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Uncoupled Two Agents Modeling Via Bilinear Optimal Control Tjahjana, R. Heru
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 4, No 1 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i1.24969

In this paper, uncoupled two agents modeling is proposed using an optimal bilinear control approach. The model is proposed using assumptions: an absence of the multi agent leader, each agent cannot control the others, each agent never collides with the others, and each agent has the same properties. The special functional cost consisting of a repellent cost is considered. The Pontryagin Maximum Principle is used to determine the optimal path for each agent. After control and optimal path for each agent are obtained some of the simulation results are exposed in this paper.Keywords: uncoupled agent; modeling; bilinear system. AbstrakDalam penelitian ini, pemodelan dua agen yang tidak berpasangan disajikan dengan pendekatan kontrol optimal bilinear. Model yang diusulkan dalam paper ini ditulis dengan asumsi: tidak adanya pemimpin dalam sistem multi agen, setiap agen tidak dapat mengendalikan atau mempengaruhi agen yang lain, setiap agen tiak boleh bertabrakan satu sama lain, dan para agen mempunyai sifat-sifat yang identik. Fungsional biaya khusus yang membuat para agen tidak bertabrakan dipertimbangkan dalam penulisan paper ini. Prinsip maksimum Pontryagin digunakan dalam penentuan lintasan optimal dari para agen. Beberapa hasil simulasi disajikan dalam paper ini.Kata Kunci: agen tak berpasangan; pemodelan; sistem bilinear.

Fuzzy Piecewise-objective Programming Approach for Integrated Supplier Selection and Production Planning Problems Considering Discounts and Fuzzy Parameters: the Static Case Harahap, Adhina Rizkillah; Sutrisno, Sutrisno; Tjahjana, Redemtus Heru; Widowati, Widowati
Jurnal Sistem Informasi Bisnis Vol 15, No 3 (2025): Volume 15 Number 3 Year 2025
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/vol15iss3pp337-343

In the manufacturing and retail sectors, the challenge of supplier selection revolves around efficiently allocating the necessary amount of raw materials to each supplier to minimize procurement costs. Concurrently, production planning focuses on maximizing output. To achieve maximum revenue, decision-makers must make optimal decisions in both areas. This paper introduces a new mathematical model, falling within the fuzzy piecewise programming domain, to support decision-making in supplier selection and production planning. It addresses integrated supplier selection and production planning issues, incorporating discounts and fuzzy factors. The aim is to optimize supply chain performance, ultimately maximizing the production activity profit. The model accommodates scenarios involving multiple raw materials, suppliers, products, and buyers. Through numerical experiments, the effectiveness of the proposed model is evaluated, demonstrating its ability to provide the optimal solution. Thus, it can be readily applied by industry decision-makers and managers.

The Cleanness Property of The Integers Modulo n (ℤn) 'Aliyah, Dheva Ufiz; Puspita, Nikken Prima; Tjahjana, Redemtus Heru
Integra: Journal of Integrated Mathematics and Computer Science Vol. 1 No. 2 (2024): July
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20241214

Assume that R is a ring with identity. A ring R is said to be clean when each of its elements can be written as the sum of an idempotent and a unit element within the ring. A stronger condition, known as strongly clean, requires that these elements commute under multiplication. As a special case, a module M over ring R is called a clean module when the endomorphism ring of the M is a clean module over R. Moreover, when the ring endomorphism of R-module M is a strongly clean, then the module M is referred to as a strongly clean. We know that the integers modulo n, denoted by ℤn, is a ring by the set of congruence classes modulo n, with standard addition and multiplication operations. In this study, we explore the cleanness properties of the ring ℤn and establish that it is a strongly clean ring. Furthermore, we study about the cleanness of ℤn as a module over ℤ and investigate the strongly cleanness of it module.

