http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/605064We apply the homotopy analysis method (HAM) for solving the multipantograph equation. The analytical results have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy analysis method. Comparisons are made to confirm the reliability of the homotopy analysis method.Fadi Awawdeh, Ahmad Adawi, and Safwan Al-Shara'© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/745463Indoor residual spraying—spraying insecticide inside houses to kill mosquitoes—is an important method for controlling malaria vectors in sub-Saharan Africa. We propose a mathematical model for both regular and non-fixed spraying, using impulsive differential equations. First, we determine the stability properties of the nonimpulsive system. Next, we derive minimal effective spraying intervals and the degree of spraying effectiveness required to control mosquitoes when spraying occurs at regular intervals. If spraying is not fixed, then we determine the “next best” spraying times. We also consider the effects of climate change on the prevalence of mosquitoes. We show that both regular and nonfixed spraying will result in a significant reduction in the overall number of mosquitoes, as well as the number of malaria cases in humans. We thus recommend that the use of indoor spraying be re-examined for widespread application in malaria-endemic areas.Robert J. Smith? and Senelani D. Hove-Musekwa© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/483267Operations researchers have always assumed that when a product's unit cost is constant and its demand curve is known and stationary, a retailer of the product would find it optimal to replenish the inventory with a fixed quantity and to sell the product always at a fixed price. We present, with proof, a model that shows that, in such a case, an e-tailer is better off using a continuously increasing price strategy than using a fixed price strategy within each inventory cycle. Sensitivity analysis shows that this strategy is particularly profitable when demand is highly price sensitive and the inventory ordering and carrying costs are high.Prafulla Joglekar, Patrick Lee, and Alireza M. Farahani© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/795869We study the impact of the efforts aimed at reducing the lead-time variability in a quality-adjusted stochastic inventory model. We assume that each lot contains a random number of defective units. More specifically, a logarithmic investment function is used that allows investment to be made to reduce lead-time variability. Explicit results for the optimal values of decision variables as well as optimal value of the variance of lead-time are obtained. A series of numerical exercises is presented to demonstrate the use of the models developed in this paper. Initially the lead-time variance reduction model (LTVR) is compared to the quality-adjusted model (QA) for different values of initial lead-time over uniformly distributed lead-time intervals from one to seven weeks. In all cases where investment is warranted, investment in lead-time reduction results in reduced lot sizes, variances, and total inventory costs. Further, both the reduction in lot-size and lead-time variance increase as the lead-time interval increases. Similar results are obtained when lead-time follows a truncated normal distribution. The impact of proportion of defective items was also examined for the uniform case resulting in the finding that the total inventory related costs of investing in lead-time variance reduction decrease significantly as the proportion defective decreases. Finally, the results of sensitivity analysis relating to proportion defective, interest rate, and setup cost show the lead-time variance reduction model to be quite robust and representative of practice.Farrokh Nasri, Javad Paknejad, and John Affisco© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/825156The aim of this paper is to formulate the mathematical relationship between firms potential ability and their applied efforts to attract the body of unattached customers. A method is devised in this paper by which management techniques imposed by a particular firm can evaluate its market share. This paper demonstrates the relationship between the applied marketing effort of management and the potential ability of the firm in determining its market share. This paper also investigates the effect of a number of simultaneous marketing impulses on the movement of the body of unattached customers and hence on the size of the market share.Mokhtar M. Metwally© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/760191Integer linear fractional programming problem with multiple objective (MOILFP) is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.Mohamed El-Amine Chergui and Mustapha Moulaï© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/463781Smooth tests for the logarithmic distribution are compared with three tests: the first is a test due to Epps and is based on a probability generating function, the second is the Anderson-Darling test, and the third is due to Klar and is based on the empirical integrated distribution function. These tests all have substantially better power than the traditional Pearson-Fisher X2 test of fit for the logarithmic. These traditional chi-squared tests are the only logarithmic tests of fit commonly applied by ecologists and other scientists.D. J. Best, J. C. W. Rayner, and O. Thas© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/218140The correspondence analysis of a two-way contingency table is now accepted as a very versatile tool for helping users to understand the structure of the association in their data. In cases where the variables consist of ordered categories, there are a number of approaches that can be employed and these generally involve an adaptation of singular value decomposition. Over the last few years, an alternative decomposition method has been used for cases where the row and column variables of a two-way contingency table have an ordinal structure. A version of this approach is also available for a two-way table where one variable has a nominal structure and the other