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Contemporary Mathematics and Applications (ConMathA)
Published by Universitas Airlangga
ISSN : -     EISSN : 26865564     DOI : https://doi.org/10.20473/conmatha
Core Subject : Science, Education,
Materials Science & Nanotechnology Mathematics
Contemporary Mathematics and Applications welcome research articles in the area of mathematical analysis, algebra, optimization, mathematical modeling and its applications include but are not limited to the following topics: general mathematics, mathematical physics, numerical analysis, combinatorics, optimization and control, operation research, statistical modeling, mathematical finance and computational mathematics.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 71 Documents
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Analisis Kestabilan dan Kontrol Optimal Model Matematika Dinamika Pelanggan Berdasarkan Kebijakan Pemasaran Muhammad Iqbal Abdi Farchan; Fatmawati Fatmawati; Cicik Alfiniyah
Contemporary Mathematics and Applications (ConMathA) Vol. 2 No. 1 (2020)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (706.178 KB) | DOI: 10.20473/conmatha.v2i1.19300

Abstract

Customer dynamics include the exchange of information and ongoing transactions between customers and the organization. This process has an important role in the company to run its business, so that the number of customers increase. To achieve this, many things are done by the company. One of the strategies is product advertising by word of mouth. The purpose of this thesis is to analyze the stability of equilibrium point and to apply the optimal control word of mouth advertising on mathematics model of the customer dynamics based on marketing policy. Mathematics model of the customer dynamics based on marketing policy without control has two equilibrium points, namely non – endemic equilibrium (E0) and endemic equilibrium (E1). Local stability of equilibrium and the existence of endemic equilibrium depends on basic reproduction number (R0). The non – endemic equilibrium tend to asymptotically stable if R0 < 1.  The problem of optimal control is solved by Pontryagin’s Maximum Principle. The simulation results show that the total number of referral and regular customer populations that are given control in the form of word of mouth advertising efforts at the end of the observation are 312 and 18470 with the control effort costs occurred in 1798364.63. While the total number of referral and regular customer populations that are not given control in the form of word of mouth advertising efforts at the end observation are 241 and 17260. Based on these results show that word of mouth advertising efforts have an effect to increase the number of referral and regular customer in accordance with the aim of providing optimal control.
Penerapan Algoritma Kunang-Kunang pada Open Vehicle Routing Problem (OVRP) Ihda Septiyafi; Herry Suprajitno; Asri Bekti Pratiwi
Contemporary Mathematics and Applications (ConMathA) Vol. 1 No. 1 (2019)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (374.67 KB) | DOI: 10.20473/conmatha.v1i1.14774

Abstract

This paper aims to solve Open Vehicle Routing Problem using Firefly Algorithm. Open Vehicle Routing Problem (OVRP) is a variant of Vehicle Routing Problem (VRP)  where vehicles used to serve customers do not return to the depot after serving the last customer on each route. The steps of the Firefly Algorithm to handle OVRP are data input and initialization parameters, generating the initial population for each firefly, sorting population sources, calculating the value of the objective function and light intensity, comparing the intensity of light, performing movement, setting the best fireflies as g-best, doing random movement in the best fireflies as long as the maximum number of iterations has not been met. The program used to complete OVRP using the Firefly Algorithm is Borland C ++ and implemented in 3 case examples, namely small data with 18 customers, moderate data with 50 customers, and large data with 100 customers with the best total mileage of 211, 344 , 970.62, and 2531.83. The results obtained from the program output indicate that the more the number of iterations and the number of fireflies, then the results of the objective function (total mileage) obtained tend to be better so that these parameters affect the value of the objective function. While the absorption coefficient value (g) does not give effect to the value of the objective function.
Hybrid Artificial Neural Network with Extreme Learning Machine Method and Cuckoo Search Algorithm to Predict Stock Prices Piping Prabawati; Auli Damayanti; Herry Suprajitno
Contemporary Mathematics and Applications (ConMathA) Vol. 1 No. 2 (2019)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (654.116 KB) | DOI: 10.20473/conmatha.v1i2.17387

Abstract

This thesis aims to predict the stock prices, using artificial neural network with extreme learning machine (ELM) method and cuckoo search algorithm (CSA). Stock is one type of investment that is in great demand in Indonesia. The portion ownership of stock is determined by how much investment is invested in the company. In this case, stock is an aggressive type of investment instrument, because stock prices can change over time. In this case, ELM is used to determine forecasting values, while CSA is applied to compile and optimize the values of weights and biases to be used in the forecasting process. After obtaining the best weights and biases, the validation test process is then carried out to determine the level of success of the training process. The data used is the daily data of the stock price of PT. Bank Mandiri (Persero) Tbk. the total is 291 data. Furthermore, the data is divided into 70% for the training process is as many as 199 data and 30% for the validation test as many as 87 data. Then compiled pattern of training and validation test patterns is 198 patterns and 82 patterns. Based on the implementation of the program, with several parameter obtained the result of  MSE training is 0.001304353, with an MSE of validation test is 0.0031517704. Because the MSE value obtained is relatively small, this indicates that the ELM-CSA network is able to recognize data patterns and is able to predict well.
Solving Close-Open Mixed Vehicle Routing Problem Using Bat Algorithm Atika Dwi Hanun Amalia; Herry Suprajitno; Asri Bekti Pratiwi
Contemporary Mathematics and Applications (ConMathA) Vol. 2 No. 1 (2020)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (636.526 KB) | DOI: 10.20473/conmatha.v2i1.19301

