Search results for: Stochastic Models

Authors: Weng Ming Chu

Abstract:

When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the non-identical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by Adlakha & Kulkarni [1], many methods and algorithms have been put forward in attempt to resolve this issue, but most have encountered this same large-size network problem. Therefore, in this research, we focus on network reduction through a Series/Parallel combined mechanism. Our suggested algorithm, named the Activity Network Reduction Algorithm (ANRA), can efficiently transfer a large-size network into an S/P Irreducible Network (SPIN). SPIN can enhance stochastic network analysis, as well as serve as the judgment of symmetry for the Graph Theory.

Keywords: Series/Parallel network, Stochastic network, Network reduction, Interdictive Graph, Complexity Index.

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Authors: F. Alborzi, H. Vafaei, M.H. Gholami, M.M. S. Esfahani

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In this article, the design of a Supply Chain Network (SCN) consisting of several suppliers, production plants, distribution centers and retailers, is considered. Demands of retailers are considered stochastic parameters, so we generate amounts of data via simulation to extract a few demand scenarios. Then a mixed integer two-stage programming model is developed to optimize simultaneously two objectives: (1) minimization the fixed and variable cost, (2) maximization the service level. A weighting method is utilized to solve this two objective problem and a numerical example is made to show the performance of the model.

Keywords: Mixed Integer Programming, Multi-objective Optimization, Stochastic Demand, Supply Chain Design, Two Stage Programming

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Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph

Abstract:

In this paper, to model a real life wind turbine, a probabilistic approach is proposed to model the dynamics of the blade elements of a small axial wind turbine under extreme stochastic wind speeds conditions. It was found that the power and the torque probability density functions even-dough decreases at these extreme wind speeds but are not infinite. Moreover, we also fund that it is possible to stabilize the power coefficient (stabilizing the output power)above rated wind speeds by turning some control parameters. This method helps to explain the effect of turbulence on the quality and quantity of the harness power and aerodynamic torque.

Keywords: Probability, Stochastic, Probability density function, Turbulence.

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Authors: A. A. Hussen, I. N. Jleta

Abstract:

Micro-electromechanical system (MEMS) accelerometers and gyroscopes are suitable for the inertial navigation system (INS) of many applications due to low price, small dimensions and light weight. The main disadvantage in a comparison with classic sensors is a worse long term stability. The estimation accuracy is mostly affected by the time-dependent growth of inertial sensor errors, especially the stochastic errors. In order to eliminate negative effects of these random errors, they must be accurately modeled. In this paper, the Allan variance technique will be used in modeling the stochastic errors of the inertial sensors. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data.

Keywords: Allan variance, accelerometer, gyroscope, stochastic errors.

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Authors: Tugrul Oktay, Mehmet Konar, Mustafa Soylak, Firat Sal, Murat Onay, Orhan Kizilkaya

Abstract:

In this paper, autonomous performance of a small manufactured unmanned helicopter is tried to be increased. For this purpose, a small unmanned helicopter is manufactured in Erciyes University, Faculty of Aeronautics and Astronautics. It is called as ZANKA-Heli-I. For performance maximization, autopilot parameters are determined via minimizing a cost function consisting of flight performance parameters such as settling time, rise time, overshoot during trajectory tracking. For this purpose, a stochastic optimization method named as simultaneous perturbation stochastic approximation is benefited. Using this approach, considerable autonomous performance increase (around %23) is obtained.

Keywords: Small helicopters, hierarchical control, stochastic optimization, autonomous performance maximization, autopilots.

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Authors: Zundong Zhang, Limin Jia, Xiaoliang Sun

Abstract:

The Beijing road traffic system, as a typical huge urban traffic system, provides a platform for analyzing the complex characteristics and the evolving mechanisms of urban traffic systems. Based on dynamic network theory, we construct the dynamic model of the Beijing road traffic system in which the dynamical properties are described completely. Furthermore, we come into the conclusion that urban traffic systems can be viewed as static networks, stochastic networks and complex networks at different system phases by analyzing the structural randomness. As well as, we demonstrate the evolving process of the Beijing road traffic network based on real traffic data, validate the stochastic characteristics and the scale-free property of the network at different phases

Keywords: Dynamic Network Models, Structural Randomness, Scale-free Property, Multi-mode character

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Authors: Mengzhuo Luo, Shouming Zhong

Abstract:

This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.

Keywords: Delay-dependent stability, Neural networks, Time varying delay, Linear matrix inequality (LMI).