Pembelajaran Integral Tak Tentu Menggunakan Articulate Storyline di MA Miftahussalam Wijayanti, Shofiyana Noor; Harahap, Adhina Rizkillah; Paramita, Arum Qurrotulaini Pradjna; Sunarsih, Sunarsih; Tjahjana, Heru
Jurnal Surya Masyarakat Vol 7, No 2 (2025): Mei 2025
Publisher : Universitas Muhammadiyah Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26714/jsm.7.2.2025.227-231

Mathematics is often considered a difficult subject and is of little interest to students, which results in students having difficulty learning independently outside of school. The difficulty of class XI students in understanding mathematics material is the background for the need to use new technology, namely articulate storylines, so that mathematics learning is more innovative and interactive. This community service activity is divided into 2 stages, namely the preparation stage and the implementation stage. In the preparation stage, the community service team conducted interviews with class XI mathematics teachers at MA Miftahussaam to find out what material was still difficult for students to understand. The second stage of this community service activity is the implementation stage which includes a pre-test, providing learning companion modules, playing the Articulate Storyline video, and post-test. The results of community service regarding the use of Articulate Storyline media at MA Miftahussalam show that the average pre-test score of 25 students is 42.2. This average value shows that the level of students' understanding ability and interest in learning about Indefinite Integral material is still below the average standard, namely less than 50. Meanwhile, the average post-test score of 25 students is 72.2. This average value shows that the level of students' understanding ability and interest in learning about Integral Uncertain material has reached the standard value, namely more than 70. Meanwhile, if calculated using percentages, the percentage increase in value from pre-test to post-test is 71.09%. This percentage level can be stated to be quite good.

Pembelajaran Integral Tak Tentu Menggunakan Articulate Storyline di MA Miftahussalam Wijayanti, Shofiyana Noor; Harahap, Adhina Rizkillah; Paramita, Arum Qurrotulaini Pradjna; Sunarsih, Sunarsih; Tjahjana, Heru
Jurnal Surya Masyarakat Vol 7, No 2 (2025): Mei 2025
Publisher : Universitas Muhammadiyah Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26714/jsm.7.2.2025.227-231

Mathematics is often considered a difficult subject and is of little interest to students, which results in students having difficulty learning independently outside of school. The difficulty of class XI students in understanding mathematics material is the background for the need to use new technology, namely articulate storylines, so that mathematics learning is more innovative and interactive. This community service activity is divided into 2 stages, namely the preparation stage and the implementation stage. In the preparation stage, the community service team conducted interviews with class XI mathematics teachers at MA Miftahussaam to find out what material was still difficult for students to understand. The second stage of this community service activity is the implementation stage which includes a pre-test, providing learning companion modules, playing the Articulate Storyline video, and post-test. The results of community service regarding the use of Articulate Storyline media at MA Miftahussalam show that the average pre-test score of 25 students is 42.2. This average value shows that the level of students' understanding ability and interest in learning about Indefinite Integral material is still below the average standard, namely less than 50. Meanwhile, the average post-test score of 25 students is 72.2. This average value shows that the level of students' understanding ability and interest in learning about Integral Uncertain material has reached the standard value, namely more than 70. Meanwhile, if calculated using percentages, the percentage increase in value from pre-test to post-test is 71.09%. This percentage level can be stated to be quite good.

Uncoupled Two Agents Modeling Via Bilinear Optimal Control Tjahjana, R. Heru
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 4 No. 1 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i1.24969

In this paper, uncoupled two agents modeling is proposed using an optimal bilinear control approach. The model is proposed using assumptions: an absence of the multi agent leader, each agent cannot control the others, each agent never collides with the others, and each agent has the same properties. The special functional cost consisting of a repellent cost is considered. The Pontryagin Maximum Principle is used to determine the optimal path for each agent. After control and optimal path for each agent are obtained some of the simulation results are exposed in this paper.Keywords: uncoupled agent; modeling; bilinear system. AbstrakDalam penelitian ini, pemodelan dua agen yang tidak berpasangan disajikan dengan pendekatan kontrol optimal bilinear. Model yang diusulkan dalam paper ini ditulis dengan asumsi: tidak adanya pemimpin dalam sistem multi agen, setiap agen tidak dapat mengendalikan atau mempengaruhi agen yang lain, setiap agen tiak boleh bertabrakan satu sama lain, dan para agen mempunyai sifat-sifat yang identik. Fungsional biaya khusus yang membuat para agen tidak bertabrakan dipertimbangkan dalam penulisan paper ini. Prinsip maksimum Pontryagin digunakan dalam penentuan lintasan optimal dari para agen. Beberapa hasil simulasi disajikan dalam paper ini.Kata Kunci: agen tak berpasangan; pemodelan; sistem bilinear.

