Articles
<![CDATA[Mathematical Modeling on the Control of Hunting Problems ]]>
<![CDATA[Redemtus Heru Tjahjana]]>;
<![CDATA[Dhimas Mahardika]]>
<![CDATA[ ComTech: Computer, Mathematics and Engineering Applications Vol. 12 No. 1 (2021): ComTech ]]>
Publisher : <![CDATA[Bina Nusantara University ]]>
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DOI: 10.21512/comtech.v12i1.6424
<![CDATA[Modeling a natural phenomenon or the action mechanism of a tool is often done in science and technology. Observations through computer simulations cost less relatively. In the research, a bullet control model moving towards the target was explored. The research aimed to try to simulate the trajectory of the bullet that could be controlled in hunting. To model a controlled bullet, the Dubins model was used. Then, the used approach was control theory. The optimal trajectory and control for bullets were designed using the Pontryagin Maximum Principle. The results show that with this principle and the dynamic system of the bullet, a system of differential equations and adjoining is obtained. The fundamental problem arises because the bullet dynamics model in the form of a differential equation system has initial and final requirements. However, the adjoint matching system has no conditions at all. This problem is solved by using numerical methods. In addition, the research proves the convergence of the calculation results with the required results. The track simulation results are also reported at the end of the research to ensure a successful control design. From the simulation results, the presented method with its convergence has successfully solved the problem of bullet control.]]>
<![CDATA[Pengaruh Penggunaan Binder terhadap Densitas dan Kalor Pembakaran Briket dari Limbah Sagu ]]>
<![CDATA[Hendri Widiyandari]]>;
<![CDATA[Wahyu Setiabudi]]>;
<![CDATA[Agus Subagio]]>;
<![CDATA[Sri Haryanti]]>;
<![CDATA[Parsaoran Siahaan]]>;
<![CDATA[Heru Tjahjana]]>
<![CDATA[ INDONESIAN JOURNAL OF APPLIED PHYSICS Vol 3, No 02 (2013): October ]]>
Publisher : <![CDATA[Department of Physics, Sebelas Maret University ]]>
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DOI: 10.13057/ijap.v3i02.1270
<![CDATA[Biomass fuel such as briquette is one of an alternative energy regarded to the shortage of the fosil fuel and rising its prices. The byproduct of sago starch industry is the waste that remain the environmental problem because of the odor. However this agricultur waste such as trunk cortex and fibre has a potential application as a raw material for briquette.The fibre and trunk cortex act as matrix material of briquette. The utilizing of sago waste as a biomass briquette and the effect of ratio of matrix/binder to the density, time of compustion and gross heat of the briquette have been elucidated sistematically. The analyzing of gross heat using adiabatic calorimetry indicated that the briquette prepared with the ratio of binder/matrix of 3:4 (mass ratio) had the maximum value of 3929.5 kal/g. The duration of combusion was proposional with density of the briquette.]]>
<![CDATA[Fuzzy Expected Value Approach to Solve Integrated Supplier Selection and Inventory Control Problem in Fuzzy Environment ]]>
<![CDATA[Sutrisno Sutrisno]]>;
<![CDATA[Widowati Widowati]]>;
<![CDATA[R. Heru Tjahjana]]>
<![CDATA[ International Journal of Supply Chain Management Vol 7, No 3 (2018): International Journal of Supply Chain Management (IJSCM) ]]>
Publisher : <![CDATA[International Journal of Supply Chain Management ]]>
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<![CDATA[In a production and inventory planning management, the future parameters like future demand, future product buying cost, future transport cost and future holding cost are obviously unknown/uncertain. To determine the optimal strategy in uncertain condition, a method that can handle the uncertainty of parameters is needed. If the historical data of the uncertain parameters are known then they can be approached by using probability distribution, but if there is no historical data then it cannot be used. In this paper, we propose a new mathematical optimization model with fuzzy parameters to solve an integrated supplier selection problem and inventory control problem in fuzzy environment where fuzzy variables are used to approach the uncertain parameters. To solve the corresponding optimization problem, we use fuzzy expected value based integer quadratic programming where the fuzzy variables are approximated by fuzzy expected value. From the numerical experiment results, the optimal strategy i.e. the optimal supplier and the optimal stored product volume were obtained and the actual inventory level followed the desired level with minimal total expected cost.]]>
<![CDATA[Joint Decision on Integrated Supplier Selection and Stock Control of Inventory System Considering Purchase Discount ]]>
<![CDATA[Widowati Widowati]]>;
<![CDATA[Sutrisno Sutrisno]]>;
<![CDATA[R. Heru Tjahjana]]>