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Authors: Paola Lecca, Lorenzo Dematte

Abstract:

Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose general form is ÔêétX(x, t) = DΔX(x, t), where X(x, t) is the state vector, D is the matrix of the diffusion coefficients and Δ is the Laplace operator. If the solute move in an homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and of solutes and on local temperature of the medium. In this paper a new stochastic reaction-diffusion model in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces of solvent and solute is presented. Such a model provides a more realistic description of the molecular kinetics in non-homogenoeus and highly structured media as the intra- and inter-cellular spaces. The movement of a molecule A from a region i to a region j of the space is described as a first order reaction Ai k- → Aj , where the rate constant k depends on the diffusion coefficient. Representing the diffusional motion as a chemical reaction allows to assimilate a reaction-diffusion system to a pure reaction system and to simulate it with Gillespie-inspired stochastic simulation algorithms. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the specific speed of reaction and diffusion events. Redi is the software tool, developed to implement the model of reaction-diffusion kinetics and dynamics. It is a free software, that can be downloaded from http://www.cosbi.eu. To demonstrate the validity of the new reaction-diffusion model, the simulation results of the chaperone-assisted protein folding in cytoplasm obtained with Redi are reported. This case study is redrawing the attention of the scientific community due to current interests on protein aggregation as a potential cause for neurodegenerative diseases.

Keywords: Reaction-diffusion systems, Fick's law, stochastic simulation algorithm.

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Authors: Siliang Wang, Minghui Wang

Abstract:

Many exist studies always use Markov decision processes (MDPs) in modeling optimal route choice in stochastic, time-varying networks. However, taking many variable traffic data and transforming them into optimal route decision is a computational challenge by employing MDPs in real transportation networks. In this paper we model finite horizon MDPs using directed hypergraphs. It is shown that the problem of route choice in stochastic, time-varying networks can be formulated as a minimum cost hyperpath problem, and it also can be solved in linear time. We finally demonstrate the significant computational advantages of the introduced methods.

Keywords: Markov decision processes (MDPs), stochastictime-varying networks, hypergraphs, route choice.

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Authors: Fl. Loury, P. Sablonière

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In this paper a stochastic scenario-based model predictive control applied to molten salt storage systems in concentrated solar tower power plant is presented. The main goal of this study is to build up a tool to analyze current and expected future resources for evaluating the weekly power to be advertised on electricity secondary market. This tool will allow plant operator to maximize profits while hedging the impact on the system of stochastic variables such as resources or sunlight shortage.

Solving the problem first requires a mixed logic dynamic modeling of the plant. The two stochastic variables, respectively the sunlight incoming energy and electricity demands from secondary market, are modeled by least square regression. Robustness is achieved by drawing a certain number of random variables realizations and applying the most restrictive one to the system. This scenario approach control technique provides the plant operator a confidence interval containing a given percentage of possible stochastic variable realizations in such a way that robust control is always achieved within its bounds. The results obtained from many trajectory simulations show the existence of a ‘’reliable’’ interval, which experimentally confirms the algorithm robustness.

Keywords: Molten Salt Storage System, Concentrated Solar Tower Power Plant, Robust Stochastic Model Predictive Control.

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Authors: Ginalber L. O. Serra

Abstract:

This work proposes a recursive weighted ELS algorithm for system identification by applying numerically robust orthogonal Householder transformations. The properties of the proposed algorithm show it obtains acceptable results in a noisy environment: fast convergence and asymptotically unbiased estimates. Comparative analysis with others robust methods well known from literature are also presented.

Keywords: Stochastic Systems, Robust Identification, Parameter Estimation, Systems Identification.

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Authors: Miloš Šeda

Abstract:

In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.

Keywords: Flow shop, job shop, mixed integer model, representation scheme.

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Authors: Xin Zhao, Yin-fan Zhu, Wei-ping Wang, Qun Li

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The Influence Diagrams (IDs) is a kind of Probabilistic Belief Networks for graphic modeling. The usage of IDs can improve the communication among field experts, modelers, and decision makers, by showing the issue frame discussed from a high-level point of view. This paper enhances the Time-Sliced Influence Diagrams (TSIDs, or called Dynamic IDs) based formalism from a Discrete Event Systems Modeling and Simulation (DES M&S) perspective, for Exploring Analysis (EA) modeling. The enhancements enable a modeler to specify times occurred of endogenous events dynamically with stochastic sampling as model running and to describe the inter- influences among them with variable nodes in a dynamic situation that the existing TSIDs fails to capture. The new class of model is named Dynamic-Stochastic Influence Diagrams (DSIDs). The paper includes a description of the modeling formalism and the hiberarchy simulators implementing its simulation algorithm, and shows a case study to illustrate its enhancements.

