MAD Dispersion Measure Makes Extremal Queue Analysis Simple

A notorious problem in queueing theory is to compute the worst possible performance of the GI/G/1 queue under mean-dispersion constraints for the interarrival- and service-time distributions. We address this extremal queue problem by measuring dispersion in terms of mean absolute deviation (MAD) instead of the more conventional variance, making available methods for distribution-free analysis. Combined with random walk theory, we obtain explicit expressions for the extremal interarrival- and service-time distributions and, hence, the best possible upper bounds for all moments of the waiting time. We also obtain tight lower bounds that, together with the upper bounds, provide robust performance intervals. We show that all bounds are computationally tractable and remain sharp also when the mean and MAD are not known precisely but are estimated based on available data instead. Summary of Contribution: Queueing theory is a classic OR topic with a central role for the GI/G/1 queue. Although this queueing system is conceptually simple, it is notoriously hard to determine the worst-case expected waiting time when only knowing the first two moments of the interarrival- and service-time distributions. In this setting, the exact form of the extremal distribution can only be determined numerically as the solution to a nonconvex nonlinear optimization problem. Our paper demonstrates that using mean absolute deviation (MAD) instead of variance alleviates the computational intractability of the extremal GI/G/1 queue problem, enabling us to state the worst-case distributions explicitly.

KOMPARASI METODE MOVING AVERAGE DAN TREND PROJECTION SEBAGAI ALAT UKUR PERENCANAAN PRODUKSI PADA UD. JAYA ABADI KABUPATEN PROBOLINGGO

The purpose of this research is to find out the comparison of forecasting calculations using the moving average and trend projection methods as a means measuring tool in production planning at UD. Jaya Abadi Probolinggo Regency. The type of research used is quantitative descriptive. Population and sample in this research is UD production data. Jaya Abadi Probolinggo Regerency from 2018 to March 2021. Data analysis using the moving average and trend projection methods which aim to predict future production or the next period. The results showed that the value of MAD (Mean Absolute Deviation) and the MSE (Mean Square Error) moving average values are higher than the MAD and the MSE trend projection, so the company you should use trend projection because when viewed from the results of the comparision of MAD and MSE, this method has a smaller error rate than the moving average method. So it can be concluded that the trend projection method can be used in planning bread production at UD. Jaya Abadi Probolinggo Regency

Peramalan Permintaan Menggunakan Time Series Forecasting Model Untuk Merancang Resources Yang Dibutuhkan IKM Percetakan

CV Adi Jaya merupakan perusahaan manufaktur yang bergerak dalam industri percetakan. Dalam memastikan kapasitas produksi yang ada dapat memenuhi permintaan konsumen diperlukan metode peramalan yang akurat. Tujuan penelitian ini adalah untuk menentukan metode peramalan terbaik dan meramalkan permintaan konsumen pada tahun 2021. Penelitian ini adalah penelitian deskriptif dengan metode yang digunakan untuk menyelesaikan permasalahan tersebut adalah metode time series dan teknik analisis menggunakan Microsoft Excel. Tingkat error yang dihasilkan dari perhitungan metode peramalan diketahui dengan penghitungan kesalahan mean absolute deviation (MAD), kemudian didapatkan tracking signal. Berdasarkan hasil analisis data, diketahui metode peramalan time series terbaik untuk meramalkan penjualan produk kemasan berbahan plastik adalah metode centered moving average 3 periode. Metode ini dipilih karena memiliki tingkat error paling rendah jika dibandingkan dengan metode lain yang dianalisis, yaitu dengan nilai MAD 65.773,08333 dan nilai tracking signal yang berada dalam batas pengendalian. Sehingga metode CMA 3 periode dapat digunakan dalam peramalan. Dari metode CMA 3 periode didapatkan peramalan permintaan konsumen di bulan Januari sampai Mei 2021 sebanyak 883.780 pcs setiap bulannya. Sehingga diperkirakan perlu adanya overtime yang tidak terlalu banyak untuk memenuhi peramalan permintaan pada bulan Januari-Mei 2021 karena kapasitas perusahaan perbulan hanya 875.000 pcs.

Numerical Analysis of Electrohydrodynamic Flow in a Circular Cylindrical Conduit by Using Neuro Evolutionary Technique

This paper analyzes the mathematical model of electrohydrodynamic (EHD) fluid flow in a circular cylindrical conduit with an ion drag configuration. The phenomenon was modelled as a nonlinear differential equation. Furthermore, an application of artificial neural networks (ANNs) with a generalized normal distribution optimization algorithm (GNDO) and sequential quadratic programming (SQP) were utilized to suggest approximate solutions for the velocity, displacements, and acceleration profiles of the fluid by varying the Hartmann electric number (Ha2) and the strength of nonlinearity (α). ANNs were used to model the fitness function for the governing equation in terms of mean square error (MSE), which was further optimized initially by GNDO to exploit the global search. Then SQP was implemented to complement its local convergence. Numerical solutions obtained by the design scheme were compared with RK-4, the least square method (LSM), and the orthonormal Bernstein collocation method (OBCM). Stability, convergence, and robustness of the proposed algorithm were endorsed by the statistics and analysis on results of absolute errors, mean absolute deviation (MAD), Theil’s inequality coefficient (TIC), and error in Nash Sutcliffe efficiency (ENSE).

