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Analisis Kestabilan Model SEIR Penyebaran Penyakit Campak dengan Pengaruh Imunisasi dan Vaksin MR Willyam Daniel Sihotang; Ceria Clara Simbolon; July Hartiny; Desrinawati Tindaon; Lasker Pangarapan Sinaga
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (281.284 KB) | DOI: 10.20956/jmsk.v16i1.6594

Abstract

Measles is a contagious infectious disease caused by a virus and has the potential to cause an outbreak. Immunization and vaccination are carried out as an effort to prevent the spread of measles. This study aims to analyze and determine the stability of the SEIR model on the spread of measles with the influence of immunization and MR vaccines. The results obtained from model analysis, namely there are two disease free and endemic equilibrium points. If the conditions are met, the measles-free equilibrium point will be asymptotically stable and the measles endemic equilibrium point will be stable. Numerical solutions show a decrease in the rate of spread of measles due to the effect of immunization and the addition of MR vaccines.
MARKOV CHAIN TO CONTROL GENERIC DRUG IN INVENTORY PROBLEM Marlina Setia Sinaga; Hamidah Nasution; Oktariani Purba; Lasker Pangarapan Sinaga
JURNAL HANDAYANI PGSD FIP UNIMED Vol 10, No 2: December 2019
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (461.43 KB) | DOI: 10.24114/jh.v10i2.18076

Abstract

Abstract: Have the generic drugs inventory been optimal, neither excessive nor deficient? Inadequate inventory can cause in losses due to increased ordering and storage costs. Shortage of generic drug will cause a decrease of public health services. Given demand generic drugs which always fluctuates, so stochastic process is the right method. In this study, the optimal level of generic drugs inventory will be analyzed by using the Markov chain. Steady state conditions were achieved when the same results obtained with the previous iteration result. There are 7 linear equations produced, each accompanied by 7 levels of inventory, optimal order quantities and also the costs.Keywords: Demand; Generic Drug; Inventory; Markov Chain.Abstrak: Apakah persediaan obat generik sudah optimal, tidak berlebih maupun kekurangan? Persediaan yang tidak optimal dapat mengakibatkan kerugian akibat bertambahnya biaya pemesanan maupun biaya penyimpanan. Kekurangan persediaan obat generik bahkan juga akan mengakibatkan turunnya tingkat layanan kesehatan masyarakat. Mengingat tingkat permintaan obat generik yang berfluktuasi maka proses stokastik menjadi pilihan metode yang tepat. Pada penelitian ini, tingkat persediaan obat generik yang optimal akan dianalisis dengan menggunakan markov chain. Kondisi steady state tercapai ketika hasil yang sama diperoleh dengan hasil dari iterasi sebelumnya. Ada 7 persamaan linier yang dihasilkan, masing-masing disertai dengan 7 tingkat persediaan dan besaran pemesanan optimal dan juga besaran biaya.Kata kunci: Permintaan, Obat Generik; Persediaan; Rantai Markov
ANALISIS OPTIMISASI PROGRAM KUADRATIK DENGAN FUNGSI PENALTY Roberto Parujian Sitanggang; Lasker Pangarapan Sinaga
JURNAL RISET RUMPUN ILMU PENDIDIKAN Vol. 2 No. 1 (2023): April : Jurnal Riset Rumpun Ilmu Pendidikan
Publisher : Pusat Riset dan Inovasi Nasional

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55606/jurripen.v2i1.812

Abstract

This study aims to analyze the optimality of a quadratic program model using the penalty function. The analysis is carried out in each case that has been made so that in each case optimal results are obtained. There are many methods that can be used to solve the quadratic program problem but in terms of the number of iterations, this research uses the penalty function and then implements it into the Matlab programming language. The results obtained in this study indicate that by using the penalty function as a parameter, the optimal value of a function can be obtained. The results of the analysis will also be more optimal by using the lagrange method depending on the parameter values obtained.
REKONSTRUKSI MODEL PROGRAM NONLINIER DENGAN FUNGSI POLINOMIAL MENJADI BENTUK PROGRAM KUADRATIK Amar Pilenon Sinaga; Lasker Pangarapan Sinaga
JURNAL RISET RUMPUN ILMU PENDIDIKAN Vol. 2 No. 1 (2023): April : Jurnal Riset Rumpun Ilmu Pendidikan
Publisher : Pusat Riset dan Inovasi Nasional

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55606/jurripen.v2i1.814

Abstract

The purpose of this research to revisits methods that are more effective in nonlinear Optimization with single variable polynomial functions at high degrees. Models with linear objective functions and constraint functions are Polynomials of third, fourth and fifth degree reconstructed into subproblems that are easier to solve, namely quadratic programs, using bilinear Auxiliary Functions and solved by MATLAB simulations. The method used is the development of Tawarmalani & Sahinidis' research regarding relaxation with Auxiliary Functions. Examples of nonlinear Optimization with polynomial functions are also given to illustrate the implementation of this algorithm. The results of the research show that the application of the development reconstruction method produces a global solution that is no better than the solution to the original problem so that it is not an effective alternative method to use.
Penerapan Model Goal Programming pada Penjadwalan Perawat di RSIA Artha Mahinrus Medan Agustin Richardo Josua Nababan; Lasker Pangarapan Sinaga
ULIL ALBAB : Jurnal Ilmiah Multidisiplin Vol. 3 No. 9: Agustus 2024
Publisher : CV. Ulil Albab Corp

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56799/jim.v3i9.4755

Abstract

Tujuan dari penelitian ini adalah untuk menerapkan model Goal Programming dalam penjadwalan perawat di RSIA Artha Mahinrus Medan yang saat ini masih melakukan penjadwalan secara manual. Rumah sakit ini memiliki 18 perawat yang dijadwalkan bekerja dalam tiga shift, yaitu pagi, sore, dan malam. Akibat dari penjadwalan secara manual ini membutuhkan waktu yang lama dan kurang efisien dikarenakan adanya ketimpangan dalam pembagian shift. Goal Programming merupakan pengembangan program linear dengan fungsi yang majemuk. Model ini diterapkan menggunakan perangkat lunak LINGO dengan mempertimbangkan sejumlah kriteria, termasuk kebutuhan operasional rumah sakit dan aturan ketenagakerjaan. Dalam memodelkan masalah penjadwalan perawat ini ada dua sistem kendala yang harus dipenuhi yaitu kendala utama dan kendala tambahan. Kendala utama adalah aturan yang harus dipenuhi sedangkan kendala tambahan yaitu aturan rumah sakit yang masih diberi toleransi terhadap pelanggarannya. Dalam memodelkan masalah penjadwalan perawat, setiap masalah diubah kedalam model matematika serta penyelesaian model goal Programming dibantu dengan software LINGO. Berdasarkan output LINGO yang diperoleh, penjadwalan perawat dengan menggunakan model goal programming memenuhi semua sistem kendala, sedangkan jadwal manual rumah sakit tidak memenuhi sistem kendala