Abstract

The purpose of this research is to solve the Close-Open Mixed Vehicle Routing Problem (COMVRP) using Bat Algorithm. COMVRP which is a combination of Close Vehicle Routing Problem or commonly known as Vehicle Routing Problem (VRP) with Open Vehicle Routing Problem (OVRP) is a problem to determine vehicles route in order to minimize total distance to serve customers without exceed vehicle capacity. COMVRP occurs when the company already has private vehicles but its capacity could not fulfill all customer demands so the company must rent several vehicles from other companies to complete the distribution process. In this case, the private vehicle returns to the depot after serving the last customer while the rental vehicle does not need to return. Bat algorithm is an algorithm inspired by the process of finding prey from small bats using echolocation. The implementation program to solve was created using Java programming with NetBeans IDE 8.2 software which was implemented using 3 cases, small data with 18 customers, medium data with 75 customers and large data with 100 customers. Based on the implementation results, it can be concluded that the more iterations, the smaller total costs are obtained, while for the pulse rate and the amount of bat tends not to affect the total cost obtained.
ANALISIS PENGARUH ANGKA KEMATIAN BAYI TERHADAP ANGKA HARAPAN HIDUP DI PROVINSI JAWA TIMUR BERDASARKAN ESTIMATOR LEAST SQUARE SPINE Anies Yulinda W; Trias Novia L.; Melati Tegarina; Nur Chamidah
Contemporary Mathematics and Applications (ConMathA) Vol. 1 No. 1 (2019)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (652.916 KB) | DOI: 10.20473/conmatha.v1i1.14775

Abstract

Life expectancy can be used to evaluate the government's performance for improving the welfare of the population in the health sector. Life expectancy is closely related to infant mortality rate. Theoretically, decreasing of infant mortality rate will cause increasing of life expectancy. A statistical method that can be used to model life expectancy is nonparametric regression model based on least square spline estimator. This method provides high flexibility to accommodate pattern of data by using smoothing technique. The best estimated model is order one spline model with one knot based on minimum generalized cross validation (GCV) value of 0.607. Each increasing of one infant mortality rate unit will cause decreasing of life expectancy of  0.2314 for infant mortality rate less than 27, and of  0.0666 for infant mortality rate more than and equals to 27. In addition, based on mean square error (MSE) of 0.492 and R2value of 76.59% for nonparametric model approach compared with MSE of 0.634 and R2 value of 71.8%  for parametric model approach, we conclude that the use of nonparametric model approach based on least square spline estimator is better than that of parametric model approach.
The Dynamics of a Discrete Fractional-Order Logistic Growth Model with Infectious Disease Hasan S Panigoro; Emli Rahmi
Contemporary Mathematics and Applications (ConMathA) Vol. 3 No. 1 (2021)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v3i1.26938

Abstract

In this paper, we study the dynamics of a discrete fractional-order logistic growth model with infectious disease. We obtain the discrete model by applying the piecewise constant arguments to the fractional-order model. This model contains three fixed points namely the origin point, the disease-free point, and the endemic point. We confirm that the origin point is always exists and unstable, the disease-free point is always exists and conditionally stable, and the endemic point is conditionally exists and stable. We also investigate the existence of forward, period-doubling, and Neimark-Sacker bifurcation. The numerical simulations are also presented to confirm the analytical results. We also show numerically the existence of period-3 solution which leads to the occurrence of chaotic behavior.
Analisis dan Strategi Pengendalian Model Matematika Interaksi Sel Kanker Leukemia Mielositik Kronis dan Sel Imunitas Nanda Amalia Rahma; Cicik Alfiniyah; Windarto Windarto
Contemporary Mathematics and Applications (ConMathA) Vol. 2 No. 2 (2020)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v2i2.23853

