcoming time period in order to obtain production scheduling and planning of bread raw materials, and to obtain the optimal policy in planning of raw material supply Results showed that a market share of total demand products every the upcoming two weeks period, the equilibrium market share in the 59th week period got production demand 0.7% of bread brownies, 12.7% of Nastro rolls bread, 63.1%, of Spc rolls bread, 2.6% Bansos rolls bread, and 22.3% of semicircle spongecake, meanwhile the optimal policy in planning of raw material supply was seen from the percentage of production demand those bread. The raw materials supply of flour, sugar, and eggs was saved 63.1% for (1) the Spc rolls production, (2) the semicircle spongecake, (3) the Nastro rolls, (4) the 2.6% for Bansos rolls, and (5) 0.7% for the brownies bread.
PERAMALAN DERET WAKTU DENGAN MENGGUNAKAN AUTOREGRESSIVE (AR), JARINGAN SYARAF TIRUAN RADIAL BASIS FUNCTION (RBF) DAN HIBRID AR-RBF PADA INFLASI INDONESIA HIKMAH, AL; Agoestanto, Arief; Arifudin, Riza
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.13987

Abstract

Tujuan penelitian ini adalah untuk menentukan hasil ramalan inflasi enam bulan berikutnya yaitu bulan Oktober 2016, November 2016, Desember 2016, Januari 2017, Februari 2017 dan Maret 2017 menggunakan metode Autoregressive (AR), Jaringan Syaraf Tiruan (JST) Radial Basis Function (RBF) dan hibrid AR-RBF. Selain itu untuk mengetahui metode mana yang lebih akurat untuk peramalan. Metode AR dapat menganalisis masalah bagian linier data. Sedangkan, metode JST RBF dapat digunakan untuk memprediksi data nonlinier. Metode hibrid AR-RBF merupakan penggabungan dua buah metode yaitu AR dan JST RBF. Metode penelitian yang digunakan yaitu kajian pustaka. Data yang digunakan yaitu tingkat inflasi Indonesia berdasarkan Indeks Harga Konsumen (IHK) pada bulan Januari 2003 sampai dengan September 2016. Hasil analisia menunjukkan bahwa hasil JST RBF memiliki hasil yang lebih akurat dari pada AR dan hibrid AR-RBF. Hal ini terlihat dari nilai MAPE JST RBF paling kecil yaitu 7,12199%. Hasil peramalan dengan metode JST RBF secara berturut-turut sebesar 3,0960%; 3,3567%; 3,4304%; 3,5468%; 3,6701% dan 3,8570%. The purpose of this research is to forecast the inflation on October 2016, November 2016, December 2016, January 2017, February 2017 and March 2017 using Autoregressive (AR), Radial Basis Function (RBF) Neural Network (NN) and hybrid AR-RBF. Except that the purpose of this reserach to get accurate method. AR methode can be use to analys problem of linear time series data. On contrasting with AR, RBF-NN method can to predict nonlinear data. While hybrid AR-RBF method is the combination of two method, AR and RBFNN. The research method will be use is examine of books. This method is examined by using the data Inflation of Indonesian according to Consumer Price Index (CPI) on January 2003 until September 2016. The result of analysis indicate that RBF NN model get more accurate result than AR model and hybrid AR-RBF. It is shown that value MAPE of RBF NN method is the smallest percentage with 7,12199%. The result of forecasting with RBFNN method on consistenly 3,0960%; 3,3567%; 3,4304%; 3,5468%; 3,6701% and 3,8570%.
PERBANDINGAN UJI HASIL SIMULASI MONTE CARLO DAN SIMULASI BOOTSTRAP DALAM ANALISIS SAHAM UNTUK MENGHITUNG NILAI VaR DATA Mawarti, lida; Sugiman, Sugiman; Kharis, Muhammad
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.14109

