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Abstrak :
Tesis ini melakukan pengukuran efisiensi Unit Usaha Syariah Bank Umum Pemerintah Nasional dan Bank Umum Swasta Nasional diperoleh dengan mengestimasi fungsi profit perbankan dan menghitung rasio BOPO. Secara teoritis, dengan mengestimasi fungsi profit, dapat diukur profit maksimum yang seharusnya diperoleh dari hasil input dan output yang digunakan. Dari hasil estimasi fungsi profit tersebut, kemudian dihitung error term dari fungsi tersebut dengan menggunakan metode Stochastic Frontier Analysis (SFA). Kemudian hasil tersebut dapat menggambarkan kondisi Unit Usaha Syariah Bank Umum Pemerintah Nasional dan Bank Umum Swasta Nasional. Hasil penelitian menunjukkan bahwa rata-rata efisiensi Unit Usaha Syariah dari Bank Umum Pemerintah Nasional dan Bank Umum Swasta Nasional yang diukur dari metode SFA maupun BOPO untuk periode 2005 sampai 2007 tidak berbeda secara signifikan.

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This research performs efficiency measurement of Islamic Banking Units (Unit Usaha Syariah) of National Public Commercial Banks and National Private Commercial Banks by estimating banking profit function and Operating Expenses to Operating Income Ratio (BOPO). Theoretically, the maximum profit, which is essentially obtained from the input and output employed, can be measured by estimating the profit function. After getting the result of the profit function estimation, its error terms are calculated by using Stochastic Frontier Analysis (SFA). The outcome will then be able to describe the condition of Islamic Banking Units of National Public Commercial Banks and National Private Commercial Banks. The result of this research shows that the efficiency average of Islamic Banking Units of National Public Commercial Banks and National Private Commercial Banks measured by using SFA method and Operating Expenses to Operating Income Ratio taken from 2005 to 2007 is not significantly different.

Abstrak :
ABSTRAK
Model epidemik SIS (Susceptible Infected Susceptible) diaplikasikan dalam pembuatan model matematis penyebaran penyakit influenza. Model penyebaran penyakit flu dibuat dengan pendekatan stokastik. Model stokastik yang digunakan dalam skripsi ini adalah model Continuous Time Markov Chain (CTMC). Pada model CTMC, dikonstruksi probabilitas transisi, ekspektasi, dan limit distribusi dari banyaknya individu yang terinfeksi penyakit flu dengan asumsi banyaknya individu terinfeksi hanya dapat bertambah satu, berkurang satu atau tetap dalam interval waktu yang sangat pendek (
t 􀀀 0). Ekspektasi dari banyaknya individu yang terinfeksi flu tidak dapat diselesaikan secara langsung, tetapi dapat diketahui bahwa rata- rata pada model stokastik lebih kecil dibandingkan dengan solusi deterministik. Dari kajian tentang limit distribusi, didapatkan bahwa probabilitas tidak ada individu terinfeksi adalah satu saat t 􀀀 ª. Simulasi numerik pada penyebaran penyakit flu diberikan sebagai pendukung untuk interpretasi model

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ABSTRACT
Mathematical model for the spread of influenza using SIS (Susceptible Infected Susceptible) Epidemic Model for constant total human population size is discussed in this undergraduate thesis. These influenza model was made with stochastic approach. Stochastic model that used in this thesis is Continuous Time Markov Chain (CTMC). Transition probability, expectation, and limiting distribution for the number of infected people were constructed in CTMC with assumption that the number of infected people might change by increasing one, decreasing one, or still in the time interval that tends to zero (
t 􀀀 0). The expectation for the number of infected people cannot be solved directly, but we will know that the mean of the stochastic SIS epidemic model is less than the deterministic solution. From limiting distribution analyses, probability that there are no infected people at t 􀀀 ª is one. Some numerical simulation for the spread of influenza is given to give a better interpretation and a better understanding about the model interpretation