Keywords: Time-sliced influence diagrams, discrete event systems, dynamic-stochastic influence diagrams, modeling formalism, simulation algorithm.

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Authors: M. A. Meslem

Abstract:

For precise geoid determination, we use a reference field to subtract long and medium wavelength of the gravity field from observations data when we use the remove-compute-restore technique. Therefore, a comparison study between considered models should be made in order to select the optimal reference gravity field to be used. In this context, two recent global geopotential models have been selected to perform this comparison study over Northern Algeria. The Earth Gravitational Model (EGM2008) and the Global Gravity Model (GECO) conceived with a combination of the first model with anomalous potential derived from a GOCE satellite-only global model. Free air gravity anomalies in the area under study have been used to compute residual data using both gravity field models and a Digital Terrain Model (DTM) to subtract the residual terrain effect from the gravity observations. Residual data were used to generate local empirical covariance functions and their fitting to the closed form in order to compare their statistical behaviors according to both cases. Finally, height anomalies were computed from both geopotential models and compared to a set of GPS levelled points on benchmarks using least squares adjustment. The result described in details in this paper regarding these two models has pointed out a slight advantage of GECO global model globally through error degree variances comparison and ground-truth evaluation.

Keywords: Quasigeoid, gravity anomalies, covariance, GGM.

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Authors: T. Kerdchuen

Abstract:

This paper proposes the stochastic tabu search (STS) for improving the measurement scheme for power system state estimation. If the original measured scheme is not observable, the additional measurements with minimum number of measurements are added into the system by STS so that there is no critical measurement pair. The random bit flipping and bit exchanging perturbations are used for generating the neighborhood solutions in STS. The Pδ observable concept is used to determine the network observability. Test results of 10 bus, IEEE 14 and 30 bus systems are shown that STS can improve the original measured scheme to be observable without critical measurement pair. Moreover, the results of STS are superior to deterministic tabu search (DTS) in terms of the best solution hit.

Keywords: Measurement Scheme, Power System StateEstimation, Network Observability, Stochastic Tabu Search (STS).

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Authors: Mahmoud Elmezain, Samar El-shinawy

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Many approaches to pattern recognition are founded on probability theory, and can be broadly characterized as either generative or discriminative according to whether or not the distribution of the image features. Generative and discriminative models have very different characteristics, as well as complementary strengths and weaknesses. In this paper, we study these models to recognize the patterns of alphabet characters (A-Z) and numbers (0-9). To handle isolated pattern, generative model as Hidden Markov Model (HMM) and discriminative models like Conditional Random Field (CRF), Hidden Conditional Random Field (HCRF) and Latent-Dynamic Conditional Random Field (LDCRF) with different number of window size are applied on extracted pattern features. The gesture recognition rate is improved initially as the window size increase, but degrades as window size increase further. Experimental results show that the LDCRF is the best in terms of results than CRF, HCRF and HMM at window size equal 4. Additionally, our results show that; an overall recognition rates are 91.52%, 95.28%, 96.94% and 98.05% for CRF, HCRF, HMM and LDCRF respectively.

Keywords: Statistical Pattern Recognition, Generative Model, Discriminative Model, Human Computer Interaction.

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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Authors: George Yungchih Wang

Abstract:

For decades financial economists have been attempted to determine the optimal investment policy by recognizing the option value embedded in irreversible investment whose project value evolves as a geometric Brownian motion (GBM). This paper aims to examine the effects of the optimal investment trigger and of the misspecification of stochastic processes on investment in real options applications. Specifically, the former explores the consequence of adopting optimal investment rules on the distributions of corporate value under the correct assumption of stochastic process while the latter analyzes the influence on the distributions of corporate value as a result of the misspecification of stochastic processes, i.e., mistaking an alternative process as a GBM. It is found that adopting the correct optimal investment policy may increase corporate value by shifting the value distribution rightward, and the misspecification effect may decrease corporate value by shifting the value distribution leftward. The adoption of the optimal investment trigger has a major impact on investment to such an extent that the downside risk of investment is truncated at the project value of zero, thereby moving the value distributions rightward. The analytical framework is also extended to situations where collection lags are in place, and the result indicates that collection lags reduce the effects of investment trigger and misspecification on investment in an opposite way.

Keywords: GBM, real options, investment trigger, misspecification, collection lags

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Authors: Tomoaki Hashimoto

Abstract:

Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the effectiveness of the obtained stability condition.

Keywords: Computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems.

