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All Journal Jurnal Teknik Industri The Journal of Experimental Life Sciences (JELS) CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Mahasiswa Matematika Jurnal Teknik Industri Communication in Biomathematical Sciences
Isnani Darti
Brawijaya University
Biochemistry, Genetics & Molecular Biology Immunology & microbiology Industrial & Manufacturing Engineering Mathematics Medicine & Pharmacology Neuroscience Social Sciences

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Perambatan Gelombang Optik pada Grating Sinusoidal dengan Chirp dan Taper Darti, Isnani
CAUCHY Vol 1, No 1 (2009): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (379.582 KB) | DOI: 10.18860/ca.v1i1.1697

Abstract

Artikel ini membahas model perambatan gelombang optik pada grating sinusoidal takhomogen. Model tersebut diturunkan dengan mereduksi secara eksak persamaan Helmholtz menjadi sistem persamaan diferensial orde satu dengan syarat awal yang dapat diselesaikan dengan metode Runge-Kutta orde empat. Metode ini disebut Metode IntegrasiLangsung (MIL). Formulasi MIL sangat sederhana baik dalam hal penurunannya maupun implementasinya karena tidak memerlukan prosedur iterasi maupun optimasi. Denganmenggunakan MIL, dipelajari perubahan respon optik pada grating sinusoidal akibat variasi amplitudo modulasi indeks (taper) dan variasi frekuensi spasial grating (chirp). Hasil simulasi menunjukkan bahwa taper menyebabkan adanya fenomena penghilangan side-lobe pada spektrum transmitansi. Adanya chirp menyebabkan penghalusan side-lobe pada spektrum transmitansi dengan semakin besar parameter chirp menyebabkan peningkatan transmitansi di sekitar pusat band-gap dari grating homogen. Selain implementasi integrasi numerik (Runge-Kutta), MIL merupakan metode eksak sehingga dapat digunakan untuk mengevaluasi validitas metode yang sering digunakan yaitu Persamaan Moda Tergandeng (PMT). Dari hasil perbandingan dapat disimpulkan bahwa secara umum PMT kurang akurat dalam menganalisis struktur grating sinusoidal baik homogen maupun tak-homogen.
Kontrol Optimal pada Model Economic Order Quantity (EOQ) dengan Inisiatif Tim Penjualan Al Fauzi, Abdul Latif; Darti, Isnani; Suryanto, Agus
Jurnal Teknik Industri Vol 19, No 1 (2017): JUNE 2017
Publisher : Institute of Research and Community Outreach - Petra Christian University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.9744/jti.19.1.21-28

Abstract

Pengendalian  tingkat persediaan stok suatu produk/barang merupakan salah satu kegiatan yang penting dalam kelancaran penjualan, yang juga berakibat pada keuntungan yang akan diperoleh dari penjualan suatu produk/barang.  Model Economic Order Quantity (EOQ) merupakan salah satu model persediaan barang yang sering digunakan untuk pengendalian persedian barang. Pada artikel ini dibahas kontrol optimal pada model EOQ dengan inisiatif tim penjualan tidak hanya pada saat kondisi setimbang saja, tetapi kontrol optimal dengan usaha tim penjualan pada setiap saat. Strategi kontrol optimal dilakukan dengan meminimumkan biaya persediaan, biaya pembelian, biaya penjualan dan biaya usaha tim penjualan. Masalah kontrol optimal diselesaikan menggunakan prinsip maksimum Pontryagin. Solusi optimal yang diperoleh disimulasikan secara numerik menggunakan metode Sweep Maju-Mundur. Berdasarkan hasil simulasi numerik dapat diketahui bahwa semakin besar koefisien tingkat permintaan barang, maka proses persediaan barang akan lebih cepat berkurang. Selain itu semakin besar usaha tim penjualan, maka proses persediaan barang akan lebih sedikit bahkan lebih cepat habis.  
KEUNTUNGAN RETAILER BERDASARKAN SIKLUS ORDER DAN KEUNTUNGAN BANK OPTIMAL Rahmah, Havida; Darti, Isnani
Jurnal Mahasiswa Matematika Vol 3, No 1 (2015)
Publisher : Jurnal Mahasiswa Matematika

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Abstract

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ANALISIS MODEL ANTRIAN M/M/c/c DENGAN RENEGING BERTIPE R_EOS (RENEGING TILL END OF SERVICE) W.A, Rinda Anggraini; darti, isnani
Jurnal Mahasiswa Matematika Vol 3, No 4 (2015)
Publisher : Jurnal Mahasiswa Matematika

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Forecasting COVID-19 Epidemic in Spain and Italy Using A Generalized Richards Model with Quantified Uncertainty Isnani Darti; Agus Suryanto; Hasan S. Panigoro; Hadi Susanto
Communication in Biomathematical Sciences Vol. 3 No. 2 (2020)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2020.3.2.1

