Multiperiod Models with Capacities in Competitive Supply Chain

This paper considers a supply chain setting where several capacitated suppliers compete for orders from a single retailer in a multiperiod environment. At each period, the retailer places orders to the suppliers in response to the prices they announce. Each supplier has a fixed capacity. We consider a make‐to‐stock setting where the retailer can carry inventory. The retailer faces exogenous, price‐dependent demand. We study the problem using ideas from fluid models. In particular, we (i) analyze when there are pure equilibrium policies in this setting and characterize the structure of these policies; (ii) consider coordination mechanisms; and (iii) present some preliminary computational results. We also consider a modified model that uses option contracts to coordinate the supply chain.     

Generalized weibull family: a structural analysis

A two shape parameter generalization of the well known family of the Weibull distributions is presented and its properties are studied. The properties examined include the skewness and kurtosis, density shapes and tail character, and relation of the members of the family to those of the Pear-sonian system. The members of the family are grouped in four classes in terms of these properties. Also studied are the extreme value distributions and the limiting distributions of the extreme spacings for the members of the family. It is seen that the generalized Weibull family contains distributions with a variety of density and tail shapes, and distributions which in terms of skewness and kurtosis approximate the main types of curves of the Pearson system. Furthermore, as shown by the extreme value and extreme spacings distributions the family contains short, medium and long tailed distributions. The quantile and density quantile functions are the principle tools used for the structural analysis of the family.     

Comparing the Childrearing Lifetimes of Britain's Divorce-Revolution Men and Women

British men and women who became parents in the 1960s and 1970s were about to experience a new regime of marital instability. The effect of this on the balance between men's and women's contributions to childrearing is potentially very large. This study estimates the co-residential foundations of the new gender balance, focusing on the measurement of lifetime number of years of living with dependent-aged children. A variant of the family-status life table is used to combine two data sources: census panel observations of family status across three points ten years apart, and survey data on the years between censuses. One-quarter of women who became parents in the 1960s, and one-third of women who became parents in the 1970s, have been or will be a lone mother at some point. Lone parenthood is the main way in which women's childrearing lifetimes differ from men's, with seven and eight years respectively of lone motherhood per ever-lone-mother of the 1960s and 1970s parenting cohorts. Men's lone-father years and greater numbers of years spent in second families together provide an average of two years offset against women's lone mother years.     

Two sets of isotones for comparing tests of exponentiality

Isotones   are a deterministic graphical device introduced by Mudholkar et al. [1991. A graphical procedure for comparing goodness-of-fit tests. J. Roy. Statist. Soc. B 53, 221–232], in the context of comparing some tests of normality. An isotone of a test is a contour of p$p$ values of the test applied to “ideal samples”, called profiles, from a two-shape-parameter family representing the null and the alternative distributions of the parameter space. The isotone is an adaptation of Tukey's sensitivity curves, a generalization of Prescott's stylized sensitivity contours, and an alternative to the isodynes   of Stephens. The purpose of this paper is two fold. One is to show that the isotones can provide useful qualitative information regarding the behavior of the tests of distributional assumptions other than normality. The other is to show that the qualitative conclusions remain the same from one two-parameter family of alternatives to another. Towards this end we construct and interpret the isotones of some tests of the composite hypothesis of exponentiality, using the profiles of two Weibull extensions, the generalized Weibull and the exponentiated Weibull families, which allow IFR, DFR, as well as unimodal and bathtub failure rate alternatives. Thus, as a by-product of the study, it is seen that a test due to Csörg? et al. [1975. Application of characterizations in the area of goodness-of-fit. In: Patil, G.P., Kotz, S., Ord, J.K. (Eds.), Statistical Distributions in Scientific Work, vol. 2. Reidel, Boston, pp. 79–90], and Gnedenko's Q(r)$Q(r)$ test [1969. Mathematical Methods of Reliability Theory. Academic Press, New York], are appropriate for detecting monotone failure rate alternatives, whereas a bivariate F$F$ test due to Lin and Mudholkar [1980. A test of exponentiality based on the bivariate F$F$ distribution. Technometrics 22, 79–82] and their entropy test [1984. On two applications of characterization theorems to goodness-of-fit. Colloq. Math. Soc. Janos Bolyai 45, 395–414] can detect all alternatives, but are especially suitable for nonmonotone failure rate alternatives.