variable has an ordinal structure. However, such an approach does not take into consideration the presence of the nominal variable. This paper explores an approach to correspondence analysis using an amalgamation of singular value decomposition and bivariate moment decomposition. A benefit of this technique is that it combines the classical technique with the ordinal analysis by determining the structure of the variables in terms of singular values and location, dispersion and higher-order moments.Eric J. Beh© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/83852A Cox process NCox directed by a stationary random measure ξ has second moment var NCox(0,t]=E(ξ(0,t])+var ξ(0,t], where by stationarity E(ξ(0,t])=(const.)t=E(NCox(0,t]), so long-range dependence (LRD) properties of NCox coincide with LRD properties of the random measure ξ. When ξ(A)=∫AνJ(u)du is determined by a density that depends on rate parameters νi(i∈𝕏) and the current state J(⋅) of an 𝕏-valued stationary irreducible Markov renewal process (MRP) for some countable state space 𝕏 (so J(t) is a stationary semi-Markov process on 𝕏), the random measure is LRD if and only if each (and then by irreducibility, every) generic return time Yjj(j∈X) of the process for entries to state j has infinite second moment, for which a necessary and sufficient condition when 𝕏 is finite is that at least one generic holding time Xj in state j, with distribution function (DF)Hj, say, has infinite second moment (a simple example shows that this condition is not necessary when 𝕏 is countably infinite). Then, NCox has the same Hurst index as the MRP NMRP that counts the jumps of J(⋅), while as t→∞, for finite 𝕏, var NMRP(0,t]∼2λ2∫0t𝒢(u)du, var NCox(0,t]∼2∫0t∑i∈𝕏(νi−ν¯)2ϖiℋi(t)du, where ν¯=∑iϖiνi=E[ξ(0,1]], ϖj=Pr{J(t)=j},1/λ=∑jpˇjμj, μj=E(Xj), {pˇj} is the stationary distribution for the embedded jump process of the MRP, ℋj(t)=μi−1∫0∞min(u,t)[1−Hj(u)]du, and 𝒢(t)∼∫0tmin(u,t)[1−Gjj(u)]du/mjj∼∑iϖiℋi(t) where Gjj is the DF and mjj the mean of the generic return time Yjj of the MRP between successive entries to the state j. These two variances are of similar order for t→∞ only when each ℋi(t)/𝒢(t) converges to some [0,∞]-valued constant, say, γi, for t→∞.D. J. Daley, T. Rolski, and R. Vesilo© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/13749We present an excursion with Jeff Hunter, visiting some of his research topics. Specifically, we will present some facts about certain people whose work seems to have influenced Jeff in his scientific career; we illustrate our presentation with postage stamps that have been issued in honour of these people. Our main guide is Hunter’s two-volume book entitled Mathematical Techniques of Applied Probability (Academic Press, 1983).George P. H. Styan and Götz Trenkler© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/94515We will place certain parts of the theory of statistical efficiency into the author's operator trigonometry (1967), thereby providing new geometrical understanding of statistical efficiency. Important earlier results of Bloomfield and Watson, Durbin and Kendall, Rao and Rao, will be so interpreted. For example, worse case relative least squares efficiency corresponds to and is achieved by the maximal turning antieigenvectors of the covariance matrix. Some little-known historical perspectives will also be exposed. The overall view will be emphasized.K. Gustafson© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/68280Consider a network of parallel finite tandem queues with two stages, where each arrival attempts to minimize its own cost due to loss. It is known that the user optimal and asymptotic system optimal policies may differ—we give examples showing that they may differ for finite systems and that as the service rate is increased at the second stage the user optimal policy may change in such a way that the total expected cost due to loss increases.Ilze Ziedins© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/37475In this paper, a procedure based on M-estimation to determine the number of regression models for the problem of regression clustering is proposed. We have shown that the true classification is attained when n increases to infinity under certain mild conditions, for instance, without assuming normality of the distribution of the random errors in each regression model.C. R. Rao, Y. Wu, and Q. Shao© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/24053Lq-penalized regression arises in multidimensional statistical modelling where all or part of the regression coefficients are penalized to achieve both accuracy and parsimony of statistical models. There is often substantial computational difficulty except for the quadratic penalty case. The difficulty is partly due to the nonsmoothness of the objective function inherited from the use of the absolute value. We propose a new solution method for the general Lq-penalized regression problem based on space transformation and thus efficient optimization algorithms. The new method has immediate applications in statistics, notably in penalized spline smoothing problems. In particular, the LASSO problem is shown to be polynomial time solvable. Numerical studies show promise of our approach.Tracy Zhou Wu, Yingyi Chu, and Yan Yu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/57619Paul Cowpertwait, Graeme Wake, Robert D. Anderson, Howard Edwards, and Shayle Searle© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/86180Using a projection approach, we obtain an asymptotic information bound for estimates of parameters in general regression models under choice-based and two-phase outcome-dependent sampling. The asymptotic variances of the semiparametric estimates of Scott and Wild (1997, 2001) are compared to these bounds and the estimates are found to be fully efficient.Alan Lee© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/98086Markov chain theory plays an important role in statistical inference both in the formulation of models for data and in the construction of efficient algorithms for inference. The use of Markov chains in modeling data has a long history, however the use of Markov chain theory in developing algorithms for