Abstract

Harapan investor terhadap investasinya adalah mendapatkan pengembalian optimal dengan tingkat risiko tertentu. Perlu adanya perhitungan risiko agar tetap berada dalam tingkatan terkendali. Salah satu metode statistika untuk mengukur besar risiko yang ditimbulkan yaitu Value at Risk (VaR). Metode untuk mengestimasi Value at Risk menggunakan Simulasi Monte Carlo dan Simulasi Bootstrap. Pada penelitian ini menggunakan software Microsoft Excel dan SPSS. Data yang digunakan adalah data penutupan saham PT Indosat Tbk dari 1 Januari 2015 sampai dengan Desember 2015. Tujuan penelitian adalah membandingkan nilai taksiran VaR menggunakan program Simulasi Monte Carlo dan Simulasi Bootstrap. Langkah yang digunakan untuk menganalisis adalah menginput data, mengidentifikasi karakteristik data,menghitung nilai return, menghitung parameter mean dan standar deviasi, menghitung nilai acak dari return, menghitung nilai acak dengan parameter, menghitung nilai risiko tertinggi, menghitung VaR, melakukan simulasi sebanyak n kali, menghitung MSE. Hasil estimasi VaR tingkat kepercayaan 95% per 1 rupiah selama 1 hari menggunakan Simulasi Monte Carlo yaitu -12615.77. Sedangkan estimasi menggunakan Simulasi Bootstrap adalah -1330.62 dengan n=113 dan B*=1000. Nilai MSE dari Simulasi Monte Carlo sebesar 0,0514925 sedangkan dari Simulasi Bootstrap adalah 0.00059420. Nilai MSE Simulasi Bootstrap lebih kecil bila dibandingkan nilai MSE Simulasi Monte Carlo.
Sistem informasi administrasi pengelolaan iuran bulanan berbasis SMS gateway dengan menggunakan model perangkat lunak prototype Adha, Nugraha Saputra; Sugiharti, Endang; Arifudin, Riza
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.14165

Abstract

Tujuan dari penelitian ini adalah untuk membuat sistem informasi administrasi pengelola iuran bulanan berbasis SMS Gateway yang dapat merekap setiap transaksi iuran bulanan sekolah serta mengirimkan SMS kepada wali murid sebagai bukti pembayaran serta wali murid dapat mengirimkan SMS kepada sistem untuk memeriksa pembayaran iuran bulanan putra/putrinya. Dalam pembuatan sistem informasi administrasi ini menggunakan software Visual Basic .Net dan MySQL sebagai pengolah database. Selain itu, model pengembangan perangkat lunak Prototype juga digunakan untuk mempermudah proses pengembangan aplikasi ini. Data yang digunakan dalam penelitian ini diperoleh berdasakan observasi lapangan di sekolah MA-Al Ishlah. Data tersebut digunakan untuk membentuk struktur database agar sistem berjalan dengan baik sesuai dengan kebutuhan. Berdasarkan hasil penenlitian, diperoleh sebuah aplikasi yang mampu membantu petugas tata usaha dalam mengelola administrasi keuangan sekolah. Pada program ini petugas tata usaha dapat melakukan pengelolaan transaksi pembayaran, membuat laporan transaksi baik laporan pembayaran maupun laporan tunggakan. The purpose of this research is to create administrative information system management of monthly fee based on SMS Gateway which can reconcile every transaction of monthly fee and send SMS to parents as proof of payment and parents can send SMS to system to check payment of monthly fee of their son/their daughter. To create this administrative information system using Visual Basic.Net software and MySQL as a database processor. In addition, Prototype software development model is also used to simplify the process of developing this application.The data used in this research is obtained based on field observation at MA-Al Ishlah school. The data is used to create the database structure for the system to run properly in accordance with the needs. Based on the results of this research, obtained an application that is able to help administrative officers in managing school financial administration. In this program administrative officers can manage payment transactions, making transaction reports both payment reports and arrears reports.
PENERAPAN ALGORITMA KRUSKAL DAN ALGORITMA SOLLIN PADA PENDISTRIBUSIAN AIR PDAM TIRTA AJI CABANG WONOSOBO DAN APLIKASINYA MENGGUNAKAN MICROSOFT VISUAL BASIC 6.0 Prasetiyo, Agustaf; Mulyono, Mulyono; Mashuri, Mashuri
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.14238