Abstrak :
Jumlah produksi minyak dan gas dari suatu lapangan penghasil hidrokarbon dapat dikaji dengan melakukan perhitungan cadangan. Salah satu cara untuk mendapatkan nilai pretorian cadangan hidrokarbon adalah dengan memodelkan reservoar pada lapisan interest dari sebuah lapangan penghasil hidrokarbon. Daerah penelitian lapangan FIAN berada pada Sub-Cekungan Jambi yang secara regional termasuk wilayah Cekungan Sumatera Selatan. Fokus penelitian berada pada lapisan Sand 1 dan Sand 2 yang merupakan zona reservoar pada lapangan FIAN. Model berbasis data seismik dan data sumur yang dalam pengolahannya menghasilkan marker geologi, dan peta struktur sebagai input dalam memodelkan reservoar dengan pendekatan geostatistik stokastik. Pemodelan fasies menggunakan metode SIS (Sequential Indicator Simulation) sedangkan pemodelan properti petrofisika menggunakan metode SGS (Sequential Gaussian Simulation). Pemodelan properti petrofisika terdiri dari pemodelan porositas, saturasi air, dan NTG (net to gross). Dari analisis fasies seismik menunjukkan bahwa lapangan FIAN berada pada lingkungan pengendapan marine atau delta yang sifatnya tenang. Lapisan Sand 1 dan Sand 2 memiliki karakteristik reservoar yang baik karena memiliki nilai properti petrofisika optimal yaitu porositas 20-30%, saturasi air 50-70%, dan NTG 70-90%. Berbasis peta isopach lapisan Sand 1 dan Sand 2 memiliki ketebalan rata-rata berturut-turut 49,34 meter dan 26,30 meter. Proses perhitungan cadangan minyak dapat dilakukan dengan memodelkan STOIIP (Stock Tank Oil Initially in Place) yang pada lapisan Sand 1 dan Sand 2 memiliki nilai 64 x 106 m3. Terdapat respons hidrokarbon yang baik pada lapisan tersebut di sebelah baratdaya lapangan FIAN. ......The amount of oil and gas production from a hydrocarbon producing field can be assessed by making a reserve calculation. One of many ways to obtain an estimated value of hydrocarbon reserves is modeling the reservoir in the interest layer of a hydrocarbon producing field. The FIAN field research area is in the Jambi Sub-Basin which is regionally included in the South Sumatra Basin. The research focus is on the Sand 1 and Sand 2 layers which are reservoir zones in the FIAN field. The model based on seismic data and well data which in processing produces geological marker, and structure maps as input in modeling the reservoir with stochastic geostatistical approach. Facies modeling is using the SIS (Sequential Indicator Simulation) method while petrophysical property modeling is using the SGS (Sequential Gaussian Simulation) method. Petropyhsical property modeling consists of porosity, water saturation, and NTG (net to gross). From the analysis of seismic facies shows that the FIAN field is in a marine or delta deposition environment with tranquil condition. Sand 1 and Sand 2 layers have good reservoir characteristics because it has optimal petrophysical values i.e. 20-30% porosity, 50-70% water saturation, and 70-90% NTG. Based on isopach maps, Sand 1 and Sand 2 layers has an average thicknesses of 49,34 meters and 26,30 meters consecutively. The process of calculating oil reserves can be done by modeling STOIIP (Stock Tank Oil Initially in Place) which at the Sand 1 and Sand 2 layers has a value of 64 x 106 m3. There is a potential hydrocarbon response in that layers at southwest of the FIAN field.

Abstrak :
Perhitungan anuitas kontingensi merupakan salah satu komponen penting yang digunakan dalam perhitungan premi di dunia asuransi. Dalam menghitung anuitas, tingkat bunga seringkali diasumsikan konstan. Sedangkan, pada kenyataannya, tingkat bunga cenderung berubah-ubah dalam waktu yang tidak menentu dalam kontrak asuransi jiwa yang umumnya memiliki periode cukup panjang. Oleh karena itu, diperlukan model tingkat bunga stokastik yang dapat menjelaskan randomness atau perilaku keacakan dari perubahan tingkat bunga. Hal ini bertujuan agar perhitungan anuitas kontingensi dapat digambarkan dengan lebih realistis yaitu sesuai dengan perilaku tingkat bunga dalam kehidupan nyata yang fluktuatif. Pada penelitian ini, akan dibangun kelas model tingkat bunga stokastik baru dengan memodelkan force of interest berdasarkan proses compound Poisson secara langsung. Proses compound Poisson yang digunakan dapat menjelaskan random jumps yang terjadi pada tingkat bunga stokastik. Pada penelitian ini ditelaah pembentukan force of interest berdasarkan proses compound Poisson, menelaah bentuk perumusan nilai sekarang, menganalisis fungsi akumulasi force of interest tingkat bunga stokastik, dan menelaah bentuk perumusan Actuarial Present Value (APV) dari anuitas kontingensi yang bersifat diskrit maupun kontinu. Seletah itu, dilakukan ilustrasi perhitungan anuitas kontingensi berdasarkan model tingkat bunga stokastik yang telah dibentuk. ......The calculation of contingency annuities is one of the important components used in calculating premiums in the insurance world. In calculating annuities, the interest rate is often assumed to be constant. Meanwhile, in reality, interest rates tend to fluctuate in an uncertain time in life insurance contracts which generally have a fairly long period. Therefore, we need a stochastic interest rate model that can explain the randomness or random behavior of interest rate changes. It is intended that the calculation of the contingency annuity can be described more realistically, namely in accordance with the fluctuating behavior of interest rates in real life. In this research, a new stochastic interest rate model class be built by modeling the force of interest based on the direct compound Poisson process. The compound Poisson process used can explain the random jumps that occur at the stochastic interest rate. This research examines the formation of force of interest based on the compound Poisson process, examines the form of the present value formulation, analyzes the function of the accumulation of force of interest stochastic interest rates, and examines the form of the formulation of Actuarial Present Value (APV) of discrete or continuous contingency annuities. After that, an illustration of the contingency annuity calculation is carried out based on the stochastic interest rate model that has been formed.

