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Item PERAMALAN HARGA GABAH DAN BERAS BULANAN DI INDONESIA DENGAN METODE ARIMA DAN METODE HOLT-WINTERS(Elfitra, 2024-01) Fadliansyah, Hery; Bustami, BustamiThe Autoregressive Integrated Moving Average (ARIMA) method is a method that combines Autoregressive and Moving Average forecasting models with differencing, generally expressed as ARIMA(𝑝, 𝑑, 𝑞). The Holt-Winters method or Triple Exponential Smoothing is a smoothing method based on three smoothing parameters, each element, namely α (level), β (trend smoothing), and γ (seasonal index). The ARIMA and Holt- Winters methods in this research are used for forecasting analysis of monthly prices of grain and rice in Indonesia with data for the period January 2013 to July 2022. The study shows that forecasting using the ARIMA method is better than the Holt-Winters method in this research based on accuracy values smaller RMSEItem PERAMALAN HARGA GABAH DAN BERAS BULANAN DI INDONESIA DENGAN METODE ARIMA DAN METODE HOLT-WINTERS(Elfitra, 2024-01) Fadliansyah, Hery; Bustami, BustamiThe Autoregressive Integrated Moving Average (ARIMA) method is a method that combines Autoregressive and Moving Average forecasting models with differencing, generally expressed as ARIMA(𝑝, 𝑑, 𝑞). The Holt-Winters method or Triple Exponential Smoothing is a smoothing method based on three smoothing parameters, each element, namely α (level), β (trend smoothing), and γ (seasonal index). The ARIMA and Holt- Winters methods in this research are used for forecasting analysis of monthly prices of grain and rice in Indonesia with data for the period January 2013 to July 2022. The study shows that forecasting using the ARIMA method is better than the Holt-Winters method in this research based on accuracy values smaller RMSEItem IURAN NORMAL DANA PENSIUN MENGGUNAKAN METODE AGGREGATE COST DAN PROJECTED UNIT CREDIT BERDASARKAN DISTRIBUSI WEIBULL(Elfitra, 2024-01) Yelni, Fitri SusridaA worker really longs for guaranteed life in old age. A worker is not always in optimal condition. So a worker must have a plan from the start in order to guarantee future prosperity when entering retirement age. One of the solutions is by joining a pension fund program. The aim of this research is to determine the present value of pension benefits, normal contributions using two methods, namely the aggregate cost method and projected unit credit based on the Weibull distrubution. Weibull distribution parameter estimates are determined using the maximum likelihood estimation and then determined using the Newton-Raphson iteration method. The soluting to the problem is obtained by determining the initial lifetime annuity. Initial term life annuity, then the present value of pension benefits. Normal contributions using the Aggregate Cost method basade on the Weibull distribution are smaller than normal contributions using the Projected Unit Credit method basad on the weibull distribution.Item PERAMALAN HARGA GABAH DAN BERAS BULANAN DI INDONESIA DENGAN METODE ARIMA DAN METODE HOLT-WINTERS(Elfitra, 2024-01) Fadliansyah, Hery; Bustam, BustamThe Autoregressive Integrated Moving Average (ARIMA) method is a method that combines Autoregressive and Moving Average forecasting models with differencing, generally expressed as ARIMA(𝑝, 𝑑, 𝑞). The Holt-Winters method or Triple Exponential Smoothing is a smoothing method based on three smoothing parameters, each element, namely α (level), β (trend smoothing), and γ (seasonal index). The ARIMA and Holt- Winters methods in this research are used for forecasting analysis of monthly prices of grain and rice in Indonesia with data for the period January 2013 to July 2022. The study shows that forecasting using the ARIMA method is better than the Holt-Winters method in this research based on accuracy values smaller RMSE.Item IURAN NORMAL DANA PENSIUN MENGGUNAKAN METODE AGGREGATE COST DAN PROJECTED UNIT CREDIT BERDASARKAN DISTRIBUSI WEIBULL(Elfitra, 2024-01) Yelni, Fitri SusridaA worker really longs for guaranteed life in old age. A worker is not always in optimal condition. So a worker must have a plan from the start in order to guarantee future prosperity when entering retirement age. One of the solutions is by joining a pension fund program. The aim of this research is to determine the present value of pension benefits, normal contributions using two methods, namely the aggregate cost method and projected unit credit based on the Weibull distrubution. Weibull distribution parameter estimates are determined using the maximum likelihood estimation and then determined using the Newton-Raphson iteration method. The