Abstract

Leukemia is a disease in the classification of cancer in the blood that is characterized by abnormal growth of blood cells in the bone marrow or lymphoid tissue, and generally occurs in leukocytes or white blood cells. White blood cells that look for types of pathogenic diseases that harm the human body and then damage it are the task of the immune system. This thesis analyzes the mathematical model of chronic myelocytic leukemia cancer cell interactions and immune cells to determine the rate of increase in the population of chronic myelocytic leukemia cancer cells to the effect of immune cells. Based on the analysis of the model obtained two equilibrium points namely the equilibrium point of the extinction of chronic myelocytic leukemia cancer cells (E0) and the equilibrium point of the coexistence of chronic myelocytic leukemia cancer cells (E1). The equilibrium point of extinction will be asymptotically stable, whereas the equilibrium point of coexistence tends to be asymptotically stable using phase fields with the help of MATLAB software. Numerical simulation results show that there is an increase in the number of chronic myelocytic leukemia cancer cell populations and a decrease in the number of vulnerable blood cell populations. When immune cells increase in population, chronic myelocytic leukemia in cancer cells decreases in population but is not significant.
Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate Dinda Ariska Putri; Windarto Windarto; Cicik Alfiniyah
Contemporary Mathematics and Applications (ConMathA) Vol. 3 No. 1 (2021)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v3i1.26939

Abstract

Voter participation in general elections is an important aspect of a democratic state structure. Participation is determined by the level of public political awareness, if the level of public political awareness is low, voter participation tends to be passive (Abstinence). A mathematical model approach to voter participation in elections that has been modified to a saturated incidence rate is needed to predict voter participation in future elections. This thesis aims to analyze the stability of the equilibrium point and apply the optimal control variable in the form of an awareness campaign. In the model without control variables, we obtain two equilibriums, namely, the non-endemic equilibrium and the endemic equilibrium. Local stability and the existence of endemic equilibrium depend on the basic reproduction number (R0), where R0=bL/(g+m)m. There is voter participation in elections when R0 < 1 and the absence of voter participation in elections when R0 > 1. We also analyze the sensitivity of parameters to determine which parameters are the most influential in this mathematical model. Furthermore, the application of control variables in the mathematical model of voter participation in elections with saturated incidence rate is determined through the Pontryagin Maximum Principle method. Numerical simulation results show that providing control variables in the form of awareness campaign it is quite effective in minimize the number of the voting population who abstained from election.
Hybrid Crow Search Algorithm - Simulated Annealing untuk Menyelesaikan Vehicle Routing Problem with Time Windows Bella Pristianisa Subari; Asri Bekti Pratiwi; Herry Suprajitno
Contemporary Mathematics and Applications (ConMathA) Vol. 2 No. 2 (2020)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v2i2.23854

Abstract

Penulisan artikel ini bertujuan untuk menyelesaikan permasalahan Vehicle Routing Problem with Time Windows (VRPTW) dengan menggunakan Hybrid Crow Search Algorithm (CSA) dengan Simulated Annealing (SA). Hybrid CSA dengan SA adalah gabungan dari kedua algoritma dengan cara melakukan proses CSA kemudian hasil terburuknya diperbaiki dengan proses SA untuk sepuluh iterasi pertama. Proses algoritma ini dimulai dengan inisialisasi parameter, membangkitkan posisi dan memori awal, menghitung fungsi tujuan, memperbarui posisi gagak, menghitung fungsi tujuan posisi baru gagak, update memori gagak, menentukan solusi terburuk dari posisi gagak kemudian dilakukan modifikasi, hasil modifikasi dengan SA menggantikan solusi terburuk pada posisi gagak, proses berlanjut sampai maksimal iterasi dipenuhi dan menentukan solusi terbaik dari memori gagak. Berdasarkan hasil implementasi pada tiga tipe data dapat disimpulkan  bahwa semakin banyak jumlah iterasi, jumlah gagak, dan proses Simulated Annealing maka nilai fungsi tujuan yang diperoleh cenderung semakin baik, sedangkan nilai probabilitas kewaspadaan (AP) tidak memberikan pengaruh pada solusi permasalahan.
Penerapan Metode Learning Vector Quantization (LVQ) untuk Mendeteksi Penyalahgunaan Narkoba Berny Pebo Tomasouw; Salmon Notje Aulele; Monalisa E. Rijoly
Contemporary Mathematics and Applications (ConMathA) Vol. 3 No. 1 (2021)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v3i1.26940

Abstract

Dalam penelitian ini, metode LVQ akan diterapkan untuk mendeteksi penyalahgunaan narkoba berdasarkan gejala-gejala yang dialami seseorang. Untuk mendapatkan tingkat akurasi terbaik, maka data pelatihan dan data pengujian dibagi ke dalam tiga skema pembagian data yakni 60/40, 70/30 dan 80/20. Setelah dilakukan proses pelatihan dan pengujian menggunakan metode LVQ dengan berbagai variasi nilai laju pembelajaran dan jumlah epoch, maka diperoleh tingkat akurasi terbaik sebesar 86.7 % pada skema pembagian data 70/30 dengan laju pembelajaran  = 0.001 dan  = 0.005.

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