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In this paper, we develop an integrated inventory model considering the imperfect quality items, inspection error, controllable lead time, and budget capacity constraint. The imperfect items were uniformly distributed and detected on the... more
In this paper, we develop an integrated inventory model considering the imperfect quality items, inspection error, controllable lead time, and budget capacity constraint. The imperfect items were uniformly distributed and detected on the screening process. However there are two types of possibilities. The first is type I of inspection error (when a non-defective item classified as defective) and the second is type II of inspection error (when a defective item classified as non-defective). The demand during the lead time is unknown, and it follows the normal distribution. The lead time can be controlled by adding the crashing cost. Furthermore, the existence of the budget capacity constraint is caused by the limited purchasing cost. The purposes of this research are: to modify the integrated vendor and buyer inventory model, to establish the optimal solution using Kuhn-Tucker's conditions, and to apply the models. Based on the result of application and the sensitivity analysis, it can be obtained minimum integrated inventory total cost rather than separated inventory.
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Research Interests:
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In this paper, we develop an integrated inventory model considering the imperfect quality items, inspection error, controllable lead time, and budget capacity constraint. The imperfect items were uniformly distributed and detected on the... more
In this paper, we develop an integrated inventory model considering the imperfect quality items, inspection error, controllable lead time, and budget capacity constraint. The imperfect items were uniformly distributed and detected on the screening process. However there are two types of possibilities. The first is type I of inspection error (when a non-defective item classified as defective) and the second is type II of inspection error (when a defective item classified as non-defective). The demand during the lead time is unknown, and it follows the normal distribution. The lead time can be controlled by adding the crashing cost. Furthermore, the existence of the budget capacity constraint is caused by the limited purchasing cost. The purposes of this research are: to modify the integrated vendor and buyer inventory model, to establish the optimal solution using Kuhn-Tucker's conditions, and to apply the models. Based on the result of application and the sensitivity analysis, it can be obtained minimum integrated inventory total cost rather than separated inventory.
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ISSN: 2502-6526 MODEL GENERALIZEDSPACE TIME AUTOREGRESSIVE INTEGRATED DENGAN EROR AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTIC (GSTARI-ARCH) Restuning Gustiasih, Dewi Retno Sari Saputro Program Studi Matematika Universitas Sebelas Maret... more
ISSN: 2502-6526 MODEL GENERALIZEDSPACE TIME AUTOREGRESSIVE INTEGRATED DENGAN EROR AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTIC (GSTARI-ARCH) Restuning Gustiasih, Dewi Retno Sari Saputro Program Studi Matematika Universitas Sebelas Maret Surakarta restuninggustiasih@gmail.com, dewiretnoss@staff.uns.ac.id
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Eigen problems and eigenmode are important components related to square matrices. In max-plus algebra, a square matrix can be represented in the form of a graph called a communication graph. The communication graph can be strongly... more
Eigen problems and eigenmode are important components related to square matrices. In max-plus algebra, a square matrix can be represented in the form of a graph called a communication graph. The communication graph can be strongly connected graph and a not strongly connected graph. The representation matrix of a strongly connected graph is called an irreducible matrix, while the representation matrix of a graph that is not strongly connected is called a reduced matrix. The purpose of this research is set the steps to determine the eigenvalues and eigenvectors of the irreducible matrix over min-plus algebra and also eigenmode of the regular reduced matrix over min-plus algebra. Min-plus algebra has an ispmorphic structure with max-plus algebra. Therefore, eigen problems and eigenmode matrices over min-plus algebra can be determined based on the theory of eigenvalues, eigenvectors and eigenmode matrices over max-plus algebra. The results of this research obtained steps to determine th...