soluting to the problem is obtained by determining the initial lifetime annuity. Initial term life annuity, then the present value of pension benefits. Normal contributions using the Aggregate Cost method basade on the Weibull distribution are smaller than normal contributions using the Projected Unit Credit method basad on the weibull distribution.Item STABILITAS MODEL PREDATOR-PREY LESLIE-GOWER DENGAN RESPON FUNGSIONAL HOLLING TIPE-I DAN ALLEE EFFECT(Elfitra, 2024-01) Oktarianti, Camelia HanaThis articel discusses the dynamic behavior of the Leslie-Gower predator-prey model which involves the interaction of two populations, namely the predator and prey populations. The model described involves a type-I Holling functional response and a prey population influenced by the Allee. In the observed model, there are six equilibrium points, namely the predator free equilibrium point and the positive equilibrium point. Shown that the model has some stability at each equilibrium points,l. Model simulations are carried out to describe population dynamics with certain parameters.Item ANALISIS DINAMIKA MODEL PREDATOR-PREY DENGAN PEMANENAN PREY NONLINEAR DAN RESPON FUNGSIONAL AKAR KUADRAT(Elfitra, 2024-01) Pangesti, Aulia BinariThis article discusses the interactions among two populations consisting of predator and prey with nonlinear prey harvesting and square root functional response. In the observed model, it is shown that the model has three types of equilibrium points, namely the origin point, predator free equilibrium point, and positive equilibrium point. It is also shown that the model has some stability under certain conditions at each equilibrium points. Simulations on the model are carried out to describe the dynamics and stability of the equilibrium point with certain parameters.Item MENYELESAIKAN PROGRAM PECAHAN LINEAR DENGAN MENGGUNAKAN PROGRAM DINAMIS MAJU(Elfitra, 2023-12) Liandra, Suci OktaviThis final project discusses the solution of fractional linear programming using dynamic programming forward methods. The solution to this problem is to find the optimal solution of the fractional linear programing by changing the fractional objective function to an approximation function using the simplified method, followed by using the simplex method until the optimal solution is obtained. Then, the optimal solution is found using the dynamic programming forward method. It can be concluded that the dynamic programming forward method produces better solution compared to the approximation of objection function methods.Item PENERAPAN DIAGRAM KONTROL DEMERIT PADA PEGENDALIAN KUALITAS PRODUK CACAT ROTTE BAKERY(Elfitra, 2023-12) Dharma, Pandu Satria; BustamiThis study discusses the application of demerit control charts to quality control of Rotte Bakery defective products which consists of three types of bread, namely Fit O Mini, Cokelat Spesial, and Fit O Vanilla. The purpose of this study is to see the quality control of defective products during the production process through visualization in the form of a demerit control chart. The demerit control chart begins by determining the weight for each type of bread, then calculating the demerit value for each subgroup, followed by determining the centerline, upper center line, and lower center line, and ends by visualizing the number of defective products using the demerit control chart. The results showed that the quality of the Fit O Mini, Chocolate Special, and Fit O Vanilla products was still under control. This can be seen in the degree of membership in each subgroup which is still present in the upper and lower limit intervals of the demerit diagram.Item PENERAPAN METODE DEKOMPOSISI UNTUK PERAMALAN HARGA SAHAM PT BANK CENTRAL ASIA TBK(Elfitra, 2023-12) Tampubolon, Omar Farrakhan; BustamiSingular Spectrum Analysis (SSA) is a non-parametric time series analysis technique used for forecasting. The advantage of this method is that it does not require the assumption of stationarity, thus making SSA a good time series data analysis technique to describe trends and other components that have a simple structure. The data used for forecasting using the Riau Province Interest Rate in the period January 2013 to January 2023. The analysis carried out is in the form of a matrix to find the Eigen value and Eigen Vector. The right SSA model in this case is obtained by window length 37 and number of groups 3 with MAPE 4.569288%. The accuracy of this SSA method is considered very good for forecasting such as the Interest Rate data in Riau Province.Item MODEL HYBRID SINGULAR SPECTRUM ANALYSIS DAN NEURAL NETWORK UNTUK PERAMALAN KENAIKAN NILAI INFLASI