statistical inference has only become popular recently. Using mark-recapture models as an illustration, we show how Markov chains can be used for developing demographic models and also in developing efficient algorithms for inference. We anticipate that a major area of future research involving mark-recapture data will be the development of hierarchical models that lead to better demographic models that account for all uncertainties in the analysis. A key issue is determining when the chains produced by Markov chain Monte Carlo sampling have converged.Richard J. Barker and Matthew R. Schofield© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/48138Patch clamp recordings from ion channels often show bursting behaviour, that is, periods of repetitive activity, which are noticeably separated from each other by periods of inactivity. A number of authors have obtained results for important properties of theoretical and empirical bursts when channel gating is modelled by a continuous-time Markov chain with a finite-state space. We show how the use of marked continuous-time Markov chains can simplify the derivation of (i) the distributions of several burst properties, including the total open time, the total charge transfer, and the number of openings in a burst, and (ii) the form of these distributions when the underlying gating process is time reversible and in equilibrium.Frank G. Ball, Robin K. Milne, and Geoffrey F. Yeo© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/56372We look at fitting regression models using data from stratified cluster samples when the strata may depend in some way on the observed responses within clusters. One important subclass of examples is that of family studies in genetic epidemiology, where the probability of selecting a family into the study depends on the incidence of disease within the family. We develop the survey-weighted estimating equation approach for this problem, with particular emphasis on the estimation of superpopulation parameters. Full maximum likelihood for this class of problems involves modelling the population distribution of the covariates which is simply not feasible when there are a large number of potential covariates. We discuss efficient semiparametric maximum likelihood methods in which the covariate distribution is left completely unspecified. We further discuss the relative efficiencies of these two approaches.Alastair Scott and Chris Wild© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/18014We consider the pricing of exotic options when the price dynamics of the underlying risky asset are governed by a discrete-time Markovian regime-switching process driven by an observable, high-order Markov model (HOMM). We assume that the market interest rate, the drift, and the volatility of the underlying risky asset's return switch over time according to the states of the HOMM, which are interpreted as the states of an economy. We will then employ the well-known tool in actuarial science, namely, the Esscher transform to determine an equivalent martingale measure for option valuation. Moreover, we will also investigate the impact of the high-order effect of the states of the economy on the prices of some path-dependent exotic options, such as Asian options, lookback options, and barrier options.Wai-Ki Ching, Tak-Kuen Siu, and Li-Min Li© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/51801We consider some simple Markov and Erlang queues with limited storage space. Although the departure processes from some such systems are known to be Poisson, they actually consist of the superposition of two complex correlated processes, the overflow process and the output process. We measure the cross-correlation between the counting processes for these two processes. It turns out that this can be positive, negative, or even zero (without implying independence). The models suggest some general principles on how big these correlations are, and when they are important. This may suggest when renewal or moment approximations to similar processes will be successful, and when they will not.Don McNickle© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/90842A generalized Weibull model that allows instantaneous or early failures is modified so that the model can be expressed as a mixture of the uniform distribution and the Weibull distribution. Properties of the resulting distribution are derived; in particular, the probability density function, survival function, and the hazard rate function are obtained. Some selected plots of these functions are also presented. An R script was written to fit the model parameters. An application of the modified model is illustrated.C. D. Lai, Michael B. C. Khoo, K. Muralidharan, and M. Xie© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/43565To increase the reliability of modules, and thus of systems assembled from them, they are frequently constructed using parallel load-sharing components. Examples include jet engines, electrical power networks, and telecommunications networks. We consider the situation when the components operate independently, but when any one of them fails, the load of the failed component is instantaneously distributed among the working components. The entire module fails when the last working component fails. We analyze the survival probability and residual life expectancy of such modules. An obvious application is to the case of the 1998 Auckland power supply failure in New Zealand.Mark Bebbington, Chin-Diew Lai, and Ričardas Zitikis© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/56404We study the integrated fishery planning problem (IFP). In this problem, a fishery manager must schedule fishing trawlers to determine when and where the trawlers should go fishing and when the trawlers should return the caught fish to the factory. The manager must then decide how to process the fish into products at the factory. The objective is to maximize profit. We have found that IFP is difficult to solve. The initial formulations for several planning horizons are solved using the AMPL modelling language and CPLEX with branch and bound. The IFP can be decomposed into a trawler-scheduling subproblem