Abstract

The Richards model and its generalized version are deterministic models that are often implemented to fit and forecast the cumulative number of infective cases in an epidemic outbreak. In this paper we employ a generalized Richards model to predict the cumulative number of COVID-19 cases in Spain and Italy, based on available epidemiological data. To quantify uncertainty in the parameter estimation, we use a parametric bootstrapping approach to construct a 95% confidence interval estimation for the parameter model. Here we assume that the time series data follow a Poisson distribution. It is found that the 95% confidence interval of each parameter becomes narrow with the increasing number of data. All in all, the model predicts daily new cases of COVID-19 reasonably well during calibration periods. However, the model fails to produce good forecasts when the amount of data used for parameter estimations is not sufficient. Based on our parameter estimates, it is found that the early stages of COVID-19 epidemic, both in Spain and in Italy, followed an almost exponentially growth. The epidemic peak in Spain and Italy is respectively on 2 April 2020 and 28 March 2020. The final sizes of cumulative number of COVID-19 cases in Spain and Italy are forecasted to be at 293220 and 237010, respectively.
Dynamics of COVID-19 Epidemic Model with Asymptomatic Infection, Quarantine, Protection and Vaccination Raqqasyi Rahmatullah Musafir; Agus Suryanto; Isnani Darti
Communication in Biomathematical Sciences Vol. 4 No. 2 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.2.3

Abstract

We discuss the dynamics of new COVID-19 epidemic model by considering asymptomatic infections and the policies such as quarantine, protection (adherence to health protocols), and vaccination. The proposed model contains nine subpopulations: susceptible (S), exposed (E), symptomatic infected (I), asymptomatic infected (A), recovered (R), death (D), protected (P), quarantined (Q), and vaccinated (V ). We first show the non-negativity and boundedness of solutions. The equilibrium points, basic reproduction number, and stability of equilibrium points, both locally and globally, are also investigated analytically. The proposed model has disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable if basic reproduction number is less than one. The endemic equilibrium point exists uniquely and is globally asymptotically stable if the basic reproduction number is greater than one. These properties have been confirmed by numerical simulations using the fourth order Runge-Kutta method. Numerical simulations show that the disease transmission rate of asymptomatic infection, quarantine rates, protection rate, and vaccination rates affect the basic reproduction number and hence also influence the stability of equilibrium points.
Freight Forwarding Company Selection Using Hybrid IFAHP-IFTODIM Method Fara El Nandhita Pratiwi; Agus Widodo; Isnani Darti
Jurnal Teknik Industri Vol. 24 No. 1 (2022): June 2022
Publisher : Institute of Research and Community Outreach - Petra Christian University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.9744/jti.24.1.37-44

Abstract

In selecting the best freight forwarding company, the concept of a Decision Support System (DSS) can be used to find the best solution from several alternatives. One of the DSS methods is the Intuitionistic Fuzzy Analytical Hierarchy Process (IFAHP) and Intuitionistic Fuzzy Tomada de Decisao Interativa Multicriterio (IFTODIM). This study applied the IFAHP method combined with the IFTODIM method to select the best freight forwarding company at PT Progressio Indonesia. PT Progression Indonesia is a manufacturing and retail company that produces furniture. There are 11 criteria used in the performance assessment of the four alternatives. This research shows that the best freight forwarding company at PT Progressio Indonesia is Kobra Express, with a comprehensive value of 1.000. The second is Herona Express, with a comprehensive value of 0.9437, followed by Indah Logistik Cargo, with a comprehensive value of 0.7005. The last is Guna Dharma Express, with a comprehensive value of 0.0000.
Dynamical Analysis and Parameter Estimation of Hepatitis B Disease Model in Malang Fitroh Aulani; Wuryansari Muharini Kusumawinahyu; Isnani Darti
The Journal of Experimental Life Science Vol. 11 No. 3 (2021)
Publisher : Postgraduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.jels.2021.011.03.03

Abstract

In this article, a model representing the spread of Hepatitis B disease is constructed as a nonlinear autonomous system. The model divides the considered human population into three classes, namely susceptible, infected, and recovered class. The dynamical analysis shows that there are two equilibrium points in the model, namely a disease-free equilibrium point and an endemic equilibrium point. The existence and stability of the equilibrium points depend on the basic reproduction number (R_0). The disease-free equilibrium point is local asymptotically stable when R_0<1 while the endemic equilibrium point exists and is local asymptotically stable if R_0>1. The five parameters of the model are estimated by applying Downhill Simplex (Nelder-Mead) Algorithm and by using the infected data cases taken from such a hospital in Malang. The estimated parameters are the transmission of infection rate, the saturation rate, the vaccination rate, the recovery rate, and the immunity loss rate. The resulting parameter estimation supports the analytical result and is used to illustrate the analytical results numerically. Based on the considered model and the result of the parameters estimation, it can be concluded that the Hepatitis B spread in Malang is controllable. Keywords: downhill simplex (Nelder-mead) algorithm, dynamical analysis, hepatitis B model, parameter estimation. 
Co-Authors Agus Widodo Al Fauzi, Abdul Latif Fara El Nandhita Pratiwi Fitroh Aulani Hadi Susanto Hasan S. Panigoro M.Pd S.T. S.Pd. I Gde Wawan Sudatha . Rahmah, Havida Raqqasyi Rahmatullah Musafir Suryanto, Agus W.A, Rinda Anggraini Wuryasari Muharini Kusumawinahyu