DI INDONESIA(Elfitra, 2023-12) Dwifattah, Muhammad Rizki; BustamiCurrent economic developments cause increasing inflation rates in a country. One of the statistical methods used to determine the increase in inflation values is forecasting using a non-parametric time series model. This research was carried out using Singular Spectrum Analysis and Neural Network as a non-parametric forecasting method with monthly data on inflation values in Indonesia from January 2003 - December 2022. This analysis was carried out by forming a square matrix from the research data so that eigenvalues and eigenvectors were obtained in each matrix. as many as 50. In the calculations, the forecast results obtained for the next 5 month period show insignificant increases and decreases. Based on the accuracy results, an error was obtained using MAPE with forecasting results for the inflation value of 9%, which can be said to be in the very good category.Item CADANGAN ZILLMER ASURANSI JIWA DWIGUNA MENGGUNAKAN DISTRIBUSI FRECHET(Elfitra, 2023-11) Prahasiwi, Syifa WahyuniLife insurance is a protection effort provided by the insurer against risks to the insured’s life that will arise from an unpredictable event. Insurance companies need to calculate reserves to prepare funds when participants request a claim. Zillmer’s reserves are modified reserves that are calculated using prospective reserves and a zillmer rate of α.This final project aims to determine Zillmer reserve of endowment life insurance for two insurance participants who are x years old by using Frechet distribution. The parameters in the Frechet distribution were estimated using maximum likelihood estimation and then determined by a Newton-Raphson iteration method. The calculation of this Zillmer’s reserve is obtained by using the prospective reserve and Zillmer’s rate. The solution of this problem is obtained by determining the initial life annuity temporary, single premium, and annual premium, then the Zillmer’s reserve formula is obtained based on the distribution of Frechet. Zillmer’s reserves for endowment life insurance using the Frechet distribution is smaller than Zillmer’s reserve for endowment life insurance using the Indonesian Mortality Table 2011Item METODE ITERASI BEBAS TURUNAN DENGAN TEKNIK SPLITTING UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR(Elfitra, 2023-11) Hudiyani, SefiyaThis article discusses a new iterative method that is derivative-free and is obtained by converting a single nonlinear equation to a system consisting of two equations. By using the splitting method, a sufficient conditions will be obtained that must be met for the convergence of this method. The convergence analysis shows that the proposed method has a third order convergence for certain parameters. Numerical comparisons between the proposed method and some other third order methods using several examples shows that the proposed method can be used as an alternative method for solving nonlinear equation.Item PENGEMBANGAN MIXTILINEAR INCIRCLE DAN EXCIRCLE PADA BISEKTOR SUDUT SUATU SEGITIGA(Elfitra, 2023-11) Jefri, SamuelWe discuss a development of mixtilinear incircle and excircle in bisectors of triangle. The development carried out demonstrates the relation that forms between the radii of mixtilinear incircles and excircles that can be constructed on the angle bisectors of 4ABC. In each triangle, three di erent mixtilinear incircles and excircles are formed. The relation between the radii of mixtilinear incircles and excircles on the angle bisectors of 4ABC is such that the ratio of the product of their radii to the angle they form is equal to the ratio of the bisecting lines that form them.Item AKAR KUADRAT DARI MATRIKS KUADRAT ORDE 3(Elfitra, 2023-11) Syahreza, Robby FerikoA new approach is presented in this article with the purpose of calculating the square roots of a quadratic matrix order 3. Determination of the explicit formula for each square roots of quadratic matrix order 3 can be determined by applying the Cayley-Hamilton Theorem to its characteristic polynomial. Some examples are given in the application of the explicit formula to determine the square roots of a quadratic matrix order 3.Item PENYELESAIAN MASALAH INVENTORI MENGGUNAKAN MODEL EOQ MULTI-ITEM DAN SIMULASI MONTE CARLO(Elfitra, 2023-11) Juwita, Rahmi SeptiaThis article discusses the solution of inventory problems using EOQ multi-item model and Monte Carlo simulation to determine problem solving techniques that can be used to managing inventory. EOQ multi-item model gives an optimal solution so that it can be saving the cost of inventory. Monte Carlo simulation is an