International Journal of Mathematical Modelling and Numerical Optimisation (9 papers in press)
Uniformly convergent numerical method for singularly perturbed 2D delay parabolic convection-diffusion problems on Bakhvalov-Shishkin mesh
by Srinivasan Natesan, Abhishek Das
Abstract: In this article, we consider a class of singularly perturbed 2D delay parabolic convection-diffusion initial-boundary-value problems. To solve the problem numerically, we consider upwind finite difference scheme on a modified Shishkin mesh (Bakhvalov-Shishkin mesh) to discretize the domain in spatial directions and we apply implicit-Euler scheme for the time derivative on uniform mesh in the temporal direction. We derive some conditions on the mesh-generating functions which are useful for the convergence of the method, uniformly with respect to the perturbation parameter. We prove that the applied scheme on the Bakhvalov-Shishkin mesh is first-order convergent in the discrete supremum norm, which is optimal and does not require any extra computational effort compare to the standard Shishkin mesh. Numerical experiments verify the theoretical results.
Keywords: Singularly perturbed 2D delay parabolic convection-diffusion problems; boundary layers; finite difference scheme; Bakhvalov-Shishkin mesh; uniform convergence.
Information technology value model and its optimal application in IT-based firms
by Lukman Abdurrahman, Suhardi Suhardi, Armein Z.R. Langi, Togar M. Simatupang
Abstract: This paper proposes the developed business performance based on the IT value model, which offers superior performance with profit maximization due to increased revenue and reduced costs. The model stands on the resource-based view theory, the partial adjustment valuation theory, and the systems engineering approach. Therefore, the model consists of firm performance, firm core competence, firm capability, and information technology resource subsystems. Each subsystem has inputs, i.e. the regular capital (K), the regular labour expense (L), and IT capital (I) where the output is y (the gross revenue). In addition, the synthesis result states that the model with the structure of the composition of each subsystem with the addition operation is more acceptable. The data used came from Telkom, Indosat, and XL, which are telco firms in Indonesia. Similarly, the IT value model optimization testing displays that the model is able to provide superior performance with increased revenue, but at a lower cost. Thus, the proposed model can address the mentioned main problems. However, it needs further studies to enhance this model.
Keywords: capital;systems engineering;information technology;model;partial adjustment;performance;revenue;cost;value.
An inventory System with Two Heterogeneous Servers and Orbital Search for Feedback Customers
by Suganya C, Amirthakodi M, Sivakumar B
Abstract: This model deals a continuous review (s, S) inventory system two heterogeneous servers, say, server - 1, server - 2. Server - 1 serve for primary customers and server - 2 is served for both primary and feedback customers. The primary customers arrival according to a Markovian arrival process (MAP) and service time for both servers has exponential distribution. The lead time is assumed to be exponential distribution. The primary customers, who finds either two servers are busy or no item is in the stock, waits in the finite waiting hall. If the waiting hall is full, then arriving, customer considered to be lost. After the completion of service the primary customer will decide either to join the orbit, which is an infinite size, for additional service or leaves the system according to a Bernoulli trail. These orbiting (feedback) customers compete for their service according to constant retrial policy, and the service times for these feedback customers are assumed to be exponential distribution. After completing the service for feedback customers server - 2 becomes idle or busy for primary customer. If the server - 2 completes the service for a primary customer, then he searches the customers in the orbit or idle according to a Bernoulli trail. The results are illustrated numerically.
Keywords: Markovian arrival process; Feedback customers; Heterogeneous serves; Service facility; Orbital search.
The impact of hygiene care and maternal immunity on stability behavior of rotavirus infection model for children under the age of five in Thailand
by RATCHADA VIRIYAPONG, Gunyarat Koompawan
Abstract: Rotavirus infection is one of the significant causes of death in infants and children under five years of age in Thailand and worldwide. In this paper, a deterministic model for rotavirus transmission of children under five years old in Thailand incorporating with hygiene care control and maternal immunity is developed. The basic reproduction number (Rv) is derived and becomes a threshold indicating the stability of both disease-free and endemic equilibrium points. Through the analysis, the results show that the disease-free equilibrium point is locally asymptotically stable when Rv < 1 and the endemic equilibrium point is locally stable when Rv > 1 and satisfies the Routh-Hurwitz criteria. Further, numerical simulation demonstrates that both hygiene care and maternal immunity to the infection due to breastfeeding should be encouraged as strategy to control rotavirus infection.
Keywords: diarrhea; rotavirus; mathematical modeling; basic reproduction
number; hygiene care; breastfeeding.