<![CDATA[ International Journal of Supply Chain Management Vol 6, No 4 (2017): International Journal of Supply Chain Management (IJSCM) ]]>
Publisher : <![CDATA[International Journal of Supply Chain Management ]]>
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<![CDATA[Stock control and supplier selection are two vital parts on supply chain and management. Integrating these parts by solving them simultaneously is a good idea for cost reducing. Furthermore, if some suppliers give a purchase discount for their product, how to determine the optimal strategy is interesting. In this paper, we propose a mathematical model in a mixed integer quadratic programming with piecewise objective function to determine the optimal strategy for integrated supplier selection and stock control of multiproduct inventory system considering purchase discount. This stock control refers to bring the stock level of each product to a reference level given by decision maker. We formulate the model in two environments which are deterministic where all parameters are known and stochastic where the demand is random. Two numerical experiments are performed to evaluate the model. From the results, the optimal strategy was generated i.e. the optimal product volume purchased from each supplier and the stock level of each product follows the reference level.]]>
<![CDATA[Fuzzy Time Series Orde Tinggi berdasarkan Rasio Interval ]]>
<![CDATA[Etna Vianita]]>;
<![CDATA[Redemtus Heru Tjahjana]]>;
<![CDATA[Titi Udjiani]]>
<![CDATA[ Jurnal Matematika UNAND Vol 11, No 1 (2022) ]]>
Publisher : <![CDATA[Jurusan Matematika FMIPA Universitas Andalas Padang ]]>
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DOI: 10.25077/jmu.11.1.53-63.2022
<![CDATA[Fuzzy time series (FTS) adalah metode peramalan untuk memprediksi data time series dibentuk dalam nilai-nilai linguistik yang diperkenalkan pertama kali oleh Song dan Chissom. Metode peramalan FTS terus berkembang misalnya pengembangan pada partisi interval pembicaraan menggunakan rasio interval oleh Huarng dan pengembangan pada fuzzy logical relationship (FLR) orde tinggi oleh Chen. Penelitian ini memodifikasi metode Chen pada langkah partisi interval pembicaraan menggunakan rasio interval untuk meningkatkan akurasi peramalan. Langkah pertama adalah pembentukan semesta pembicaraan. Kedua, mempartisi semesta pembicaraan menjadi beberapa interval dengan menggunakan rasio interval. Ketiga, fuzzyfikasi. Keempat, membangun relasi logika fuzzy (FLR) dan grup relasi logika fuzzy (FLRG). Kelima, defuzzyfikasi. Hasil penggabungan metode Huarng-Chen dibandingkan dengan metode Chen. Simulasi yang dilakukan menggunakan data produksi karet Indonesia tahun 2000-2020. Hasil dan eror dari metode diuji menggunakan mean square error (MSE) dan average forecasting error rate (AFER). Diperoleh hasil modifikasi menghasilkan eror yang lebih kecil daripada metode sebelumnya.]]>
<![CDATA[Control of inventory system with random demand and product damage during delivery using the linear quadratic gaussian method ]]>
<![CDATA[Sutrisno Sutrisno]]>;
<![CDATA[Widowati Widowati]]>;
<![CDATA[R. Heru Tjahjana]]>
<![CDATA[ Indonesian Journal of Electrical Engineering and Computer Science Vol 22, No 3: June 2021 ]]>
Publisher : <![CDATA[Institute of Advanced Engineering and Science ]]>
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DOI: 10.11591/ijeecs.v22.i3.pp1748-1753
<![CDATA[This study formulates a dynamical system for the control of a single product inventory system in accordance with the random value of demand and the percentage of damaged product during the delivery process. The formulated model has the form of a linear state-space system comprising of two disturbances, which represents the random value of demand and the percentage of the damaged product during delivery. The optimal value of the product amount ordered to the supplier is properly calculated by using the linear quadratic gaussian (LQG) method. The controller is used by the manager to make inventory level decisions under the uncertainty of demand and damaged items during the product delivery process. The result showed that the optimal product order for each review time was achieved, and the inventory level was used to obtain the right set point properly. Moreover, based on comparison with other research results, the proposed model was well performed.]]>
<![CDATA[OPTIMAL CONTROL MODELLING OF COVID-19 OUTBREAK IN SEMARANG CITY INDONESIA ]]>
<![CDATA[Dhimas Mahardika]]>;
<![CDATA[R. Heru Tjahjana]]>;
<![CDATA[Sunarsih Sunarsih]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 2 (2020) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v3i2.8546
