Search results for: stochastic volatility model

Authors: Taha Benarbia, Kay W. Axhausen, Anugrah Ilahi

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Electric car sharing system as ecologic transportation increasing in the world. The complexity of managing electric car sharing systems, especially one-way trips and battery autonomy have direct influence to on supply and demand of system. One must be able to precisely model the demand and supply of these systems to better operate electric car sharing and estimate its effect on mobility management and the accessibility that it provides in urban areas. In this context, our work focus to develop performances optimization model of the system based on discrete event simulation and stochastic Petri net. The objective is to search optimal decisions and management parameters of the system in order to fulfil at best demand while minimizing undesirable situations. In this paper, we present new model of electric cars sharing with relocation based on monitoring system. The proposed approach also help to precise the influence of battery charging level on the behaviour of system as important decision parameter of this complex and dynamical system.

Keywords: electric car-sharing systems, smart mobility, Petri nets modelling, discrete event simulation

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Authors: Syaza Isma, Timothy Higgins

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In Malaysia, increased take-up rates of tertiary student borrowing, and reliance on retirement savings to fund children's education show the importance of public higher education financing schemes (PTPTN). PTPTN has been operating for 2 decades now; however, there are some critical issues and challenges that include low loan recovery and loan default that suggest a detailed consideration of student loan/financing scheme alternatives is crucial. In addition, the decline in funding level per student following introduction of the new PTPTN full and partial loan scheme has raised ongoing concerns over the sustainability of the scheme to provide continuous financial assistance to students in tertiary education. This research seeks to assess these issues that put greater efficiency in an effort to ensure equitable access to student funding for current and future generations. We explore the extent of repayment hardship under the current loan arrangements that presumably led to low recovery from the borrowers, particularly low-income graduates. The concept of manageable debt exists in the design of income-contingent repayment schemes, as practiced in Australia, New Zealand, UK, Hungary, USA (in limited form), the Netherlands, and South Korea. Can Income Contingent Loans (ICL) offer the best practice for an education financing scheme, and address the issue of repayment hardship and concurrently, can a properly designed ICL scheme provide a solution to the current issues and challenges facing Malaysia student financing? We examine the different potential ICL models using deterministic and stochastic approach to simulate income of graduates.

Keywords: deterministic, income contingent loan, repayment burden, simulation, stochastic

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Authors: André Python

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To this day, terrorism persists as a worldwide threat, exemplified by the recent deadly attacks in January 2015 in Paris and the ongoing massacres perpetrated by ISIS in Iraq and Syria. In response to this threat, states deploy various counterterrorism measures, the cost of which could be reduced through effective preventive measures. In order to increase the efficiency of preventive measures, policy-makers may benefit from accurate predictive models that are able to capture the complex spatial dynamics of terrorism occurring at a local scale. Despite empirical research carried out at country-level that has confirmed theories explaining the diffusion processes of terrorism across space and time, scholars have failed to assess diffusion’s theories on a local scale. Moreover, since scholars have not made the most of recent statistical modelling approaches, they have been unable to build up predictive models accurate in both space and time. In an effort to address these shortcomings, this research suggests a novel approach to systematically assess the theories of terrorism’s diffusion on a local scale and provide a predictive model of the local spatial dynamics of terrorism worldwide. With a focus on the lethal terrorist events that occurred after 9/11, this paper addresses the following question: why and how does lethal terrorism diffuse in space and time? Based on geolocalised data on worldwide terrorist attacks and covariates gathered from 2002 to 2013, a binomial spatio-temporal point process is used to model the probability of terrorist attacks on a sphere (the world), the surface of which is discretised in the form of Delaunay triangles and refined in areas of specific interest. Within a Bayesian framework, the model is fitted through an integrated nested Laplace approximation - a recent fitting approach that computes fast and accurate estimates of posterior marginals. Hence, for each location in the world, the model provides a probability of encountering a lethal terrorist attack and measures of volatility, which inform on the model’s predictability. Diffusion processes are visualised through interactive maps that highlight space-time variations in the probability and volatility of encountering a lethal attack from 2002 to 2013. Based on the previous twelve years of observation, the location and lethality of terrorist events in 2014 are statistically accurately predicted. Throughout the global scope of this research, local diffusion processes such as escalation and relocation are systematically examined: the former process describes an expansion from high concentration areas of lethal terrorist events (hotspots) to neighbouring areas, while the latter is characterised by changes in the location of hotspots. By controlling for the effect of geographical, economical and demographic variables, the results of the model suggest that the diffusion processes of lethal terrorism are jointly driven by contagious and non-contagious factors that operate on a local scale – as predicted by theories of diffusion. Moreover, by providing a quantitative measure of predictability, the model prevents policy-makers from making decisions based on highly uncertain predictions. Ultimately, this research may provide important complementary tools to enhance the efficiency of policies that aim to prevent and combat terrorism.

