Journal Jurnal Matematika "MANTIK"

40 articles
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Faisol Faisol, Masdukil Makruf
Jurnal Matematika "MANTIK", Volume 3, pp 101-104; doi:10.15642/mantik.2017.3.2.101-104

Abstract:Product distribution process is an effort to convey a product of consumer handlebar with a planned and programmed system. Cluster method is a grouping of the nearest market location, then analyzed the location of potential facilities through center of gravity. GVRP (Generalized Vehicle Routing Problem) is one of the algorithms in the cluster method [1]. In the GVRP describes the route determination to minimize the required distribution costs. GVRP is a generalization of VRP, so the point of the graph is partitioned into several sets of specific points, called clusters [2]. In this research, modification of GVRP model for multi-capacity vehicle case can determine the route and minimize the cost of distribution. Taken case on UD. Damai Asih for the distribution of Madura writes batik to 25 districts in East Java. From the results of running using MATLAB 7.8.0 obtained the efficiency of the distribution cost of 8.71% of the initial cost before doing the clustering based on distance and maximum capacity of the car of Rp. 6,969,480.00. After the filtering based on the distance and maximum capacity of the car obtained a cost of Rp. 6.365.500.00. The highest value of efficiency is obtained in cluster four, while the lowest efficiency value is obtained in cluster eight. The existence of cost efficiency is due to the different mileage in the clustering process.
Ihda Hasbiyati, Hasriati Hasriati
Jurnal Matematika "MANTIK", Volume 3, pp 83-86; doi:10.15642/mantik.2017.3.2.83-86

Abstract:Stochastic programming problem is mathematical problem (linear, integer, mixed integer, and nonlinier) with stochastic element lies data. To get reasonable solution and optimal with its stochastic data is needed several method. Applicable method in trouble stochastic programming are L-Shape decomposition and lagrange decomposition. Each method can determine optimal solution to troubleshoots stochastic programming
Fery Firmansah, Muhammad Ridlo Yuwono
Jurnal Matematika "MANTIK", Volume 3, pp 87-95; doi:10.15642/mantik.2017.3.2.87-95

Abstract:Graph class which has the characteristic of odd harmonious labeling is called as odd harmonious graph. Net graph is a graph which is gained by using operation Cartesian product of two line graphs. The construction of snake-net graph is inspired by the definition of snake graph replacing the round graph to net graph. In this paper, the study will show that snake-net graph fulfill the characteristic of odd harmonious graph in such a way snake-net graph is the odd harmonious graph. In the end of this paper, it is also shown that the union of snake-net graph is also called as the odd harmonious graph.
Leli Deswita
Jurnal Matematika "MANTIK", Volume 3, pp 96-100; doi:10.15642/mantik.2017.3.2.96-100

Abstract:This study examines and analyzes mathematical model of mixed convection in horizontal plate. The heat transfer uses the model of a two dimensional nonlinear partial differential equations system. Then, this equation is derived first into the dimensionless equation form, and then it is changed into system of nonlinear ordinary differential equations form using similarity transformation. This system of nonlinear ordinary differential equations is solved by using the finite-difference scheme method, also with the mathematics program with software Matlab. The results obtained form this program is to determine skin friction coefficient , wall temperature velocity profiles and temperature profiles
Yulia Retno Sari
Jurnal Matematika "MANTIK", Volume 3, pp 65-73; doi:10.15642/mantik.2017.3.2.65-73

Abstract:A positive discrete descriptor system has been widely used in modeling economics, engineering, chemistry and others. In this research, we studied the necessary conditions and sufficient conditions for a positive discrete descriptors system is achieved positive and controlled postively. In addition, it is also studied on sufficient terms and conditions which ensure that discrete systems are null controlled. By using linear algebraic method and Inverse Drazin, this research has proved several theorems for discrete descriptors system achieved positive, controlled positively and controlled null. In addition, examples are given as illustrations to reinforce the validity of the proven theorems.
Nahlia Rakhmawati, Ririn Febriyanti
Jurnal Matematika "MANTIK", Volume 3, pp 51-56; doi:10.15642/mantik.2017.3.2.51-56