Abstrak :
While there are several texts on how to solve and analyze stochastic programs, this is the first text to address basic questions about how to model uncertainty, and how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering disciplines where the instructor wants to explain where models come from and what the fundamental issues are.

Abstrak :
Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects.

Abstrak :
Penelitian tentang model persediaan telah banyak dilakukan dan menjadi solusi bagi perusahaan dalam menghadapi ketidakpastiaan dari permintaan pelanggan. Selain data permintaan yang bersifat stokastik, sering pula ditemukan leadtime kedatangan bahan baku di suatu perusahaan yang bersifat stokastik. Sering kali leadtime yang bersifat stokastik dihitung menjadi leadtime yang tetap untuk menyederhanakan perhitungan dan perancangan model persediaan. Hal ini dapat memicu terjadinya stockout pada kenyataan di lapangan, karena tidak memperhitungkan kejadian leadtime kedatangan bahan baku yang berubah atau tidak tetap seperti yang ditentukan. Sehingga penelitian ini dibuat untuk menganalisis bagaimana pengaruh leadtime yang bersifat stokastik pada performa sistem persediaan di suatu perusahaan manufaktur perusahaan di Indonesia. Penelitian ini menggunakan simulasi Monte Carlo untuk melakukan RNG data berjumlah 5000 periode. Simulasi Monte Carlo dipilih karena data permintaan kebutuhan bahan baku komponen pehiasan tidak mengikuti distribusi normal. Dalam penelitian ini juga akan memakai model persediaan (R,Q) untuk membandingkan total biaya yang dikeluarkan ketika menggunakan model persediaan dengan leadtime stokastik atau menggunakan model persediaan dengan leadtime tetap. ......Research on the inventory model has been done a lot and is a solution for companies in dealing with uncertainty of customer demand. In addition to stochastic demand data, it is often found the lead time for the arrival of raw materials in a company that is stochastic. Often a stochastic leadtime is calculated to be a fixed leadtime to simplify the calculation and design of the inventory model. This can trigger a stockout in reality, because it does not calculate the occurrence of the lead time for the arrival of raw materials that changes or does not remain as determined. So this research was made to analyze how the effect of stochastic leadtime on the performance of the inventory system in a manufacturing company in Indonesia. This study uses a Monte Carlo simulation to perform RNG data totaling 5000 periods. The Monte Carlo simulation was chosen because the data on the demand for the raw material requirements of the decking components did not follow a normal distribution. In this study, we will also use the inventory model (R, Q) to compare the total costs incurred when using an inventory model with stochastic leadtime or using an inventory model with a fixed leadtime.

Abstrak :
The book provides a sound mathematical base for life insurance mathematics and applies the underlying concepts to concrete examples. Moreover the models presented make it possible to model life insurance policies by means of Markov chains. Two chapters covering ALM and abstract valuation concepts on the background of Solvency II complete this volume. Numerous examples and a parallel treatment of discrete and continuous approaches help the reader to implement the theory directly in practice.

Abstrak :
This study addresses the hub network design problem considering demand uncertainty and hub congestion effects. The problem is formulated as a two-stage stochastic program with recourse model. The model provides a consistent set of hub locations, while adjusting network configuration in response to different demand realizations. A case study collected from real-world data was used to test the proposed model, and a sensitivity analysis was performed to know how several important parameters affected the solution