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Authors: Syeda Maria Ali Shah, Asif Mansoor, Talat Sharafat Rehmani, Safia Mirza

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The stock market of any country acts as a predictor of the economy. The spread of the COVID-19 pandemic has severely impacted the global financial markets. Besides, it has also critically affected the economy of Pakistan. In this study, we consider the role of the Karachi Stock Exchange (KSE) with regard to the Pakistan Stock Exchange and quantify the impact on macroeconomic variables in presence of COVID-19. The suitable macroeconomic variables are used to quantify the impact of COVID-19 by developing the stochastic model. The sufficiency of the computed model is attained by means of available techniques in the literature. The estimated equations are used to forecast the impact of pandemic on macroeconomic variables. The constructed model can help the policymakers take counteractive measures for restricting the influence of viruses on the Karachi Stock Market.

Keywords: COVID-19, Karachi Stock Market, macroeconomic variables, stochastic model, forecasting.

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Authors: N. C. Sarkar, A. Bhaskar, Z. Zheng

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The driving behavior in area-based (i.e., non-lane based) traffic is induced by the presence of other individuals in the choice space from the driver’s visual perception area. The driving behavior of a subject vehicle is constrained by the potential leaders and leaders are frequently changed over time. This paper is to determine a stochastic model for a parameter of modified intelligent driver model (MIDM) in area-based traffic (as in developing countries). The parametric and non-parametric distributions are presented to fit the parameters of MIDM. The goodness of fit for each parameter is measured in two different ways such as graphically and statistically. The quantile-quantile (Q-Q) plot is used for a graphical representation of a theoretical distribution to model a parameter and the Kolmogorov-Smirnov (K-S) test is used for a statistical measure of fitness for a parameter with a theoretical distribution. The distributions are performed on a set of estimated parameters of MIDM. The parameters are estimated on the real vehicle trajectory data from India. The fitness of each parameter with a stochastic model is well represented. The results support the applicability of the proposed modeling for parameters of MIDM in area-based traffic flow simulation.

Keywords: Area-based traffic, car-following model, micro-simulation, stochastic modeling.

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Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

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Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: Decentralized, optimal control, output, singular perturb.

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Authors: Abeer Amayri, Akif A. Bulgak

Abstract:

Due to today’s globalization as well as outsourcing practices of the companies, the Supply Chain (SC) performances have become more dependent on the efficient movement of material among places that are geographically dispersed, where there is more chance for disruptions. One such disruption is the quality and delivery uncertainties of outsourcing. These uncertainties could lead the products to be unsafe and, as is the case in a number of recent examples, companies may have to end up in recalling their products. As a result of these problems, there is a need to develop a methodology for selecting suppliers globally in view of risks associated with low quality and late delivery. Accordingly, we developed a two-stage stochastic model that captures the risks associated with uncertainty in quality and delivery as well as a solution procedure for the model. The stochastic model developed simultaneously optimizes supplier selection and purchase quantities under price discounts over a time horizon. In particular, our target is the study of global organizations with multiple sites and multiple overseas suppliers, where the pricing is offered in suppliers’ local currencies. Our proposed methodology is applied to a case study for a US automotive company having two assembly plants and four potential global suppliers to illustrate how the proposed model works in practice.

Keywords: Global supply chains, quality, stochastic programming, supplier selection.

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Authors: Nima Farkhondeh Jahromi, George Papaefthymiou, Lou van der Sluis

Abstract:

The incorporation of renewable energy sources for the sustainable electricity production is undertaking a more prominent role in electric power systems. Thus, it will be an indispensable incident that the characteristics of future power networks, their prospective stability for instance, get influenced by the imposed features of sustainable energy sources. One of the distinctive attributes of the sustainable energy sources is exhibiting the stochastic behavior. This paper investigates the impacts of this stochastic behavior on the small disturbance rotor angle stability in the upcoming electric power networks. Considering the various types of renewable energy sources and the vast variety of system configurations, the sensitivity analysis can be an efficient breakthrough towards generalizing the effects of new energy sources on the concept of stability. In this paper, the definition of small disturbance angle stability for future power systems and the iterative-stochastic way of its analysis are presented. Also, the effects of system parameters on this type of stability are described by performing a sensitivity analysis for an electric power test system.

Keywords: Power systems stability, Renewable energy sources, Stochastic behavior, Small disturbance rotor angle stability.