IMPLEENTASI MODEL HYBRID DALAM MEMPREDIKSI PENYEBARAN COVID-19 DI WILAYAH JAWA BARAT

Di awal tahun 2020, dunia dikagetkan dengan kejadian infeksi berat dengan penyebab yang belum diketahui, yang berawal dari laporan dari Cina kepada World Health Organization (WHO) terdapatnya 44 pasien pneumonia yang berat di suatu wilayah yaitu Kota Wuhan, Provinsi Hubei, China, tepatnya di akhir tahun 2019. Pada perkembangannya, wabah ini kemudian diidentifikasi sebagai wabah Virus Covid-19. Penambahan jumlah kasus COVID-19 berlangsung sangat cepat, sampai dengan 16 Februari 2020, secara global dilaporkan 51.857 kasus terkonfirmasi di 25 negara dengan 1.669 kematian (CFR 3,2%). Di Indonesia ada lebih dari 2 ribu kasus ditemukan dan hampir 200 orang telah meninggal. Di wilayah Jawa barat, kasus positif Covid-19 juga terus bertambah. Data penyebaran virus Corona Covid-19 di Jawa Barat mengalami perubahan, Rabu (1/4/2020). Terpantau melalui situs resmi Pusat Informasi dan Koordinasi Covid-19 Provinsi Jawa Barat (Pikobar), jumlah orang terpapar positif Corona mencapai 198 orang. Data yang diakses dari pikobar.jabarprov.go.id tersebut juga merilis sudah ada 11 pasien yang dinyatakan sembuh dan diperbolehkan pulang dari rumah sakit. Sementara jumlah pasien yang meninggal dunia berjumlah 21 orang. Sedangkan untuk pasien dalam pengawasan (PDP), jumlah yang telah diproses dalam pengawasan mencapai 727 orang. Sedangkan yang telah selesai menjalani pengawasan mencapai 242 orang. Total PDP di Jabar berjumlah 969 orang. Berbekal dari data Pusat Informasi dan Koordinasi Covid-19 Jawa Barat, penulis tertarik melakukan penelitian untuk memprediksi penyebaran kasus positif Covid-19 di Jawa Barat. Dalam penelitian ini, model yang digunakan adalah Hybrid. Data set yang digunakan adalah data pasien positif Covid-19 mulai bulan April 2020 sampai dengan bulan Februari 2021. Berdasarkan hasil penelitian yang sudah dilakukan, model Hybrid mampu memprediksi jumlah penyebaran kasus Covid-19 di Jawa Barat. Hal ini dibuktikan dengan hasil training teknik Hybrid memiliki error rate sebesar 0,4615, yang dilanjutkan dengan analisa akurasi prediksi selama tiga bulan, yaitu bulan Desember 2020, Januari, dan Febrauri 2021. Dari hasil prediksi, model Hybrid memiliki nilai rata – rata Mean Absolute Deviation (MAD) sebesar 351. Sedangkan berdasarkan analisa prediksi dengan teknik Mean Absolute Percentage Error (MAPE) memiliki rata rata tingkat kesalahan sebesar 0,2061 atau 20,6%.

Estimation of Parameters of Pert Distribution by Using Method of Moments

The method of moments has been widely used for estimating the parameters of a distribution. Usually lower order moments are wont to find the parameter estimates as they're known to possess less sampling variability. The method of moments may be a technique for estimating the parameters of a statistical model. It works by finding values of the parameters that end in a match between the sample moments and therefore the population moments (as implied by the model). the Method of moment Estimator is used to find out Estimates the parameters of PERT Distribution. We also compare equispaced and unequispaced Optimally Constructed Grouped data by the method of an Asymptotically Relative Efficiency. We also computed Average Estimate (AE), Variance (VAR), Standard Deviation (STD), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Simulated Error (SE) and Relative Absolute Bias (RAB) for both the parameters under grouped sample supported 1000 simulations to assess the performance of the estimators. Keywords: Method of Moments, PERT Distribution, equispaced and unequipped Optimal Grouped sample

Portfolio Optimization with a Mean–Absolute Deviation–Entropy Multi-Objective Model