Abstract

Kruskal algorithm and Sollin algorithm are algorithms on graph theory which can be used to find minimum spanning tree for weighted graph. The problem in this research is how the result of minimum water distribution of Tirta Aji Municipal Waterworks Wonosobo branch that in the form of minimum spanning tree using Kruskal algorithm and Sollin algorithm, and how to build an application to find minimum spanning tree from water pipes distribution of Tirta Aji Municipal Waterworks Wonosobo branch using Microsoft Visual Basic 6.0 from Kruskal algorithm and Sollin algorithm. Based on the obtained secondary data, it can be arranged a network. From this network it can be obtained the minimum spanning tree by using Kruskal algorithm and Sollin algorithm. Kruskal algorithm and Sollin algorithm were applied to build an application on Microsoft Visual Basic 6.0, then that application can be used to find the minimum spanning tree from the water pipes distribution. Based on the result of this research, it can be concluded that the weight of minimum spanning tree using Kruskal algorithm, Sollin algorithm and this application is same, that is 36.715 m. It means, the water pipes distribution of Tirta Aji Municipal Waterworks Wonosobo branch can be thrifted up to 9.027 m from the total pipes length before, that is 45.742 m. Kruskal and Sollin algorithm are algorithms on graph theory which can be used to find minimum spanning tree. The problem in this research is how the result of minimum water distribution of Tirta Aji Municipal Waterworks using Kruskal algorithm and Sollin algorithm, and how to build an application to find minimum spanning tree from water pipes distribution of Tirta Aji Municipal Waterworks using Microsoft VB 6.0 from Kruskal and Sollin algorithm. Based on the obtained secondary data, it can be arranged a network. From this network it can be obtained the minimum spanning tree by using Kruskal and Sollin algorithm. Kruskal and Sollin algorithm were applied to build an application on Microsoft VB 6.0, then that application can be used to find the minimum spanning tree from the water pipes distribution. Based on the result of this research, it can be concluded that the weight of minimum spanning tree using Kruskal algorithm, Sollin algorithm and this application is same, that is 36.715 m. It means, the water pipes distribution of Tirta Aji Municipal Waterworks can be thrifted up to 9.027 m from the total pipes length before, that is 45.742 m
The Queue System Optimization on Motorcycle Service Based on Aspiration Level Model (Case Study of Workshop Ahass Handayani Motor (1706) Semarag) Oktaviyanty, Hetty; Dwidayati, Nur Karomah; Agoestanto, Arief
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.20765

Abstract

The purpose of this research is to determine the optimal number of server by using queuing system based on aspiration level model at Ahass Handayani Motor (1706) Semarang workshop. In general, queues arise due to service needs that exceed the capacity and service facilities available. Therefore, to provide excellent service for customers, required an optimal service system. The study was conducted by taking primary data for two days in rush hour. The results obtained, the queue system at the workshop Ahass Handayani Motor (1706) Semarang using FIFO queue discipline with 6 servers. The arrival time distribution is the poisson distribution and the service time distribution is the exponential distribution. So we get the queue model (M / M / 6) :( GD / ∞ / ∞). Based on the aspiration level model, the queuing model in the workshop of Ahass Handayani Motor (1706) Semarang is optimal with 6 servers. With condition: 1) customer does not wait more than 2 hours to be served, 2) server idle time not more than 10 minutes. Size of server effectiveness is said to be optimal because it has an average waiting time in the system for 1.6361 hours on May 22, 2017 with a percentage of idle time of the waiters 7,5947% and the average waiting time in the system for 2.01 hours on the 23rd May 2017 with the percentage of unemployed servants 7,2188%.
PENERAPAN ALJABAR MAX-PLUS PADA PENGATURAN SISTEM ANTRIAN TRAFFIC LIGHT Wibowo, Andi; Wijayanti, Kristina; Veronica, Rahayu Budhiati
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.21338