Abstract:The existence of ideal public transportation is still a dream of many cities in Indonesia, including the city of Jombang. The high consumption of Jombang people to motor vehicles, causing traffic jams in the school area. In this research, a directed graph from 3 rural transit routes to get the design of scheduling model using max-plus algebra. From the analysis results to the model obtained the period of departure of rural transport is 10 minutes once, with two initial departure time interval. Arranged departure schedules allow rural transport always at every meeting point during school hours.
Deltha Airuzsh Lubis, Muhamad Budiman Johra, Gumgum Darmawan
Jurnal Matematika "MANTIK", Volume 3, pp 74-82; doi:10.15642/mantik.2017.3.2.74-82

Abstract:Consumer Price Index (CPI) are the indicators used to measure the inflation and deflation of a group of goods and services in general. Forecasting CPI to be important as early detection in facing price hikes. This study uses the SSA and SARIMA. SARIMA a parametric model that requires various assumptions while SSA is a nonparametric technique that is free from a variety of assumptions, but both methods require seasonal patterns in the data. Based on the research results, methods of SSA with length window(L) of 24 and a grouping of 4 (1 group of seasonal and 3 groups of trends) and SARIMA models of order (0,1,1), (0,1,1) 6 is the most accurate and reliable models in forecasting CPI to the value Padang Sidempuan City. Forecasting CPI Padang Sidempuan City for the next 5 months with SSA method and SARIMA (0,1,1), (0,1,1) 6 shows the pattern of a trend is likely to increase but forecasting the 5th month with SSA method showed a surge in the value of CPI high or high inflation will occur.
Noor Saif Muhammad Mussafi
Jurnal Matematika "MANTIK", Volume 3, pp 57-64; doi:10.15642/mantik.2017.3.2.57-64

Abstract:This research seeks to analyze the development of syariah stock optimization method using Nonlinear Programming in order to provide an optimal portfolio as a reference in improving the quality of syariah capital market in Indonesia. The research design used is descriptive qualitative by presenting a Shariah stock history data within a certain period that is analyzed and modeled for later sought solving. The data in this research is the stock price information syariah incorporated in the Jakarta Islamic Index (JII). Selected data with Reward to Variability (RVAL) were then analyzed using theories in financial mathematics and developed using quadratic programming. The result of this research is systematic step formulation to maximize profit level and minimize risk level of syariah share investment incorporated in JII in January 2015-December 2016 time domain. This research also concludes that by this method can be known the proportion of funds that can be invested in five best issuers. In the sample taken, for the expected profit level of 5.5% to 7.5%, then an investor is advised to embed its shares consecutively to AKRA, ICBP, PTPP, TLKM and WSKT on average of 29.74% ; 13.42%; 18.14%; 29.58%; And 9.1% with risk between 0.028301593% to 0.029386615%.
Rina Sri Kalsum Siregar, Dina Prariesa, Gumgum Darmawan
Jurnal Matematika "MANTIK", Volume 3, pp 5-12; doi:10.15642/mantik.2017.3.1.5-12

Abstract:The purpose of this study was to look at seasonal patterns in the data of Gross Domestic Product (GDP) quarterly in the year 2000-2016 and the implementation of Singular Spectral Analysis (SSA) in the data of GDP to predict the data of GDP in 2017. The SSA method used is the method of recurrent forecasting with bootstrap confidence interval to look at its beliefs of the interval. The source of data derived from the data of GDP in 2000-2016 with the base year in 2000 compiled by the Central Statistics Agency (CSA). The results showed that the SSA method can be used as a reliable method and can be valid that view from the value of MAPE size is 0.82 and the size of the tracking signal at -4.00.
Abdussakir Abdussakir
Jurnal Matematika "MANTIK", Volume 3, pp 1-4; doi:10.15642/mantik.2017.3.1.1-4

Abstract:Commuting graph C(G) of a non-Abelian group G is a graph that contains all elements of G as its vertex set and two distinct vertices in C(G) will be adjacent if they are commute in G. In this paper we discuss commuting graph of dihedral group D2n. We show radius, diameter, cycle multiplicity, and metric dimension of this commuting graph in several theorems with their proof.
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