<![CDATA[Corona virus infection is lethal and life threatening to human life, for prevention it is necessary to carry out quarantined for a portion of susceptible, exposed, and infected population, this kind of quarantine is intended to reduce the spread of the corona virus. The optimal control that will be carried out in this research is conducting quarantine for a portion of susceptible, exposed, and infected individuals. This control function will be applied to the dynamic modelling of Covid-19 spread using Pontryagin Minimum Principle. We will describe the formulation of dynamic system of Covid-19 spread with optimal control, then we use Pontryagin Minimum Principle to find optimal solution of the control. The optimal control will aim to minimize the number of infected population and control measures. Numerical experiments will be performed to illustrate and compare the graph of Covid-19 spread model with and without control.]]>
<![CDATA[LOGISTIC MODEL DEVELOPMENT OF COVID-19 SPREAD WITH PHYSICAL DISTANCING INTERVENTION ]]>
<![CDATA[Okky Widya Arditya]]>;
<![CDATA[Widowati Widowati]]>;
<![CDATA[Sutimin Sutimin]]>;
<![CDATA[R. Heru Tjahjana]]>;
<![CDATA[Priyo Sidik Sasongko]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 1 (2021) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v4i1.8385
<![CDATA[In early 2020, covid-19 spread fast in the worldwide and cause the high death. The disease started from the Asian region which resulted in a viral pandemic in 2020. In order to anticipate the increasing of the cases, a strategy is needed to inhibit its transmission. The mathematical model approach is important tool for predicting of covid-19 spread in populations. In this paper we propose and analyze the dynamical behaviour of a developed logistic model by considering the effect of the contact patterns in reducing the covid-19 spread process. To verify the developed logistic model, numerical simulation was given with case study of covid-19 spread for patients under supervision in Central Java Province, Indonesia. Based on simulation results, it was found that physical distancing can reduce the growth of the covid-19 spread for patient under supervision. It can be seen from the number of covid-19 spread for patients under supervision with physical distancing intervention smaller compared to without physical distancing intervention.]]>
<![CDATA[PELABELAN TOTAL SUPER TRIMAGIC SISI PADA BEBERAPA GRAF ]]>
<![CDATA[Robertus Heri Utomo]]>;
<![CDATA[Heru Tjahjana]]>;
<![CDATA[Bambang Irawanto]]>;
<![CDATA[Lucia Ratnasari]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 1 (2018) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v1i1.4
<![CDATA[This paper is addressed to discuss the edge super trimagic total labeling on some graphs which are corona, double ladder, quadrilateral snake and alternate triangular snake. The main results are the edge super trimagic total label for these graphs. Furthermore, it was prove that corona is a graph with edge super trimagic total labeling, a double ladder with odd ladder is graph with edge super trimagic total labeling, quadrilateral snake is a graph with edge super trimagic total labeling and finally an alternate triangular snake with odd ladder is graph with edge super trimagic total labeling.]]>
<![CDATA[MODELING PREDICTIVE TRACKING CONTROL FOR MAX-PLUS LINEAR SYSTEMS IN MANUFACTURING ]]>
<![CDATA[Lathifatul Aulia]]>;
<![CDATA[Widowati Widowati]]>;
<![CDATA[R. Heru Tjahjana]]>;
<![CDATA[Sutrisno Sutrisno]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 2 (2020) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v3i2.8605
<![CDATA[Discrete event systems, also known as DES, are class of system that can be applied to systems having an event that occurred instantaneously and may change the state. It can also be said that a discrete event system occurs under certain conditions for a certain period because of the network that describes the process flow or sequence of events. Discrete event systems belong to class of nonlinear systems in classical algebra. Based on this situation, it is necessary to do some treatments, one of which is linearization process. In the other hand, a Max-Plus Linear system is known as a system that produces linear models. This system is a development of a discrete event system that contains synchronization when it is modeled in Max-Plus Algebra. This paper discusses the production system model in manufacturing industries where the model pays the attention into the process flow or sequence of events at each time step. In particular, Model Predictive Control (MPC) is a popular control design method used in many fields including manufacturing systems. MPC for Max-Plus-Linear Systems is used here as the approach that can be used to model the optimal input and output sequences of discrete event systems. The main advantage of MPC is its ability to provide certain constraints on the input and output control signals. While deciding the optimal control value, a cost criterion is minimized by determining the optimal time in the production system that modeled as a Max-Plus Linear (MPL) system. A numerical experiment is performed in the end of this paper for tracking control purposes of a production system. The results were good that is the controlled system showed a good performance.]]>