A study on M/G/1 retrial queueing system with three different types of customers under working vacation policy
by P. Rajadurai
Abstract: This paper deals with a single server retrial queueing system with working vacations and vacation interruption. There are three different types of customers are considered, which are priority customers, ordinary customers and negative customers. The priority customers do not form any queue and have an exclusive preemptive priority to receive their services over ordinary customers. The negative customer is arriving during the service time of any positive customer, will remove the positive customer from the service. If the interrupted customer is an ordinary customer, he will leave the system. As soon as the orbit becomes empty at the time of service completion, the server goes for a working vacation. The server works at a lower speed during a working vacation period. Using the supplementary variable technique, the steady state probability generating function of the system and its orbit are found. Some numerical examples are presented.
Keywords: retrial queues; priority queues; negative customers; working vacations; supplementary variable technique;.
New Semi-Analytical Method for Solving Two Point Nth Order
Fuzzy Boundary Value Problem
by A.L.I. JAMEEL, Nidal Ratib Anakira, ABEDEL-KARREM Alomari, Doaa Alsharo, Azizan Saaban
Abstract: In this paper, a semi analytical algorithm, namely Homotopy Analysis Method (HAM) is presented for the first time to obtain approximate analytical solutions of nth order two point fuzzy boundary value problems (TPFBVP) involving ordinary differential equations. This method allows for the solution of the TPFBVP to be calculated in the form of an infinite series with the components that can be easily calculated. The HAM utilizes a convergence control parameter to control the convergence region of the infinite series solution. Numerical experiment is tested to highlight the important features of the HAM algorithm. Comparison of the HAM results and available exact solution reveal that this algorithm is effective and simple and for solving TPFBVP.
Keywords: Fuzzy numbers; Two point fuzzy boundary value problems; Homotopy Analysis Method.
BOUNDARY ELEMENT APPROACH OF SOLVING FREDHOLM AND VOLTERRA INTEGRAL EQUATIONS
by Sudeshna Banerjea, Rumpa Chakraborty, Anushree Samanta
Abstract: A simple numerical technique namely boundary element method is employed here tornsolve Fredholm and Volterra integral equations of second kind. In this method the integral equation is converted in to a system of linear algebraic equations by discretizing the range of the integration and interval of definition into finite number of line elements. By solving the system of linear equations by standard technique the solution of the integral equation is obtained for points in each line element. The method is computationally very simple and gives quite accurate results.
Keywords: Fredholm and Volterra integral equation. Boundary element method. Linernelements; System of linear equations; Approximate solution; Relative error.
Portfolio Optimization with Nonlinear Transaction Costs
by Jimbo Henri Claver
Abstract: In this paper, we consider the portfolio selection problem, with nonlinear transaction costs, basic constraints and probabilistic constraints. Such a problem cannot be handled by the usual quadratic or convex optimization methods. We develop a heuristic method which yields to computation of efficient (suboptimal) solution of the problem. We describe our heuristic method for finding optimal portfolio based on solving many small optimization problems over large generation number, thus we obtain a good suboptimal solution. Experimental results are demonstrated with various widely used indexes: stocks in US market: U.S. three months treasury bills, U.S. long term government bonds, S&P 500, Wilshire 5000, NASDAQ, Lehman Brothers corporate bond index, EAFE foreign stock index, and Gold recorded from (Jan 2000 Jan 2008) with enhanced performance. Finally, our results suggest that nonlinear transactions costs improve considerably the value of optimal portfolio over investment period, especially for portfolio with smaller among of assets.
Keywords: Portfolio selection; exponential transaction cost; efficient frontier; optimization; expected return; portfolio risk; portfolio gain.
New Hybrid Algorithm based on Nonmonotone spectral gradient and Simultaneous Perturbation
by Zineb Tabbakh, Rachid Ellaia, Abderrahmane Habbal
Abstract: In this paper, we introduce a new hybrid method called Nonmonotone Spectral Gradient and Simultaneous Perturbation (NSGSP).
It combines the advantages of nonmonotone spectral gradient (NSG), and simultaneous perturbation (SP) methods.
The main idea of our approach is to use the simultaneous perturbation (SP) method in order to get a non expensive estimate of the gradient, and exploit the good properties of the nonmonotone spectral gradient (NSG) method in order to compute an efficient line search.
Several numerical experiments are provided. The results indicate that the new method is effective and outperforms most of other popular methods.
Keywords: Nonmonotone line search; spectral gradient method; Simultaneous Perturbation.