Configuration of flexibility strategies under supply uncertainty

In this paper, we study a buyer׳s configuration of flexibility strategies under supply uncertainty. His main supplier׳s production process is uncertain, and he can either choose pricing flexibility (setting prices depending on the available supply) or operational flexibility (requesting a contingent order from a backup supplier). As the buyer may or may not find a suitable contingent supplier ex post, we study two scenarios that the backup supplier׳s supply is infinite, and that this supply is random. We also include the factor that the main supplier may determine the wholesale price. We demonstrate that the adoption of flexibility strategies is controlled by threshold policies in different scenarios whether the main supplier determines the wholesale price or not. We also investigate how the buyer׳s attribute (finding a suitable contingent supplier) affects the configuration of flexibility strategies.     

Generalized Estimation of the BLUP in Mixed-Effects Models: A Comparison with ML and REML

The Best Linear Unbiased Predictor (BLUP) in mixed models is a function of the variance components and they are estimated using maximum likelihood (ML) or restricted ML methods. Nonconvergence of BLUP would occur due to a drawback of the standard likelihood-based approaches. In such situations, ML and REML either do not provide any BLUPs or all become equal. To overcome this drawback, we provide a generalized estimate (GE) of BLUP that does not suffer from the problem of negative or zero variance components, and compare its performance against the ML and REML estimates of BLUP. Simulated and published data are used to compare BLUP.     

A Bivariate Distribution Family with Specified Correlation Coefficient and Given Marginals

For given continuous distribution functions F(x) and G(y) and a Pearson correlation coefficient ρ, an algorithm is provided to construct a sequence of continuous bivariate distributions with marginals equal to F(x) and G(y) and the corresponding correlation coefficient converges to ρ. The algorithm can be easily implemented using S-Plus or R. Applications are given to generate bivariate random variables with marginals including Gamma, Beta, Weibull, and uniform distributions.     

Multilevel regression mixture analysis

Summary.  A two-level regression mixture model is discussed and contrasted with the conventional two-level regression model. Simulated and real data shed light on the modelling alternatives. The real data analyses investigate gender differences in mathematics achievement from the US National Education Longitudinal Survey. The two-level regression mixture analyses show that unobserved heterogeneity should not be presupposed to exist only at level 2 at the expense of level 1. Both the simulated and the real data analyses show that level 1 heterogeneity in the form of latent classes can be mistaken for level 2 heterogeneity in the form of the random effects that are used in conventional two-level regression analysis. Because of this, mixture models have an important role to play in multilevel regression analyses. Mixture models allow heterogeneity to be investigated more fully, more correctly attributing different portions of the heterogeneity to the different levels.     

Precedence probabilities and their applications

In precedence tests, the test powers are given by the probabilities P(Y_(i) > X_(j)) for some i and j, where X_(j) and Y_(i) are the order statistics of two independent random samples. Such probabilities can also arise in reliability theory. In this paper, we investigate the properties of these probabilities and their applications.     

On some probability distributions associated with random walks

The probability distribution of the total number of games to ruin in a gambler's ruin random walk with initial position n, the probability distribution of the total size of an epidemic starting with n cases and the probability distribution of the number of customers served during a busy period M/M/1 when the service starts with n waiting customers are identical. All these can be easily obtained by using Lagrangian expansions instead of long combinatorial methods. The binomial, trinomial, quadrinomial and polynomial random walks of a particle have been considered with an absorbing barrier at 0 when the particle starts its walks from a point n, and the pgfs. and the probability distributions of the total number of jumps (trials) before absorption at 0 have been obtained. The values for the mean and variance of such walks have also been given.     

Optimal Designs for Random Coefficient Regression Models with Heteroscedastic Errors

The purpose of this article is to present the optimal designs based on D-, G-, A-, I-, and D _β-optimality criteria for random coefficient regression (RCR) models with heteroscedastic errors. A sufficient condition for the heteroscedastic structure is given to make sure that the search of optimal designs can be confined at extreme settings of the design region when the criteria satisfy the assumption of the real valued monotone design criteria. Analytical solutions of D-, G-, A-, I-, and D _β-optimal designs for the RCR models are derived. Two examples are presented for random slope models with specific heteroscedastic errors.     

Shrinkage Structure of Partial Least Squares

Partial least squares regression (PLS) is one method to estimate parameters in a linear model when predictor variables are nearly collinear. One way to characterize PLS is in terms of the scaling (shrinkage or expansion) along each eigenvector of the predictor correlation matrix. This characterization is useful in providing a link between PLS and other shrinkage estimators, such as principal components regression (PCR) and ridge regression (RR), thus facilitating a direct comparison of PLS with these methods. This paper gives a detailed analysis of the shrinkage structure of PLS, and several new results are presented regarding the nature and extent of shrinkage.     

SOJOURN TIMES IN NON-HOMOGENEOUS QBD PROCESSES WITH PROCESSOR SHARING

We study sojourn times of customers in a processor sharing queue with a service rate that varies over time, depending on the number of customers and on the state of a random environment. An explicit expression is derived for the Laplace–Stieltjes transform of the sojourn time conditional on the state upon arrival and the amount of work brought into the system. Particular attention is paid to the conditional mean sojourn time of a customer as a function of his required amount of work, and we establish the existence of an asymptote as the amount of work tends to infinity. The method of random time change is then extended to include the possibility of a varying service rate. By means of this method, we explain the well-established proportionality between the conditional mean sojourn time and required amount of work in processor sharing queues without random environment. Based on numerical experiments, we propose an approximation for the conditional mean sojourn time. Although first presented for exponentially distributed service requirements, the analysis is shown to extend to phase-type services. The service discipline of discriminatory processor sharing is also shown to fall within the framework.     

Random Accessibility as a Parallelism to Reliability Studies on Simple Graphs

ABSTRACT

Graphs are classified according to the numbers of vertices and edges they contain. For simple graphs a concept of accessibility is defined and its relation to the graph reliability problem is investigated. Exact results are derived for special subclasses of bipartite and tripartite graphs in relation to accessibility. Several conjectures on the relation of accessibility and all-terminal reliability are numerically illustrated without proof.