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Jurnal Kajian Matematika dan Aplikasinya
Published by Universitas Negeri Malang
ISSN : -     EISSN : 27227650     DOI : -
Core Subject : Education,
Mathematics
The aim of this journal publication is to disseminate research results and new theories that have been achieved in the area of mathematics. Jurnal Kajian Matematika dan Aplikasinya (JKMA) particularly focuses on the main issues in the development of the sciences of mathematics, in the fields of algebra, analysis, applied mathematics, combinatorics, computational sciences, geometry, and statistics.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 26 Documents
 1   2   3 
BEBERAPA KELAS GRAF RAMSEY MINIMAL UNTUK LINTASAN P_3 VERSUS P_5 Desi Rahmadani; Hilda Assiyatun; Mohammad Agung
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 2, No 1 (2021): January
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v2i12021p14-18

Abstract

In 1930, Frank Plumpton Ramsey has introduced Ramsey's theory, in his paper titled On a Problem of Formal Logic. This study became morepopular since Erdős and Szekeres applied Ramsey's theory to graph theory. Suppose given the graph F, G and H. The notation F → (G, H)  states thatfor any red-blue coloring of the edges of F implies F containing a red subgraph of G or a blue subgraph of H. The graph F is said to be the Ramsey graph for graph G versus H (pair G and H) if F → (G, H). Graph F is called Ramsey minimal graph for G versus H if  first, F → (G, H) and second, F satisfies the minimality property i.e. for each e ∈ E (F), then F-e ↛ (G, H). The class of all Ramsey (G, H) minimal graphs is denoted by (G, H). The class (G, H) is called Ramsey infinite or finite if  (G, H) is infinite or finite, respectively. The study about Ramsey minimal graph is still continuously being developed and examined, although in general it is not easy to characterize or determine the graphs included in the (G, H), especially if  (G, H) is an infinite Ramsey class. The characterization of graphs in (, ) has been obtained. However, the characterization of graphs in (, ), for every 3 ≤ m < n is still open. In this article, we will determine some infinite classes of Ramsey minimal graphs  for paths  versus . 
ANALISIS DINAMIK MODEL MANGSA PEMANGSA DENGAN FUNGSI RESPON MICHAELIS MENTEN DAN PEMANENAN Kridha Pusawidjayanti
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 2, No 2 (2021): July
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v2i22021p1-6

Abstract

The Predator-Prey model is an interesting study because it involves an ecosystem of two species that can provide benefits to human life. The purpose of this study was to determine the stability at the equilibrium points of the predator-prey model and the response function of Michaelis Menten and harvesting. This research method is a literature collection method that begins with the construction of the model, finds the equilibrium points, gets stability at the equilibrium points, then confirms the analytical result using numerical simulations. The predator-prey model with harvest assumptions and Michaelis Menten’s response function gets three equilibrium points, namely E_1, E_2, and E_3. E_1 and E_2 are asymptotically stable under certain conditions, while E_3 is unstable.
PEMODELAN KLAIM ASURANSI MENGGUNAKAN PENDEKATAN BAYESIAN DAN MARKOV CHAIN MONTE CARLO Azizah Azizah
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 2, No 2 (2021): July
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v2i22021p7-13

Abstract

The determination of the correct prediction of claims frequency and claims severity is very important in the insurance business to determine the outstanding claims reserve which should be prepared by an insurance company. One approach which may be used to predict a future value is the Bayesian approach. This approach combines the sample and the prior information The information is used to construct the posterior distribution and to determine the estimate of the parameters. However, in this approach, integrations of functions with high dimensions are often encountered. In this Thesis, a Markov Chain Monte Carlo (MCMC) simulation is used using the Gibbs Sampling algorithm to solve the problem. The MCMC simulation uses ergodic chain property in Markov Chain. In Ergodic Markov Chain, a stationary distribution, which is the target distribution, is obtained. The MCMC simulation is applied in Hierarchical Poisson Model. The OpenBUGS software is used to carry out the tasks. The MCMC simulation in Hierarchical Poisson Model can predict the claims frequency.
PENERAPAN ALGORITMA EXPECTATION-MAXIMIZATION (EM) DALAM MENGELOMPOKKAN POPULARITAS OBJEK WISATA DI MALANG RAYA BERDASARKAN INDIKATOR BANYAK PENGUNJUNG Nur Atikah; Swasono Rahardjo; Trianingsih Eni Lestari; Lucky Tri Oktoviana
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 2, No 2 (2021): July
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v2i22021p14-20