Keywords: diffusion process, terrorism, spatial dynamics, spatio-temporal modeling

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Authors: Gubhinder Kundhi, Paul Rilstone

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Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: edgeworth expansions, higher order asymptotics, saddlepoint expansions, weak instruments

Procedia PDF Downloads 277

Authors: Hossein Jafari, Xiangfang Li, Lijun Qian, Alexander Aved, Timothy Kroecker

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Traditionally in sensor networks and recently in the Internet of Things, numerous heterogeneous sensors are deployed in distributed manner to monitor a phenomenon that often can be model by an underlying stochastic process. The big time-series data collected by the sensors must be analyzed to detect change in the stochastic process as quickly as possible with tolerable false alarm rate. However, sensors may have different accuracy and sensitivity range, and they decay along time. As a result, the big time-series data collected by the sensors will contain uncertainties and sometimes they are conflicting. In this study, we present a framework to take advantage of Evidence Theory (a.k.a. Dempster-Shafer and Dezert-Smarandache Theories) capabilities of representing and managing uncertainty and conflict to fast change detection and effectively deal with complementary hypotheses. Specifically, Kullback-Leibler divergence is used as the similarity metric to calculate the distances between the estimated current distribution with the pre- and post-change distributions. Then mass functions are calculated and related combination rules are applied to combine the mass values among all sensors. Furthermore, we applied the method to estimate the minimum number of sensors needed to combine, so computational efficiency could be improved. Cumulative sum test is then applied on the ratio of pignistic probability to detect and declare the change for decision making purpose. Simulation results using both synthetic data and real data from experimental setup demonstrate the effectiveness of the presented schemes.

Keywords: CUSUM, evidence theory, kl divergence, quickest change detection, time series data

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Authors: Jiahui Yang, John Quigley, Lesley Walls

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In this paper, the authors develop a stochastic model regarding the investment in supplier delivery performance development from a buyer’s perspective. The authors propose a multivariate model through a Multinomial-Dirichlet distribution within an Empirical Bayesian inference framework, representing both the epistemic and aleatory uncertainties in deliveries. A closed form solution is obtained and the lower and upper bound for both optimal investment level and expected profit under uncertainty are derived. The theoretical properties provide decision makers with useful insights regarding supplier delivery performance improvement problems where multiple delivery statuses are involved. The authors also extend the model from a single supplier investment into a supplier portfolio, using a Lagrangian method to obtain a theoretical expression for an optimal investment level and overall expected profit. The model enables a buyer to know how the marginal expected profit/investment level of each supplier changes with respect to the budget and which supplier should be invested in when additional budget is available. An application of this model is illustrated in a simulation study. Overall, the main contribution of this study is to provide an optimal investment decision making framework for supplier development, taking into account multiple delivery statuses as well as multiple projects.

Keywords: decision making, empirical bayesian, portfolio optimization, supplier development, supply chain management

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Authors: Seon Soon Choi

Abstract:

The fatigue crack growth is stochastic because of the fatigue behavior having an uncertainty and a randomness. Therefore, it is necessary to determine the probability distribution of a grown crack size at a specific fatigue crack propagation life for maintenance of structure as well as reliability estimation. The essential purpose of this study is to present the good probability distribution fit for the grown crack size at a specified fatigue life in a rolled magnesium alloy under different specimen thickness conditions. Fatigue crack propagation experiments are carried out in laboratory air under three conditions of specimen thickness using AZ31 to investigate a stochastic crack growth behavior. The goodness-of-fit test for probability distribution of a grown crack size under different specimen thickness conditions is performed by Anderson-Darling test. The effect of a specimen thickness on variability of a grown crack size is also investigated.

Keywords: crack size, fatigue crack propagation, magnesium alloys, probability distribution, specimen thickness

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Authors: Razyeh Behbahani, Martin L. Plumer, Ivan Saika-Voivod

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Micromagnetic simulations based on the stochastic Landau-Lifshitz-Gilbert equation are used to calculate dynamic magnetic hysteresis loops relevant to magnetic hyperthermia applications. With the goal to effectively simulate room-temperature loops for large iron-oxide based systems at relatively slow sweep rates on the order of 1 Oe/ns or less, a coarse-graining scheme is proposed and tested. The scheme is derived from a previously developed renormalization-group approach. Loops associated with nanorods, used as building blocks for larger nanoparticles that were employed in preclinical trials (Dennis et al., 2009 Nanotechnology 20 395103), serve as the model test system. The scaling algorithm is shown to produce nearly identical loops over several decades in the model grain sizes. Sweep-rate scaling involving the damping constant alpha is also demonstrated.