alternatives technique that are associated with uncertainty or probability which is in the solution used past data and variable random to predict inventory in the future. Therefore, EOQ multi-item model and Monte Carlo simulation are problem solving technique that can be used to managing inventory.Item PENERAPAN TEORI PERMAINAN DALAM MENENTUKAN STRATEGI OPTIMAL MEDIA SOSIAL DENGAN PEMROGRAMAN LINEAR DAN ALGORITMA BROWN(Elfitra, 2023-11) Damayanti, OlifiaThis article discusses the application of game theory on social media competition using linear programming and Brown’s algorithm. This problem aims to determine the optimal strategy for each social media. The social media in this study are Instagram, Tiktok, and Twitter. Alternative strategies are information strategy, communication strategy, promotion strategy, and entertainment strategy. Based on the survey conducted, the survey results can form a matrix payoff. Matrix payoff of m×n size with m, n ≥ 2 can be solved by Brown’s algorithm and domination. The domination is used to reduce the matrix of m × n size becoming smaller, then the matrix can be solved by linear programming using the simplex method. Linear programming and Brown’s algorithm gives the same results, optimal strategy for Instagram are communication strategy and entertainment strategy. The optimal strategies for Tiktok are information strategy, promotion strategy and entertainment strategy. The optimal strategy for Twitter are information strategy and entertainment strategy.Item METODE ITERASI ORDE LIMA MENGGUNAKAN FUNGSI BOBOT DAN BASINS OF ATTRACTION(Elfitra, 2023-11) Oktarina, OktarinaThis article discusses a two-step iterative method for solving nonlinear equations. This method is obtained by modifying Newton’s method using a weight function. Analytically, it is shown that using Taylor expansion and geometric series, this iter- ation method has a convergence order of five and requires four function evaluations for each iteration. This fifth order iteration method has an efficiency index of 1.495. Numerical computations show the new method is comparable to other fifth-order methods discussed. This article also discusses basins of attraction, namely a visual depiction of the dynamic behavior of an iteration method for nonlinear equations from various starting points.Item MANFAAT PENSIUN NORMAL DENGAN METODE ENTRY AGE NORMAL BERDASARKAN DISTRIBUSI RAYLEIGH(Elfitra, 2023-11) Ainun, NurThe welfare of workers at retirement age is an important factor in ensuring ful llment of needs in old age, especially workers who work for a company or a government agency. Workers must have an early plan that can guarantee future welfare when entering retirement age. Given the economic development and technological advances that will trigger an increase in needs, a worker will certainly not always be able to work well especially after reaching a certain age. Workers' productivity will decline and workers will enter retirement age where needs still exist and will continue to exist while after retirement workers no longer get income from their previous jobs. One solution that can be done is to join a pension fund program. This research aims to determine normal retirement bene ts, normal contributions and actuarial liabilities with the normal entry age method based on the Rayleigh distribution. The parameters in the Rayleigh distribution were estimated using maximum likelihood estimation and then Maple 13 software was used to obtain the estimation results.The solution of problem is obtained by determining the probability of death, initial life annuity temporary, bene ts, normal contributions and actuarial liabilities with the normal entry age method and then formula is obtained based on the distribution of Rayleigh. The amount of pension bene ts, normal contributions and actuarial liabilities obtained by using the normal entry age based on the Rayleigh distribution is smaller than the case study conducted at Pt.Taspen Pekanbaru branch.Item OPTIMISASI PRODUKSI MENGGUNAKAN PROGRAM LINEAR MULTI OBJECTIVE FUZZY DENGAN SUMBER DAYA FUZZY DAN KENDALA FUZZY(Elfitra, 2023-11) Putri, Luthfiyah UtamiThis paper discusses the mathematical modeling of linear programming problems production using the fuzzy multi objective linear programming method. This problem aims to optimize production by fulfilling constraints determined to achieve the goal of maximum profit and more efficient use of time. Mathematical models in this problem is designed using the LINGO 19.0 application. Computational results shows that the fuzzy multi objective linear programming method is more efficient used to achieve goals.