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Authors: Yanqi Yang, Chongshan Liao, Cheuk Hin Ho, Susan Bridges

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Aim: To investigate students’ perceptions of using e-models in an inquiry-based curriculum. Approach: 52 second-year dental students completed a pre- and post-test questionnaire relating to their perceptions of e-models and their use in inquiry-based learning. The pre-test occurred prior to any learning with e-models. The follow-up survey was conducted after one year's experience of using e-models. Results: There was no significant difference between the two sets of questionnaires regarding students’ perceptions of the usefulness of e-models and their willingness to use e-models in future inquiry-based learning. Most students preferred using both plaster models and e-models in tandem. Conclusion: Students did not change their attitude towards e-models and most of them agreed or were neutral that e-models are useful in inquiry-based learning. Whilst recognizing the utility of 3D models for learning, students' preference for combining these with solid models has implications for the development of haptic sensibility in an operative discipline.

Keywords: E-models, inquiry-based curriculum, education.

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Authors: Miljan B. Petrović, Dušan B. Petrović, Goran S. Nikolić

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This paper describes a method for AWGN (Additive White Gaussian Noise) variance estimation in noisy stochastic signals, referred to as Multiplicative-Noising Variance Estimation (MNVE). The aim was to develop an estimation algorithm with minimal number of assumptions on the original signal structure. The provided MATLAB simulation and results analysis of the method applied on speech signals showed more accuracy than standardized AR (autoregressive) modeling noise estimation technique. In addition, great performance was observed on very low signal-to-noise ratios, which in general represents the worst case scenario for signal denoising methods. High execution time appears to be the only disadvantage of MNVE. After close examination of all the observed features of the proposed algorithm, it was concluded it is worth of exploring and that with some further adjustments and improvements can be enviably powerful.

Keywords: Noise, signal-to-noise ratio, stochastic signals, variance estimation.

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Authors: Franklin Nantui Mabe, Samuel A. Donkoh, Seidu Al-Hassan

Abstract:

Rice yields among agro-ecological zones are heterogeneous. Farmers, researchers and policy makers are making frantic efforts to bridge rice yield gaps between agro-ecological zones through the promotion of improved agricultural technologies (IATs). Farmers are also modifying these IATs and blending them with indigenous farming practices (IFPs) to form farmer innovation systems (FISs). Also, different metafrontier models have been used in estimating productivity performances and their drivers. This study used the two-step stochastic metafrontier model to estimate the productivity performances of rice farmers and their determining factors in GSZ, FSTZ and CSZ. The study used both primary and secondary data. Farmers in CSZ are the most technically efficient. Technical inefficiencies of farmers are negatively influenced by age, sex, household size, education years, extension visits, contract farming, access to improved seeds, access to irrigation, high rainfall amount, less lodging of rice, and well-coordinated and synergized adoption of technologies. Albeit farmers in CSZ are doing well in terms of rice yield, they still have the highest potential of increasing rice yield since they had the lowest TGR. It is recommended that government through the ministry of food and agriculture, development partners and individual private companies promote the adoption of IATs as well as educate farmers on how to coordinate and synergize the adoption of the whole package. Contract farming concept and agricultural extension intensification should be vigorously pursued to the latter.

Keywords: Efficiency, farmer innovation systems, improved agricultural technologies, two-step stochastic metafrontier approach.

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Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov

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We have conducted the optimal synthesis of rootmean- squared objective filter to estimate the state vector in the case if within the observation channel with memory the anomalous noises with unknown mathematical expectation are complement in the function of the regular noises. The synthesis has been carried out for linear stochastic systems of continuous - time.

Keywords: Mathematical expectation, filtration, anomalous noise, memory.

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Authors: Madhukar Nagare, Pankaj Dutta

Abstract:

Inventory decisional environment of short life-cycle products is full of uncertainties arising from randomness and fuzziness of input parameters like customer demand requiring modeling under hybrid uncertainty. Prior inventory models incorporating fuzzy demand have unfortunately ignored stochastic variation of demand. This paper determines an unambiguous optimal order quantity from a set of n fuzzy observations in a newsvendor inventory setting in presence of fuzzy random variable demand capturing both fuzzy perception and randomness of customer demand. The stress of this paper is in providing solution procedure that attains optimality in two steps with demand information availability in linguistic phrases leading to fuzziness along with stochastic variation. The first step of solution procedure identifies and prefers one best fuzzy opinion out of all expert opinions and the second step determines optimal order quantity from the selected event that maximizes profit. The model and solution procedure is illustrated with a numerical example.

Keywords: Fuzzy expected value, Fuzzy random demand, Hybrid uncertainty, Optimal order quantity, Single-period inventory

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Authors: M. Mokhtar, A. Shuib, D. Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: Portfolio optimization, Mathematical programming, Multi-objective programming, Solution approaches.

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