and a fish-processing subproblem in two different ways by relaxing different sets of constraints. We tried conventional decomposition techniques including subgradient optimization and Dantzig-Wolfe decomposition, both of which were unacceptably slow. We then developed a decomposition-based pricing method for solving the large fishery model, which gives excellent computation times. Numerical results for several planning horizon models are presented.M. Babul Hasan and John F. Raffensperger© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/20489Ordinal consensus ranking problems have received much attention in the management science literature. A problem arises in situations where a group of k decision makers (DMs) is asked to rank order n alternatives. The question is how to combine the DM rankings into one consensus ranking. Several different approaches have been suggested to aggregate DM responses into a compromise or consensus ranking; however, the similarity of consensus rankings generated by the different algorithms is largely unknown. In this paper, we propose a new hybrid distance-based ideal-seeking consensus ranking model (DCM). The proposed hybrid model combines parts of the two commonly used consensus ranking techniques of Beck and Lin (1983) and Cook and Kress (1985) into an intuitive and computationally simple model. We illustrate our method and then run a Monte Carlo simulation across a range of k and n to compare the similarity of the consensus rankings generated by our method with the best-known method of Borda and Kendall (Kendall 1962) and the two methods proposed by Beck and Lin (1983) and Cook and Kress (1985). DCM and Beck and Lin's method yielded the most similar consensus rankings, whereas the Cook-Kress method and the Borda-Kendall method yielded the least similar consensus rankings. Madjid Tavana, Frank LoPinto, and James W. Smither© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/94850This article considers a continuous review perishable (s,S) inventory system in which the demands arrive according to a Markovian arrival process (MAP). The lifetime of items in the stock and the lead time of reorder are assumed to be independently distributed as exponential. Demands that occur during the stock-out periods either enter a pool which has capacity N(<∞) or are lost. Any demand that takes place when the pool is full and the inventory level is zero is assumed to be lost. The demands in the pool are selected one by one, if the replenished stock is above s, with time interval between any two successive selections distributed as exponential with parameter depending on the number of customers in the pool. The waiting demands in the pool independently may renege the system after an exponentially distributed amount of time. In addition to the regular demands, a second flow of negative demands following MAP is also considered which will remove one of the demands waiting in the pool. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady state case. The measures of system performance in the steady state are calculated and the total expected cost per unit time is also considered. The results are illustrated numerically.Paul Manuel, B. Sivakumar, and G. Arivarignan© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/58248The key point of the tolerance relation or similarity relation presented in the literature is to assign a “null” value to all missing attribute values. In other words, a “null” value may be equal to any value in the domain of the attribute values. This may cause a serious effect in data analysis and decision analysis because the missing values are just “missed” but they do exist and have an influence on the decision. In this paper, we will introduce the modified similarity relation denoted by MSIM that is dependent on the number of missing values with respect to the number of the whole defined attributes for each object. According to the definition of MSIM, many problems concerning the generalized decisions are solved. This point may be used in scaling in statistics in a wide range. Also, a new definition of the discernibility matrix, deduction of the decision rules, and reducts in the present of the missing values are obtained.E. A. Rady, M. M. E. Abd El-Monsef, and W. A. Abd El-Latif© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/36729Sukanto Bhattacharya and Kuldeep Kumar© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/53606We consider the problem of determining realistic and easy-to-schedule lot sizes in a multiproduct, multistage manufacturing environment. We concentrate on a specific type of production, namely, flow shop type production. The model developed consists of two parts, lot sizing problem and scheduling problem. In lot sizing problem, we employ binary integer programming and determine reorder intervals for each product using power-of-two policy. In the second part, using the results obtained of the lot sizing problem, we employ mixed integer programming to determine schedules for a multiproduct, multistage case with multiple machines in each stage. Finally, we provide a numerical example and compare the results with similar methods found in practice.Esra Ekinci and Arslan M. Ornek© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/39460It has often been argued that there exists an underlying biological basis of utility functions. Taking this line of argument a step further in this paper, we have aimed to computationally demonstrate the biological basis of the Black-Scholes functional form as applied to classical option pricing and hedging theory. The evolutionary optimality of the classical Black-Scholes function has been computationally established by means of a haploid genetic algorithm model. The objective was to minimize the dynamic hedging error for a portfolio of assets that is built to replicate the payoff from a European multi-asset option. The functional form that is seen to evolve over successive generations which best attains this optimization objective is the classical Black-Scholes function extended to a multiasset scenario.Sukanto Bhattacharya and Kuldeep Kumar© 2008, Hindawi Publishing Corporation. All rights reserved.