Keywords: coarse-graining, hyperthermia, hysteresis loops, micromagnetic simulations

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Authors: Yangrae Cho, Jinseok Kim, Yongtae Park

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Mobile app service ecosystem has been abruptly emerged, explosively grown, and dynamically transformed. In contrast with product markets in which product sales directly cause increment in firm’s income, customer’s usage is less visible but more valuable in service market. Especially, the market situation with cutthroat competition in mobile app store makes securing and keeping of users as vital. Although a few service firms try to manage their apps’ usage patterns by fitting on S-curve or applying other forecasting techniques, the time series approaches based on past sequential data are subject to fundamental limitation in the market where customer’s attention is being moved unpredictably and dynamically. We therefore propose a new conceptual approach for detecting usage pattern of mobile app service with Hidden Markov Model (HMM) which is based on the dual stochastic structure and mainly used to clarify unpredictable and dynamic sequential patterns in voice recognition or stock forecasting. Our approach could be practically utilized for app service firms to manage their services’ lifecycles and academically expanded to other markets.

Keywords: mobile app service, usage pattern, Hidden Markov Model, pattern detection

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Authors: R. Hellmuth

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The method of factory planning has changed a lot, especially when it is about planning the factory building itself. Factory planning has the task of designing products, plants, processes, organization, areas, and the building of a factory. Regular restructuring is becoming more important in order to maintain the competitiveness of a factory. Restrictions in new areas, shorter life cycles of product and production technology as well as a VUCA world (Volatility, Uncertainty, Complexity and Ambiguity) lead to more frequent restructuring measures within a factory. A digital factory model is the planning basis for rebuilding measures and becomes an indispensable tool. Furthermore, digital building models are increasingly being used in factories to support facility management and manufacturing processes. The main research question of this paper is, therefore: What kind of digital factory model is suitable for the different areas of application during the operation of a factory? First, different types of digital factory models are investigated, and their properties and usabilities for use cases are analysed. Within the scope of investigation are point cloud models, building information models, photogrammetry models, and these enriched with sensor data are examined. It is investigated which digital models allow a simple integration of sensor data and where the differences are. Subsequently, possible application areas of digital factory models are determined by means of a survey and the respective digital factory models are assigned to the application areas. Finally, an application case from maintenance is selected and implemented with the help of the appropriate digital factory model. It is shown how a completely digitalized maintenance process can be supported by a digital factory model by providing information. Among other purposes, the digital factory model is used for indoor navigation, information provision, and display of sensor data. In summary, the paper shows a structuring of digital factory models that concentrates on the geometric representation of a factory building and its technical facilities. A practical application case is shown and implemented. Thus, the systematic selection of digital factory models with the corresponding application cases is evaluated.

Keywords: building information modeling, digital factory model, factory planning, maintenance

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Authors: Chin-Chia Jane

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In a transportation network, travel time refers to the transmission time from source node to destination node, whereas reliability refers to the probability of a successful connection from source node to destination node. With an increasing emphasis on quality of service (QoS), both performance indexes are significant in the design and analysis of transportation systems. In this work, we extend the well-known flow network model for transportation networks so that travel time and reliability are integrated into the QoS measurement simultaneously. In the extended model, in addition to the general arc capacities, each intermediate node has a time weight which is the travel time for per unit of commodity going through the node. Meanwhile, arcs and nodes are treated as binary random variables that switch between operation and failure with associated probabilities. For pre-specified travel time limitation and demand requirement, the QoS of a transportation network is the probability that source can successfully transport the demand requirement to destination while the total transmission time is under the travel time limitation. This work is pioneering, since existing literatures that evaluate travel time reliability via a single optimization path, the proposed QoS focuses the performance of the whole network system. To compute the QoS of transportation networks, we first transfer the extended network model into an equivalent min-cost max-flow network model. In the transferred network, each arc has a new travel time weight which takes value 0. Each intermediate node is replaced by two nodes u and v, and an arc directed from u to v. The newly generated nodes u and v are perfect nodes. The new direct arc has three weights: travel time, capacity, and operation probability. Then the universal set of state vectors is recursively decomposed into disjoint subsets of reliable, unreliable, and stochastic vectors until no stochastic vector is left. The decomposition is made possible by applying existing efficient min-cost max-flow algorithm. Because the reliable subsets are disjoint, QoS can be obtained directly by summing the probabilities of these reliable subsets. Computational experiments are conducted on a benchmark network which has 11 nodes and 21 arcs. Five travel time limitations and five demand requirements are set to compute the QoS value. To make a comparison, we test the exhaustive complete enumeration method. Computational results reveal the proposed algorithm is much more efficient than the complete enumeration method. In this work, a transportation network is analyzed by an extended flow network model where each arc has a fixed capacity, each intermediate node has a time weight, and both arcs and nodes are independent binary random variables. The quality of service of the transportation network is an integration of customer demands, travel time, and the probability of connection. We present a decomposition algorithm to compute the QoS efficiently. Computational experiments conducted on a prototype network show that the proposed algorithm is superior to existing complete enumeration methods.