Abstract

The Malang Raya Area is one of the tourist destinations in East Java..Batu City is an area of Malang Raya which is visited by many for sightseeing. Given the development of tourism in Malang Raya, it is necessary to classify the popularity of tourist objects so that they can be used as a reference in policymaking by the tourism office and tourism object managers. In this study, the Expectation Maximation (EM) algorithm is used to determine the clustering of tourist objects in Malang Raya using data on the number of visitors. The results of grouping the popularity of leading tourist attractions in Malang Raya based on the number of visitors are divided into 5 groups, namely: Group 1: Selecta; Group 2: Balekambang, Wendit Baths, and Brawijaya Souvenir Tour; Group 3: Transport Museum, Coban Rondo, Animal Museum, Jatim Park, BNS, Picking Apples “Makmur Abadi and Agro Wonosari Tea Plantation; Group 4: Kusuma Agro Wisata, Kampoeng Kidz, Cangar Hot Springs, Eco Green Park, Predator Fun Park, Coban Rais Tourism Area, Mount Banyak, Mahajaya T-Shirt & Souvenirs, Ngliyep and Selorejo Dam; Group 5: “Dammadhipa Arama” Temple, “Kaliwatu” Rafting, Batu Rafting, Coban Talun Tourism Wana, Tirta Nirwana Baths, Songgoriti Natural Hot Springs, Wonderland Waterpark, Friends of Water Rafting, Independent Apple Picking, Apple Agro Stone, Tourism Village.
BASIS UNTUK SKEMA ASOSIASI GRUP MATRIKS ATAS Z3 Nur Hamid; Cahyu Guswita; Saiful Islam; M. Faiz Nailun Ni&#039;am
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 2, No 2 (2021): July
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v2i22021p21-25

Abstract

Some combinatorial problems in Mathematics can be studied via association scheme. By this scheme, algebra structure called Bose-Mesner algebra can be obtained. In this article, we show the explicit forms of the idempotent primitive of an association scheme for the group of order 48. Keywords: Association scheme, idempotent primitif
STUDI ALGORITMA IGVNS, ALGORITMA GVNS, DAN ALGORITMA ABC PADA MULTIPLE TRIP VEHICLE ROUTING PROBLEM (MTVRP) Nurul Faridhatul Aini; Vita Kusumasari; Desi Rahmadani
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 2, No 2 (2021): July
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v2i22021p26-31

Abstract

The Multiple Trip Vehicle Routing Problem (MTVRP) is one of the VRP variants with vehicle capacity constraints, and the limited number of vehicles allows each vehicle to distribute more than one route so as to minimize the number of vehicles used. The algorithm used in this study is the Improved General Variable Neighborhood Search (IGVNS) algorithm. The IGVNS algorithm is a hybrid between the GVNS algorithm and the VNS algorithm. The calculation results of the IGVNS algorithm will be compared with the GVNS algorithm and the ABC algorithm. The main stages of the IGVNS and GVNS algorithms are initial solution formation, perturbation, and solution improvement. The main stages of the ABC algorithm are initialization, solution improvement and optimization. Based on manual calculations using 8 points, the ABC algorithm produces a distance of 86 km and a service time of 1.47 hours, the GVNS algorithm produces a distance of 80 km and a service time of 1.37 hours, the IGVNS algorithm produces a distance of 79 km and service time is 1.35 hours. Based on one example of the ABC algorithm, the calculation solution using the IGVNS algorithm shows more optimal results. Based on the results of parameter testing, the  parameter affects the calculation results, that is the greater the  value, the more optimal the resulting solution. While the  parameter does not affect the calculation results because it shows constant results in two successive iterations carried out.
ALGORITMA GENERAL VARIABLE NEIGHBORHOOD SEARCH PADA CAPACITATED VEHICLE ROUTING PROBLEM WITH TIME WINDOWS DAN IMPLEMENTASINYA Ulil Ilmi Fadila; Sapti Wahyuningsih; Darmawan Satyananda
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 3, No 1 (2022): January
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v3i12022p1-7