Investors wish to obtain the best trade-off between the return and risk. In portfolio optimization, the mean-absolute deviation model has been used to achieve the target rate of return and minimize the risk. However, the maximization of entropy is not considered in the mean-absolute deviation model according to past studies. In fact, higher entropy values give higher portfolio diversifications, which can reduce portfolio risk. Therefore, this paper aims to propose a multi-objective optimization model, namely a mean-absolute deviation-entropy model for portfolio optimization by incorporating the maximization of entropy. In addition, the proposed model incorporates the optimal value of each objective function using a goal-programming approach. The objective functions of the proposed model are to maximize the mean return, minimize the absolute deviation and maximize the entropy of the portfolio. The proposed model is illustrated using returns of stocks of the Dow Jones Industrial Average that are listed in the New York Stock Exchange. This study will be of significant impact to investors because the results show that the proposed model outperforms the mean-absolute deviation model and the naive diversification strategy by giving higher a performance ratio. Furthermore, the proposed model generates higher portfolio mean returns than the MAD model and the naive diversification strategy. Investors will be able to generate a well-diversified portfolio in order to minimize unsystematic risk with the proposed model.

An elliptical blade is not a true ellipse, but a superellipse–Evidence from two Michelia species

The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., (x/a)2 + (y/b)2 = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., |x/a|n +|y/b|n = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala, and M. maudiae), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of < 0.05 for the nonlinear fitting of SE to leaf geometry, i.e., the mean absolute deviation from the polar point to leaf marginal points was smaller than 5% of the radius of a hypothesized circle with its area equaling leaf area. The estimates of n for the two species were ˂ 2, indicating that all sampled leaves conformed to SE and not to EE. This study confirms the existence of SE in leaves, linking this to its potential functional advantages, particularly the possible influence of leaf shape on hydraulic conductance.

Prediksi Tingkat Produksi Buah Kelapa Sawit dengan Metode Single Moving Average

Palm oil is one of the largest agricultural products in Indonesia and has a high economic value and can improve the welfare of oil palm farmers. The amount of oil palm fruit production is not always stable or increasing, but increases up and down which is influenced by many factors. This study aims to estimate the average amount of oil palm fruit production every year and prepare anticipatory steps in the event of a decrease in oil palm fruit production. The image processed in this study was the production of palm fruit in a few years which was generated from the results of oil palm plantations. Furthermore, data is processed using the Single Moving Avarage method. This method is a method of forecasting or predictions using a number of actual data to generate predictive values ​​in the future. The results of testing on the single moving average method can be seen forecasts of oil palm fruit production in 2021 using Moving Averge 3 of 200.749 tons with Mean Absolute Deviation 19.604, Mean Squared Error 456.963.281 and Mean Absolute Percent Error 10,0%. Moving Averge 4 was 206.771 tons with the Mean Absolute Deviation 27.333, Mean Squared Error 752.202.579 and Mean Absolute Percent Error 14,2%. Moving Averge 5 was 210.908 tons with Mean Absolute Deviation 26.890, Mean Squared Error 723.072.100 and Mean Absolute Percent Error 14.1%. The test results using the Single Moving Average method can be concluded that forecasting using Moving Average 3 can be used because the relative error level is smaller than Moving Average 4 and 5, with the value of the Mean Absolute Percent error of 10.0% and Mean Absolute Deviation 19.604.

Kajian Adaptive Neuro-Fuzzy Inference System (ANFIS) Dalam Memprediksi Penerimaan Mahasiswa Baru Pada Universitas Buana Perjuangan Karawang

- The process of admitting new students is an annual routine activity that occurs in a university. This activity is the starting point of the process of searching for prospective new students who meet the criteria expected by the college. One of the colleges that holds new student admissions every year is Buana Perjuangan University, Karawang. There have been several studies that have been conducted on predictions of new students by other researchers, but the results have not been very satisfying, especially problems with the level of accuracy and error. Research on ANFIS studies to predict new students as a solution to the problem of accuracy. This study uses two ANFIS models, namely Backpropagation and Hybrid techniques. The application of the Adaptive Neuro-Fuzzy Inference System (ANFIS) model in the predictions of new students at Buana Perjuangan University, Karawang was successful. Based on the results of training, the Backpropagation technique has an error rate of 0.0394 and the Hybrid technique has an error rate of 0.0662. Based on the predictive accuracy value that has been done, the Backpropagation technique has an accuracy of 4.8 for the value of Mean Absolute Deviation (MAD) and 0.156364623 for the value of Mean Absolute Percentage Error (MAPE). Meanwhile, based on the Mean Absolute Deviation (MAD) value, the Backpropagation technique has a value of 0.5 and 0.09516671 for the Mean Absolute Percentage Error (MAPE) value. So it can be concluded that the Hybrid technique has a better level of accuracy than the Backpropation technique in predicting the number of new students at the University of Buana Perjuangan Karawang. Keywords: ANFIS, Backpropagation, Hybrid, Prediction