Keywords: quality of service, reliability, transportation network, travel time

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Authors: Bukhari M. S. Sillah, Imran Khokhar, Muhammad Nauman Khan

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This paper studies the technical efficiency of Saudi banking sector using stochastic frontier model. A sample of 12 banks over the period 2000-2011 is selected to investigate their technical efficiencies in mobilizing deposits, producing investment and generating income. The banks are categorized as Saudi-owned banks, Saudi-foreign-owned banks and Islamic banks. The findings show some consistent pattern of these bank types; and there exist significant disparities among the banks in term of technical efficiency. The Banque Saudi Fransi stands out as a benchmark bank for the industry, and it is a Saudi-foreign owned bank type. The Saudi owned bank types have shown fluctuating performance during the period; and the Islamic bank types are no significantly different from Saudi-owned bank types.

Keywords: technical efficiency, production frontier model, Islamic banking

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Authors: Giovanni Masala, Stefania Marica

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Forecasting electricity load plays a crucial role regards decision making and planning for economical purposes. Besides, in the light of the recent privatization and deregulation of the power industry, the forecasting of future electricity load turned out to be a very challenging problem. Empirical data about electricity load highlights a clear seasonal behavior (higher load during the winter season), which is partly due to climatic effects. We also emphasize the presence of load periodicity at a weekly basis (electricity load is usually lower on weekends or holidays) and at daily basis (electricity load is clearly influenced by the hour). Finally, a long-term trend may depend on the general economic situation (for example, industrial production affects electricity load). All these features must be captured by the model. The purpose of this paper is then to build an hourly electricity load model. The deterministic component of the model requires non-linear regression and Fourier series while we will investigate the stochastic component through econometrical tools. The calibration of the parameters’ model will be performed by using data coming from the Italian market in a 6 year period (2007- 2012). Then, we will perform a Monte Carlo simulation in order to compare the simulated data respect to the real data (both in-sample and out-of-sample inspection). The reliability of the model will be deduced thanks to standard tests which highlight a good fitting of the simulated values.

Keywords: ARMA-GARCH process, electricity load, fitting tests, Fourier series, Monte Carlo simulation, non-linear regression

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Authors: Azam Abkhiz, Abolghasem Nasir

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To achieve sustainable competitive advantage in the market, it is necessary to provide and improve customer satisfaction and Loyalty. To reach this objective, companies need to identify and analyze their customers. Thus, it is critical to measure the level of customer satisfaction and Loyalty very carefully. This study attempts to build a conceptual model to provide clear insights of customer loyalty. Using Bayesian networks (BNs), a model is proposed to evaluate customer loyalty and its consequences, such as repurchase and positive word-of-mouth. BN is a probabilistic approach that predicts the behavior of a system based on observed stochastic events. The most relevant determinants of customer loyalty are identified by the literature review. Perceived value, service quality, trust, corporate image, satisfaction, and switching costs are the most important variables that explain customer loyalty. The data are collected by use of a questionnaire-based survey from 1430 customers of a home appliances manufacturer in Iran. Four scenarios and sensitivity analyses are performed to run and analyze the impact of different determinants on customer loyalty. The proposed model allows businesses to not only set their targets but proactively manage their customer behaviors as well.