Abstract

Penelitian ini bertujuan untuk mengatur sistem antrian traffic light menggunakan aljabar max-plus. Penelitian ini berdasarkan data kepadatan arus dan data durasi traffic light pada persimpangan. Kemudian, disusun graf yang menggambarkan kondisi persimpangan dan merepresentasikan arah dari pergerakan masing-masing jalur. Selanjutnya disusun aturan sinkronisasi yang sesuai dengan graf dan pemodelan dari aljabar max-plus. Langkah berikutnya adalah membahas penjadwalan yang periodik dari barisan keadaan sistem traffic light. Analisis dari model aljabar max-plus sistem antrian traffic light menggunakan algoritma power diperoleh periode rata-rata durasi lampu hijau tiap fase adalah detik. Hasil analisis memperoleh hasil perhitungan untuk persimpangan Jarakah Semarang dengan . Berdasarkan periode tersebut, durasi traffic light lebih proporsional dari data primer dan sesuai dengan kepadatan masing-masing simpang di persimpangan Jarakah Semarang. Sedangkan untuk persimpangan Lotte Mart Semarang diperoleh hasil dan berdasarkan periode tersebut menunjukkan durasi traffic light menjadi lebih optimal untuk mengurai kepadatan kendaraan yang melintasi persimpangan tersebut.
ESTIMASI PARAMETER REGRESI ROBUST MODEL SEEMINGLY UNRELATED REGRSSION (SUR) DENGAN METODE GENERALIZED LEAST SQUARE (GLS) Yulianto, Dimas Arif; Sugiman, Sugiman; Agoestanto, Arief
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.21463

Abstract

Penelitian ini bertujuan untuk: (1) memperoleh hasil estimasi parameter pada data yang mengandung pencilan dengan menggunakan estimasi parameter regresi robust metode Least Trimmed Square (LTS); (2) memperoleh sistem persamaan regresi robust pada model Seemingly Unrelated Regression (SUR) dengan metode Generalized Least Square (GLS). Pada penelitian ini menggunakan data nilai inflasi umum di Kota Salatiga, Kota Pekalongan, Kabupaten Rembang, dan Kabupaten Demak. Estimasi parameter regresi pada data yang menggandung pencilan lebih baik menggunakan metode regresi robust daripada menggunakan metode OLS karena menghasilkan nilai R-Square yang lebih besar. Estimasi regresi robust padamodel Seemingly Unrelated Regression (SUR) metode Generlaized Least Square (GLS) lebih baik digunakan untuk mengestimasi pada data panel yang semua datanya mengandung pencilan karena menghasilkan nilai residual yang kecil.
OPTIMIZATION OF SERIES QUEUE SYSTEM AT SAMSAT (ONE ROOF SYSTEM) SERVICE FACILITY BASED ON ASPIRATION LEVEL Astuti, Niken Yulia; Dwidayati, Nur Karomah; Sunarmi, Sunarmi
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.24402