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Proses stokastik merupakan salah satu bidang kajian dalam matematika yang dapat digunakan untuk memprediksi atau menjelaskan fenomena-fenomena dalam kehidupan sehari-hari. Proses titik merupakan bagian dari proses stokastik dan merupakan... more
Proses stokastik merupakan salah satu bidang kajian dalam matematika yang dapat digunakan untuk memprediksi atau menjelaskan fenomena-fenomena dalam kehidupan sehari-hari. Proses titik merupakan bagian dari proses stokastik dan merupakan subjek utama dalam statistik seismologi. Pada kejadian gempa bumi, sebuah gempa besar biasanya diikuti gempa lainnya atau gempa susulan. Model epidemic type aftershock sequence (ETAS) merupakan model pada proses titik yang mempertimbangkan keterkaitan gempa satu dengan yang lainnya. Model ETAS dinyatakan dengan fungsi intensitas bersyarat yang berguna untuk mengetahui peluang kemunculan terjadinya gempa bumi. Tujuan penelitian ini adalah membahas model ETAS dan menerapkannya pada data gempa bumi di Sumatra. Hasil dari penelitian ini yaitu model ETAS terbentuk dari fungsi intensitas bersyarat yang memiliki 5 parameter dan mempertimbangkan variabel waktu serta magnitudo. Dengan metode estimasi likelihood maksimum diperoleh estimasi parameter model ...
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Geography and Seismology
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The annihilator graph of a semiring S, denoted by AG(S), is the graph whose vertex set is the set of all nonzero zero-divisors of S. In commutative semiring S, two distinct vertices are adjacent if and only if ann(xy) ≠ ann(x) ∪ ann(y),... more
The annihilator graph of a semiring S, denoted by AG(S), is the graph whose vertex set is the set of all nonzero zero-divisors of S. In commutative semiring S, two distinct vertices are adjacent if and only if ann(xy) ≠ ann(x) ∪ ann(y), where ann(x) = {s ∈ S|sx = 0}. Similarly in noncommutative semiring S, two distinct vertices are connected by an edge if and only if either l. ann(xy) ≠ l. ann(x) ∪ l. ann(y), l. ann(yx) ≠ l. ann(x) ∪ l. ann(y), r. ann(xy) ≠ r. ann(x) ∪ r. ann(y), or r. ann(yx) ≠ r. ann(x) ∪ r. ann(y) where l. ann(x) = {s ∈ S|sx = 0} and r. ann(x) = {s ∈ S|xs = 0}. In this paper we study the properties of the right annihilator and the left annihilator of semiring of matrices over Boolean semiring Mn (ℬ) and then use these results to determine the diameter of the graph AG(Mn (ℬ)).
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Mixture autoregressive (MAR) Model is a mixture of Gaussian autoregressive (AR) components. The mixture model is capable for modelling of nonlinear time series with multimodal conditional distributions. This paper discusses about the... more
Mixture autoregressive (MAR) Model is a mixture of Gaussian autoregressive (AR) components. The mixture model is capable for modelling of nonlinear time series with multimodal conditional distributions. This paper discusses about the parameters estimation using EM algorithm. All possible models are then applied to national maize production data. In this case, the BIC is used for the MAR model selection.
Hybrid model discussed in this paper combining ARIMA and backpropagation is applied to grain price forecasting in Indonesia for period January 2008 until April 2013. The grain price time series consists of linear and nonlinear patterns.... more
Hybrid model discussed in this paper combining ARIMA and backpropagation is applied to grain price forecasting in Indonesia for period January 2008 until April 2013. The grain price time series consists of linear and nonlinear patterns. Backpropagations can recognize non linear patterns that can not be done by ARIMA. In order to find the best model, some combinations of prepocessing transformations, the number of input and hidden units, and the activation function were applied in the contruction of the network structure. Based on the experiments, it can be showed that ARIMA backpropagation hybrid model provides more accurate results than ARIMA model. The hybrid model would rather be used in the short-term forecasting, no more than three periods.
Eigen problems and eigenmode are important components related to square matrices. In max-plus algebra, a square matrix can be represented in the form of a graph called a communication graph. The communication graph can be strongly... more
Eigen problems and eigenmode are important components related to square matrices. In max-plus algebra, a square matrix can be represented in the form of a graph called a communication graph. The communication graph can be strongly connected graph and a not strongly connected graph. The representation matrix of a strongly connected graph is called an irreducible matrix, while the representation matrix of a graph that is not strongly connected is called a reduced matrix. The purpose of this research is set the steps to determine the eigenvalues and eigenvectors of the irreducible matrix over min-plus algebra and also eigenmode of the regular reduced matrix over min-plus algebra. Min-plus algebra has an ispmorphic structure with max-plus algebra. Therefore, eigen problems and eigenmode matrices over min-plus algebra can be determined based on the theory of eigenvalues, eigenvectors and eigenmode matrices over max-plus algebra. The results of this research obtained steps to determine th...