Keywords: customer satisfaction, customer loyalty, Bayesian networks, home appliances industry

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Authors: Georg Brunnthaller, Sandra Stein, Wilfried Sihn

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Logistics service providers are facing increasing volatility concerning future transport demand. Short-term planning horizons and planning uncertainties lead to reduced capacity utilisation and increasing empty mileage. To overcome these challenges, a model is proposed to continuously pre-plan future transport capacity in order to redesign and adjust the intermodal fleet accordingly. It is expected that the model will enable logistics service providers to organise more economically and ecologically sustainable transport chains in a more flexible way. To further describe such planning aspects, this paper gives a structured literature review on transport planning problems. The focus is on strategic and tactical planning levels, comprising relevant fleet-sizing-, network-design- and choice-of-carriers-problems. Models and their developed solution techniques are presented and the literature review is concluded with an outlook to our future research objectives

Keywords: choice of transport mode, fleet-sizing, freight transport planning, multimodal, review, service network design

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Authors: Georg Brunnthaller, Sandra Stein, Wilfried Sihn

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Transportation service providers are facing increasing volatility concerning future transport demand. Short-term planning horizons and planning uncertainties lead to reduced capacity utilization and increasing empty mileage. To overcome these challenges, a model is proposed to continuously pre-plan future transportation capacity in order to redesign and adjust the intermodal fleet accordingly. It is expected that the model will enable logistics service providers to organize more economically and ecologically sustainable transport chains in a more flexible way. To further describe these planning aspects, this paper gives an overview on transportation planning problems in a structured way. The focus is on strategic and tactical planning levels, comprising relevant fleet-sizing, service-network-design and choice-of-carriers-problems. Models and their developed solution techniques are presented, and the literature review is concluded with an outlook to our future research directions.

Keywords: freight transportation planning, multimodal, fleet-sizing, service network design, choice of transportation mode, review

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Authors: Bai-Chen Xie, Biao Li

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With the deepening of international exchanges and investment, the international comparison of power grid firms has become the focus of regulatory authorities. Ignoring the differences in the economic environment, resource endowment, technology, and other aspects of different countries or regions may lead to efficiency bias. Based on the Meta-frontier model, this paper divides China and Japan into two groups by using the data of China and Japan from 2006 to 2020. While preserving the differences between the two countries, it analyzes and compares the efficiency of the transmission and distribution industries of the two countries. Combined with the four-component stochastic frontier model, the efficiency is divided into transient and persistent efficiency. We found that there are obvious differences between the transmission and distribution sectors in China and Japan. On the one hand, the inefficiency of the two countries is mostly caused by long-term and structural problems. The key to improve the efficiency of the two countries is to focus more on solving long-term and structural problems. On the other hand, the long-term and structural problems that cause the inefficiency of the two countries are not the same. Quality factors have different effects on the efficiency of the two countries, and this different effect is captured by the common frontier model but is offset in the overall model. Based on these findings, this paper proposes some targeted policy recommendations.

Keywords: transmission and distribution industries, transient efficiency, persistent efficiency, meta-frontier, international comparison

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Authors: Seon Soon Choi

Abstract:

It is necessary to predict a fatigue crack propagation life for estimation of structural integrity. Because of an uncertainty and a randomness of a structural behavior, it is also required to analyze stochastic characteristics of the fatigue crack propagation life at a specified fatigue crack size. The essential purpose of this study is to present the good probability distribution fit for the fatigue crack propagation life at a specified fatigue crack size in magnesium alloys under various fatigue load ratio conditions. To investigate a stochastic crack growth behavior, fatigue crack propagation experiments are performed in laboratory air under several conditions of fatigue load ratio using AZ31. By Anderson-Darling test, a goodness-of-fit test for probability distribution of the fatigue crack propagation life is performed and the good probability distribution fit for the fatigue crack propagation life is presented. The effect of load ratio on variability of fatigue crack propagation life is also investigated.

Keywords: fatigue crack propagation life, load ratio, magnesium alloys, probability distribution

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Authors: J. J. Vargas, N. Prieto, L. A. Toro

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Control charts are commonly used to monitor processes involving either variable or attribute of quality characteristics and determining the control limits as a critical task for quality engineers to improve the processes. Nonetheless, in some applications it is necessary to include an estimation of efficiency. In this paper, the ability to define the efficiency of an industrial process was added to a control chart by means of incorporating a data envelopment analysis (DEA) approach. In depth, a Bayesian estimation was performed to calculate the posterior probability distribution of parameters as means and variance and covariance matrix. This technique allows to analyse the data set without the need of using the hypothetical large sample implied in the problem and to be treated as an approximation to the finite sample distribution. A rejection simulation method was carried out to generate random variables from the parameter functions. Each resulting vector was used by stochastic DEA model during several cycles for establishing the distribution of each efficiency measures for each DMU (decision making units). A control limit was calculated with model obtained and if a condition of a low level efficiency of DMU is presented, system efficiency is out of control. In the efficiency calculated a global optimum was reached, which ensures model reliability.