Abstract

Antrian dapat ditemui pada beberapa fasilitas pelayanan umum misalnya di Kantor Sistem Administrasi Manunggal Satu Atap (SAMSAT). Tujuan dari penelitian ini untuk mengetahui model sistem antrian yang saat ini diterapkan di Kantor SAMSAT Kota Tegal untuk mengetahui ukuran keefektifan proses pelayanan wajib pajak, dan memberikan sistem antrian yang optimal berdasarkan tingkat aspirasi. Dari hasil penelitian diperoleh bahwa pada SAMSAT Kota Tegal mengikuti model sistem antrian Single Channel Multiple Phase (antrian tandem atau seri). Rincian model antrian pada loket pendaftaran, pembayaran, dan penyerahan STNK adalah [G/G/1]:[GD/∞/∞]. Ini berarti sistem antrian mengikuti pola kedatangan yang berdistribusi General sedangkan waktu pelayanan berdistribusi General dengan jumlah pelayan meliputi 1 petugas di tiap loketnya. Hasil efektivitas dari sistem antrian di Loket SAMSAT Kota Tegal adalah hari Senin, 19 Maret 2018 dengan Lq = 5,0993, Ls = 5,7451, Wq = 12,6078, Ws = 14,2045, dan W = 35,42%. %. Pada hari Selasa, 20 Maret 2018 dengan Lq = 4,3054, Ls = 4,8791, Wq = 12,4754, Ws = 14,1375, dan W = 42,64%. Pada hari Rabu, 21 Maret 2018 dengan Lq = 4,1846, Ls = 4,7469, Wq = 12,4156, Ws = 14,0839, dan W = 43,77%. Pada hari Kamis, 22 Maret 2018 dengan Lq = 4,3002, Ls = 4,8947, Wq = 11,6106, Ws = 13,2158, dan W = 40,55%. Waktu menunggu yang diinginkan pengunjung dan pihak SAMSAT tidak lebih dari 20 menit dan waktu menganggur petugas yang diperbolehkan oleh SAMSAT Kota Tegal adalah 20% maka banyaknya petugas ideal pada tiap loketnya yaitu 1 orang petugas. Abstract Queues can be found in some public service facilities such as in SAMSAT Office (One Roof System). The purpose of this research is to know the model of queuing system currently applied in SAMSAT of Tegal City to know the effectiveness of taxpayer service process, and provide an optimal queue system based on the level of aspiration. The result showed that the SAMSAT of Tegal city follow the model of a queuing system Single Channel Multiple Phase (queue tandem or series). The details of the queuing model at registration counters, payments, and checkers of STNK delivery are [G/G/1]:[GD/∞/∞]. This means the queuing system follows the General distributed arrival pattern while the General Distributed service time with the number of waiters includes 1 officer at each counter. The effectiveness of queuing system in SAMSAT of Tegal City is on Sunday, 19 March 2018 with Lq = 5,0993, Ls = 5,7451, Wq = 12,6078, Ws = 14,2045, dan W = 35,42%. On Tuesday, 20 March 2018 with Lq = 4,3054, Ls = 4,8791, Wq = 12,4754, Ws = 14,1375, dan W = 42,64%. On Wednesday, 21 March 2018 with Lq = 4,1846, Ls = 4,7469, Wq = 12,4156, Ws = 14,0839, dan W = 43,77%. And Thursday, 22 March 2018 with Lq = 4,3002, Ls = 4,8947, Wq = 11,6106, Ws = 13,2158, dan W = 40,55% Waiting time desired visitors and parties SAMSAT no more than 20 minutes and idle time officers allowed by SAMSAT of Tegal City is 20% then the number of ideal officers at each counter that is 1 officer.
PEMODELAN MATEMATIKA PENYEBARAN PENYAKIT TUBERKULOSIS DENGAN STRATEGI DOTS Rizki Ramadhan, Mustiko; Waluya, stevanus Budi; Kharis, Muhammad
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.27389

Abstract

Indonesia merupakan negara ke-4 dengan jumlah pasien tuberculosis (TB) terbanyak di dunia. Penelitian ini membahas model matematika untuk penyebaran penyakit TB dengan strategi DOTS (Directly Observed Treatment Short-course) dengan menggunakan model SEITR, sebagai upaya dalam menekan kasus TB. Tujuan penelitian ini adalah membangun model matematika, menganalisis titik kestabilan, dan menginterpretasikan simulasi model matematika dengan maple. Dalam pembangunan model diperoleh model matematika dengan dua titik kesetimbangan yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Analisis yang dilakukan menghasilkan angka rasio reproduksi dasar (R0). Setelah menganalisis dua titik kesetimbangan dapat disimpulkan bahwa titik kesetimbangan bebas penyakit akan stabil asimtotik lokal apabila R0<1. Sedangkan titik kesetimbangan endemik akan stabil asimtotik lokal apabila R0>1. Selanjutnya, untuk mengilustrasikan model dilakukan simulasi model menggunakan maple menghasilkan beberapa fakta, yaitu semakin kecil nilai peluang individu terinfeksi TB (β) dan semakin besar nilai laju individu TB aktif menjalani pengobatan DOTS (ω) akan memperkecil populasi penderita TB aktif. Indonesia is the 4th in the number of tuberculosis (TB) patients in the world. This study discusses the mathematical models for the spread of TB with DOTS strategy using a SEITR model, in an effort to suppress TB cases. The purpose of this study is to develop a mathematical model, analyze the point of stability, and interpret the simulation of mthematical models with maple. In the contruction of the model is obtined mathematical model with two points of equilibrium that is the point of disease-free equilibrium d edemi equilibrium point. The analysis carried out to produce numbers basic reproduction ratio (R0). After analyzing two equilibrium point it can be concluded that the disease-free equilibrium point will be the local asymtotically stable if R0<1. While the endemic equilibrium point will be the asymtotically stable if R0>1. Furthermore, to illstrate the model of the simulation model using maple program produces some of the fact, ie the smaller the probability of individuals infected with TB (β)and the greater the value of the rate of individuals undergoing treatment DOTS for active TB (ω) will reduce the population of active TB.

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