Abstract

The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is one of the variants of the Vehicle Routing Problem (VRP), which is the problem of determining the optimal route from the depot to the consumer which is located spread out with different requests. In CVRPTW problem solving considers capacity and time constraints. Determining the optimal route can reduce costs and energy spent during the distribution process. The General Variable Neighborhood Search (GVNS) algorithm can be applied to the CVRPTW problem. The GVNS algorithm is an improvement on the VNS algorithm using RVND. The GVNS algorithm starts with finding the initial solution, continues with perturbation, and then the repair procedure is carried out. Perturbation and improvements to the GVNS algorithm are performed repeatedly according to the predetermined IterMax. The GVNS algorithm for CVRPTW will be implemented using the Borland Delphi 7.0 programming language. The product in the form of this application can be used more practically to solve CVRPTW problems using the GVNS algorithm.Keywords: Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), General Variable Neighborhood Search (GVNS) Algorithm, Randomized Variable Neighborhood Descent (RVND)
PERAMALAN PENJUALAN JUMLAH KRIPIK DI SNACK CENTER MENGGUNAKAN METODE TRIPLE EXPONENTIAL SMOOTHING Siti Nurul Afiyah; Nur Lailatul Aqromi
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 3, No 1 (2022): January
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v3i12022p8-14

Abstract

Snack Center is a gift center that offers various kinds of products to consumers who have a lot of untapped sales transaction data to support business and services. In addition, the goods arrangement system is carried out without standardization so that the goods cannot be run. In order to make the sales process more optimal, a chip sales forecasting system was made using the triple exponential smoothing method at the Batu City Snack Center by entering the data that has been obtained. The data is the result of sales in the previous period. In the triple exponential smoothing method, three smoothing calculations are carried out, then determine the alpha value to compare the smallest error percentage level. From the results of the data that has been tested with a sales forecasting system for chips with sales data from 2020-2021, the forecast value for recommendations for the next month, namely January 2022, is 30 packs of chips at alpha parameter 0.3 with least MAPE 9.598 percent.Keywords: Chips sale, forecasting, triple exponential smoothing
ALGORITMA GRAVITIONAL EMULATION LOCAL SEARCH PADA CVRP DAN IMPLEMENTASINYA Febri Nur Azis; Sapti Wahyuningsih; Darmawan Satyananda
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 3, No 1 (2022): January
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v3i12022p23-29

Abstract

Permasalahan optimalisasi distribusi dapat dipecahkan dengan menggunakan algoritma pada varian Vehicle Routing Problem (VRP). Salah satu varian dari VRP adalah Capacitated Vehicle Routing Problem (CVRP) yaitu dengan tambahan kendala kapasitas kendaraan yang identik. Algoritma Gravitational Emulation Local Search (GELS) dapat digunakan untuk menentukan solusi CVRP. Algorima GELS merupakan gabungan dari algoritma genetika dan local search (best improvement local search). Pada artikel ini dibahas langkah algoritma dan diimplementasikan ke dalam computer menggunakan aplikasi Borland Delphi 7.  Input program berupa ukuran populasi, probabilitas crossover, probabilitas mutasi, maksimum iterasi, kapasitas kendaraan, banyaknya titik, dan permintaan setiap customer. Output berupa hasil rute dengan jarak yang ditempuh serta divisualisasi rutenya dengan gambar graph. .Diberikan contoh penyelesaian permasalahan dengan contoh 7 titik terdiri dari satu depot dan enam customer. Hasil tampilan program berupa matrik bobot titik, permintaan, dan hasil berupa rute optimal. Aplikasi program GELS pada CVRP secara praktis dapat digunakan untuk penyelesaian optimasi distribusi.
PENERAPAN ANALISIS DISKRIMINAN LINIER ROBUST DALAM PENGKLASIFIKASIAN INDEKS KEPEDULIAN TERHADAP ISU KEPENDUDUKAN (IKIK) Nabilatul Fahma; Trianingsih Eni Lestari
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 3, No 1 (2022): January
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v3i12022p30-36

Abstract

Abstract Robust linear discriminant analysis is used to classify data that contains outlier by replacing classical parameters in linear discriminant analysis with robust parameters. This study aims to classify the Index of Concern for Population Issues (IKIK) of 34 provinces in 2020 into two categories namely target fulfilled IKIK and target not fulfilled IKIK using robust linear discriminant analysis. The independen variabels used are quantity dimensions (X_1), quality dimensions (X_2), mobility dimensions (X_3), and environment dimensions (X_4). The results obtained are 17 provinces were categorized as target fulfilled IKIK, 17 provinces as target not fulfilled IKIK. There are 2 robust discriminant functions formed, each for target fulfilled and target not fulfilled IKIK. The accuracy of the robust linear discriminant functions formed is 97,06%, the APER value of the discriminant functions is 2,94% and the PressQ value = 30,11 is greater than the value of (Chi_(3,0.05)^2) = 7.81. This shows that the discriminant functions can classify observations accurately.Keywords: classification, Index of Concern for Population Issues, robust discriminant analysis

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