Keywords: data envelopment analysis, DEA, Multivariate control chart, rejection simulation method

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Authors: Alev Atak

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We study the endogeneity in the cryptocurrency market over the branching ratio of the Hawkes process and evaluate the movement of self-excitability in the financial markets. We consider a semi-parametric self-exciting point process regression model where the excitation function is assumed to be smooth and decreasing but otherwise unspecified, and the baseline intensity is assumed to be a linear function of the regressors. We apply the empirical analysis to the three largest crypto assets, i.e. Bitcoin - Ethereum - Ripple, and provide a comparison with other financial assets such as SP500, Gold, and the volatility index VIX observed from January 2015 to December 2020. The results depict variable and high levels of endogeneity in the basket of cryptocurrencies under investigation, underlining the evidence of a significant role of endogenous feedback mechanisms in the price formation process.

Keywords: hawkes process, cryptocurrency, endogeneity, reflexivity

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Authors: Zunaira Asif, Zhi Chen

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The sustainable measures on air quality management are recognized as one of the most serious environmental concerns in the mining region. The mining operations emit various types of pollutants which have significant impacts on the environment. This study presents a stochastic control strategy by developing the air pollution control model to achieve a cost-effective solution. The optimization method is formulated to predict the cost of treatment using linear programming with an objective function and multi-constraints. The constraints mainly focus on two factors which are: production of metal should not exceed the available resources, and air quality should meet the standard criteria of the pollutant. The applicability of this model is explored through a case study of an open pit metal mine, Utah, USA. This method simultaneously uses meteorological data as a dispersion transfer function to support the practical local conditions. The probabilistic analysis and the uncertainties in the meteorological conditions are accomplished by Monte Carlo simulation. Reasonable results have been obtained to select the optimized treatment technology for PM_2.5, PM₁₀, NO_x, and SO₂. Additional comparison analysis shows that baghouse is the least cost option as compared to electrostatic precipitator and wet scrubbers for particulate matter, whereas non-selective catalytical reduction and dry-flue gas desulfurization are suitable for NO_x and SO₂ reduction respectively. Thus, this model can aid planners to reduce these pollutants at a marginal cost by suggesting control pollution devices, while accounting for dynamic meteorological conditions and mining activities.

Keywords: air pollution, linear programming, mining, optimization, treatment technologies

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Authors: Reni M. Sagayaraj, Anand Gnana S. Selvam, Reynald R. Susainathan

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In this paper, we consider stochastic queueing models for Steady-state behavior of a multi-phase M/M/1 queue in random evolution subject to catastrophe failure. The arrival flow of customers is described by a marked Markovian arrival process. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. This model contains a repair state, when a catastrophe occurs the system is transferred to the failure state. The paper focuses on the steady-state equation, and observes that, the steady-state behavior of the underlying queueing model along with the average queue size is analyzed.

Keywords: M/G/1 queuing system, multi-phase, random evolution, steady-state equation, catastrophe failure

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Authors: Abraham Castellanos, Christophe Durville, Sophie Echenim

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In this article, a portfolio optimization problem is performed in a Solvency II context: it illustrates how advanced optimization techniques can help to tackle complex operational pain points around the monitoring, control, and stability of Solvency Capital Requirement (SCR). The market SCR of a portfolio is calculated as a combination of SCR sub-modules. These sub-modules are the results of stress-tests on interest rate, equity, property, credit and FX factors, as well as concentration on counter-parties. The market SCR is non convex and non differentiable, which does not make it a natural optimization criteria candidate. In the SCR formulation, correlations between sub-modules are fixed, whereas risk-driven portfolio allocation is usually driven by the dynamics of the actual correlations. Implementing a portfolio construction approach that is efficient on both a regulatory and economic standpoint is not straightforward. Moreover, the challenge for insurance portfolio managers is not only to achieve a minimal SCR to reduce non-invested capital but also to ensure stability of the SCR. Some optimizations have already been performed in the literature, simplifying the standard formula into a quadratic function. But to our knowledge, it is the first time that the standard formula of the market SCR is used in an optimization problem. Two solvers are combined: a bundle algorithm for convex non- differentiable problems, and a BFGS (Broyden-Fletcher-Goldfarb- Shanno)-SQP (Sequential Quadratic Programming) algorithm, to cope with non-convex cases. A market SCR minimization is then performed with historical data. This approach results in significant reduction of the capital requirement, compared to a classical Markowitz approach based on the historical volatility. A comparative analysis of different optimization models (equi-risk-contribution portfolio, minimizing volatility portfolio and minimizing value-at-risk portfolio) is performed and the impact of these strategies on risk measures including market SCR and its sub-modules is evaluated. A lack of diversification of market SCR is observed, specially for equities. This was expected since the market SCR strongly penalizes this type of financial instrument. It was shown that this direct effect of the regulation can be attenuated by implementing constraints in the optimization process or minimizing the market SCR together with the historical volatility, proving the interest of having a portfolio construction approach that can incorporate such features. The present results are further explained by the Market SCR modelling.