STABILITY ANALYSIS OF THE MODEL SVEI_a I_sR ON COVID-19 SPREAD Permatasari, Tiara Adinda; Tjahjana, Redemtus Heru; Widowati, Widowati
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 2 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.29819

The COVID-19 pandemic has presented a major challenge in understanding the dynamics of disease transmission in a region. DKI Jakarta is the province with the highest number of COVID-19 cases in Indonesia. In this article, the SVEIₐIₛR model (Susceptible, Vaccinated, Exposed, Asymptomatic, Symptomatic, and Recovered) is examined to model the spread of COVID-19 in DKI Jakarta Province. The basic reproduction number is obtained through the Next Generation Matrix (NGM) approach, whereas the local stability analysis is carried out using the Routh–Hurwitz criterion. Furthermore, there are two equilibrium points obtained, which are the disease-free equilibrium and the endemic equilibrium. The stability of the equilibrium point is analyzed based on the value of the basic reproduction number. The endemic equilibrium point is considered asymptotically stable if the basic reproduction number is less than one. To demonstrate the behavior of the COVID-19 transmission model, numerical simulations are conducted using data obtained from DKI Jakarta Province. The results of the analysis indicate that, the COVID-19 transmission model is asymptotically stable at the diseas-free equilibrium point with R0=0.001897843854. This indicates that, over time, the COVID-19 disease will eventually disappear from the population.

Optimal Control Approach For HIV-1 Infection in CD4+T Cells with RTI and PI Treatments R. Heru Tjahjana; Sutimin Sutimin
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 6 No. 2 (2020)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar

The purpose of this paper is to expose the optimal approach of controlling HIV-1 infection in CD4+T cells with Reverse Transcriptease Inhibitors (RTI) and Protease Inhibitors (PI) treatments. The scope of the paper includes a proposed model of the dynamic system of HIV-1 infection in CD4 cells with RTI and PI as controls and a proposed objective function model that minimizes infected CD4+T Cells, the population of free virus and therapeutic costs. From the dynamics system model and objective function model, we designed an optimal control for HIV-1 infection control. In this paper, we obtained optimal control for RTI and PI therapies. The results of this paper are as follows: by using the optimal control approach, we obtained infectious control strategy that minimizes actively infected CD4+T Cells, the population of free virus and the cost of treatment. In other words, optimal control is a good approach in determining infection control strategies that minimizes the objective function.

Local Stability Analysis of Mathematic Model SEIHR-VW on Dengue Haemorrhagic Fever Transmission Nolaika Arsiani Norramandhany; Widowati Widowati; Redemtus Heru Tjahjana
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 11 No. 2 (2025)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.ijcsam.v11i2.6054

Dengue fever is caused by the dengue virus (DENV) and is mainly transmitted by mosquitoes, particularly Aedes aegypti. In this study, we develop a mathematical model to describe and analyze how dengue spreads within a population. The mathematical model is expressed as a nonlinear system of differential equations and consists of seven compartments (SEIHRVW): susceptible, exposed, infected, hospitalized, and recovered humans, along with susceptible and infected mosquitoes. The model has two possible equilibrium points: a non-endemic and endemic equilibrium point. To better understand the dynamics of the model, we calculate the basic reproduction number (R0) using the Next Generation Matrix (NGM) method, and then the Routh-Hurwitz criterion method is applied to analyze the local stability of both equilibrium points. The results indicate that the nonendemic equilibrium point is asymptotically stable when R0 < 1, while the endemic equilibrium point becomes asymptotically stable when R0 > 1. In general, our analysis concludes that the proposed dengue transmission model is asymptotically stable at the endemic equilibrium point, with R0 = 3.85011.

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