Keywords: financial risk, numerical optimization, portfolio management, solvency capital requirement

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Authors: Nassim Bessaad, Qilian Bao, Zhao Jiangkang

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The fiber optics gyroscope in the strap-down inertial navigation system (FOG-SINS) suffers from precision degradation due to the influence of random errors. In this work, an enhanced Allan variance (AV) stochastic modeling method combined with discrete wavelet transform (DWT) for signal denoising is implemented to estimate the random process in the FOG signal. Furthermore, we devise a measurement-based iterative adaptive Sage-Husa nonlinear filter with augmented states to integrate a star tracker sensor with SINS. The proposed filter adapts the measurement noise covariance matrix based on the available data. Moreover, the enhanced stochastic modeling scheme is invested in tuning the process noise covariance matrix and the augmented state Gauss-Markov process parameters. Finally, the effectiveness of the proposed filter is investigated by employing the collected data in laboratory conditions. The result shows the filter's improved accuracy in comparison with the conventional Kalman filter (CKF).

Keywords: inertial navigation, adaptive filtering, star tracker, FOG

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Authors: Wheyming Tina Song, Chi-Hao Hong, Peisyuan Lin

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An important performance measure for stochastic manufacturing networks is the system reliability, defined as the probability that the production output meets or exceeds a specified demand. The system parameters include the capacity of each workstation and numbers of the conforming parts produced in each workstation. We establish that eighteen archival publications, containing twenty-one examples, provide incorrect values of the system reliability. The author recently published the Song Rule, which provides the correct analytical system-reliability value; it is, however, computationally inefficient for large networks. In this paper, we use Monte Carlo simulation (implemented in C and Flexsim) to provide estimates for the above-mentioned twenty-one examples. The simulation estimates are consistent with the analytical solution for small networks but is computationally efficient for large networks. We argue here for three advantages of Monte Carlo simulation: (1) understanding stochastic systems, (2) validating analytical results, and (3) providing estimates even when analytical and numerical approaches are overly expensive in computation. Monte Carlo simulation could have detected the published analysis errors.

Keywords: Monte Carlo simulation, analytical results, leading digit rule, standard error

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Authors: Sunantha Teyarachakul

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We consider the worker-learning Newsvendor Model, under the case of lost-sales for unmet demand, with the research objective of proposing the cost-minimization order policy and lot size, scheduled to arrive at the beginning of the selling-period. In general, the New Vendor Model is used to find the optimal order quantity for the perishable items such as fashionable products or those with seasonal demand or short-life cycles. Technically, it is used when the product demand is stochastic and available for the single selling-season, and when there is only a one time opportunity for the vendor to purchase, with possibly of long ordering lead-times. Our work differs from the classical Newsvendor Model in that we incorporate the human factor (specifically worker learning) and its influence over the costs of processing units into the model. We describe this by using the well-known Wright’s Learning Curve. Most of the assumptions of the classical New Vendor Model are still maintained in our work, such as the constant per-unit cost of leftover and shortage, the zero initial inventory, as well as the continuous time. Our problem is challenging in the way that the best order quantity in the classical model, which is balancing the over-stocking and under-stocking costs, is no longer optimal. Specifically, when adding the cost-saving from worker learning to such expected total cost, the convexity of the cost function will likely not be maintained. This has called for a new way in determining the optimal order policy. In response to such challenges, we found a number of characteristics related to the expected cost function and its derivatives, which we then used in formulating the optimal ordering policy. Examples of such characteristics are; the optimal order quantity exists and is unique if the demand follows a Uniform Distribution; if the demand follows the Beta Distribution with some specific properties of its parameters, the second derivative of the expected cost function has at most two roots; and there exists the specific level of lot size that satisfies the first order condition. Our research results could be helpful for analysis of supply chain coordination and of the periodic review system for similar problems.

Keywords: inventory management, Newsvendor model, order policy, worker learning

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Authors: Sai Hung Cheung, Zhe Shao

Abstract:

It is of our great interest to quantify the risk to structural dynamic systems due to earthquake-induced tsunamis in view of recent earthquake-induced tsunamis in Padang, 2004 and Tohoku, 2011 which brought huge losses of lives and properties. Despite continuous advancement in computational simulation of the tsunami and wave-structure interaction modeling, it still remains computationally challenging to evaluate the reliability of a structural dynamic system when uncertainties related to the system and its modeling are taken into account. The failure of the structure in a tsunami-wave-structural system is defined as any response quantities of the system exceeding specified thresholds during the time when the structure is subjected to dynamic wave impact due to earthquake-induced tsunamis. In this paper, an approach based on a novel integration of a recently proposed moving least squares response surface approach for stochastic sampling and the Subset Simulation algorithm is proposed. The effectiveness of the proposed approach is discussed by comparing its results with those obtained from the Subset Simulation algorithm without using the response surface approach.

Keywords: response surface, stochastic simulation, structural reliability tsunami, risk

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Authors: Abdullah Eqal Al Mazrooei

Abstract:

In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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Authors: Ipek Kivanc, Demet Ozgur-Unluakin

Abstract:

Over the past years, technological innovations and advancements have played an important role in the industrial world. Due to technological improvements, the degree of complexity of the systems has increased. Hence, all systems are getting more uncertain that emerges from increased complexity, resulting in more cost. It is challenging to cope with this situation. So, implementing efficient planning of maintenance activities in such systems are getting more essential. Partially Observable Markov Decision Processes (POMDPs) are powerful tools for stochastic sequential decision problems under uncertainty. Although maintenance optimization in a dynamic environment can be modeled as such a sequential decision problem, POMDPs are not widely used for tackling maintenance problems. However, they can be well-suited frameworks for obtaining optimal maintenance policies. In the classical representation of the POMDP framework, the system is denoted by a single node which has multiple states. The main drawback of this classical approach is that the state space grows exponentially with the number of state variables. On the other side, factored representation of POMDPs enables to simplify the complexity of the states by taking advantage of the factored structure already available in the nature of the problem. The main idea of factored POMDPs is that they can be compactly modeled through dynamic Bayesian networks (DBNs), which are graphical representations for stochastic processes, by exploiting the structure of this representation. This study aims to demonstrate how maintenance planning of dynamic systems can be modeled with factored POMDPs. An empirical maintenance planning problem of a dynamic system consisting of four partially observable components deteriorating in time is designed. To solve the empirical model, we resort to Symbolic Perseus solver which is one of the state-of-the-art factored POMDP solvers enabling approximate solutions. We generate some more predefined policies based on corrective or proactive maintenance strategies. We execute the policies on the empirical problem for many replications and compare their performances under various scenarios. The results show that the computed policies from the POMDP model are superior to the others. Acknowledgment: This work is supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under grant no: 117M587.

Keywords: factored representation, maintenance, multi-component system, partially observable Markov decision processes

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Authors: Alexander E. Hramov, Vadim V. Grubov, Alexey A. Koronovskii, Maria K. Kurovskaуa, Anastasija E. Runnova

Abstract:

The perception of visual signals in the brain was among the first issues discussed in terms of multistability which has been introduced to provide mechanisms for information processing in biological neural systems. In this work the influence of the cognitive noise on the visual perception of multistable pictures has been investigated. The study includes an experiment with the bistable Necker cube illusion and the theoretical background explaining the obtained experimental results. In our experiments Necker cubes with different wireframe contrast were demonstrated repeatedly to different people and the probability of the choice of one of the cubes projection was calculated for each picture. The Necker cube was placed at the middle of a computer screen as black lines on a white background. The contrast of the three middle lines centered in the left middle corner was used as one of the control parameter. Between two successive demonstrations of Necker cubes another picture was shown to distract attention and to make a perception of next Necker cube more independent from the previous one. Eleven subjects, male and female, of the ages 20 through 45 were studied. The choice of the Necker cube projection was detected with the Electroencephalograph-recorder Encephalan-EEGR-19/26, Medicom MTD. To treat the experimental results we carried out theoretical consideration using the simplest double-well potential model with the presence of noise that led to the Fokker-Planck equation for the probability density of the stochastic process. At the first time an analytical solution for the probability of the selection of one of the Necker cube projection for different values of wireframe contrast have been obtained. Furthermore, having used the results of the experimental measurements with the help of the method of least squares we have calculated the value of the parameter corresponding to the cognitive noise of the person being studied. The range of cognitive noise parameter values for studied subjects turned to be [0.08; 0.55]. It should be noted, that experimental results have a good reproducibility, the same person being studied repeatedly another day produces very similar data with very close levels of cognitive noise. We found an excellent agreement between analytically deduced probability and the results obtained in the experiment. A good qualitative agreement between theoretical and experimental results indicates that even such a simple model allows simulating brain cognitive dynamics and estimating important cognitive characteristic of the brain, such as brain noise.

Keywords: bistability, brain, noise, perception, stochastic processes

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