A Model for Resource Constrained Production and Inventory Management

We present a general model for multi-item production and inventory management problems that include a resource restriction. The decision variables in the model can take on a variety of interpretations, but will typically represent cycle times, production batch sizes, number of production runs, or order quantities for each item. We consider environments where item demand rates are approximately constant and performing an activity such as producing a batch of a product or placing an order results in the consumption of a scarceresource that is shared among the items. Some examples of shared resources include limited machine capacity, a restriction on the amount of money that can be tied up in stock, orlimited storage capacity. We focus on the case where the decision variables must be integer valued or selected from a discrete set of choices, such as when an integer number of production runs is desired for each item, or in order quantity problems where the items come in pack sizes containing more than one unit and, therefore, the order quantities must be an integer multiple of the pack sizes. We develop a heuristic and a branch and bound algorithm for solving the problem. The branch and bound algorithm includes reoptimization procedures and the heuristic to improve its performance. Computational testing indicates that the algorithms are effective for solving the general model.     

Migrant fertility in Ghana: selection versus adaptation and disruption as causal mechanisms

The aim of the study presented in this paper is to disentangle the roles of three mechanisms -- selection, adaptation, and disruption -- in influencing migrant fertility in Ghana. Using data from the 1998 Ghana Demographic and Health Survey, we fit Poisson and sequential logit regression models to discern the effects of the above mechanisms on cumulative fertility and annual probabilities of birth. Characteristics of migrants from four types of migration stream are examined and compared with those of non-migrants at origin and destination. We find substantial support for the selection hypothesis among both rural-urban and urban-rural migrants. Disruption is evident only in the fertility timing of second and higher-order births in Ghana. Our finding that migrants bear children at about the same rates as the natives at destination implies that the growth rate of cities will slow down quickly and that the rural population will continue to have high fertility. Thus to achieve a reduction in the national fertility level, family planning activities need to be directed towards rural areas.     

Generation Status,Social Capital,and the Routes Out of High School

This study investigates immigrant-native differences in the activities of adolescents 2 years after their sophomore year of high school. We employ longitudinal data for the modeling of duration, nativity and generation differences in education and employment activities during late adolescence. We ask if the same human and social capital characteristics employed as explanations for nativity differences in achievement are predictive of high school participation versus other activities such as labor force participation within a cohort of adolescents. Despite their lower levels of human capital and lower previous academic performance, recent immigrants who arrive in the United States as adolescents are more likely than those who arrive earlier or those born in the United States to persevere in high school. Access to familial social capital and attitudinal measures help explain some of this effect. As for those who do leave school early, socioeconomic status and language background play a role in the activities respondents pursue. While recent immigrants are more likely to persevere in high school, once they leave they are no more likely to pursue additional education than their U.S. born counterparts.     

Horizontal Hostility; Relations Between Similar Minority Groups

Two studies were conducted to examine the relations between similar minority groups. We predicted that minority group members would show horizontal hostility, a form of prejudice, against members of a similar, but more mainstream, minority group. The results of both studies confirmed this hypothesis. In Study 1, members of 3 Jewish congregations (reform, conservative, orthodox) showed prejudice against a member of a similar but slightly more secular congregation. In Study 2, members of a college varsity soccer team showed prejudice against junior varsity players. We conclude by suggesting that horizontal hostility is the result of social changes since Allport (1954) wrote The Nature of Prejudice. Members of minority groups value their minority social identity, even when the group is stigmatized. The positive value of minority social identity causes group members to look down on members of similar, more mainstream groups.     

Testing for Regime Switching

We analyze use of a quasi‐likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a Markov regime‐switching context. This test exploits mixture properties implied by the regime‐switching process, but ignores certain implied serial correlation properties. When formulated in the natural way, the setting is nonstandard, involving nuisance parameters on the boundary of the parameter space, nuisance parameters identified only under the alternative, or approximations using derivatives higher than second order. We exploit recent advances by Andrews (2001) and contribute to the literature by extending the scope of mixture models, obtaining asymptotic null distributions different from those in the literature. We further provide critical values for popular models or bounds for tail probabilities that are useful in constructing conservative critical values for regime‐switching tests. We compare the size and power of our statistics to other useful tests for regime switching via Monte Carlo methods and find relatively good performance. We apply our methods to reexamine the classic cartel study of Porter (1983) and reaffirm Porter's findings.     

Uncertainties in Pharmacokinetic Modeling for Perchloroethylene. I. Comparison of Model Structure, Parameters, and Predictions for Low-Dose Metabolism Rates for Models Derived by Different Authors

In recent years physiologically based pharmacokinetic models have come to play an increasingly important role in risk assessment for carcinogens. The hope is that they can help open the black box between external exposure and carcinogenic effects to experimental observations, and improve both high-dose to low-dose and interspecies projections of risk. However, to date, there have been only relatively preliminary efforts to assess the uncertainties in current modeling results. In this paper we compare the physiologically based pharmacokinetic models (and model predictions of risk-related overall metabolism) that have been produced by seven different sets of authors for perchloroethylene (tetrachloroethylene). The most striking conclusion from the data is that most of the differences in risk-related model predictions are attributable to the choice of the data sets used for calibrating the metabolic parameters. Second, it is clear that the bottom-line differences among the model predictions are appreciable. Overall, the ratios of low-dose human to bioassay rodent metabolism spanned a 30-fold range for the six available human/rat comparisons, and the seven predicted ratios of low-dose human to bioassay mouse metabolism spanned a 13-fold range. (The greater range for the rat/human comparison is attributable to a structural assumption by one author group of competing linear and saturable pathways, and their conclusion that the dangerous saturable pathway constitutes a minor fraction of metabolism in rats.) It is clear that there are a number of opportunities for modelers to make different choices of model structure, interpretive assumptions, and calibrating data in the process of constructing pharmacokinetic models for use in estimating "delivered" or "biologically effective" dose for carcinogenesis risk assessments. We believe that in presenting the results of such modeling studies, it is important for researchers to explore the results of alternative, reasonably likely approaches for interpreting the available data--and either show that any conclusions they make are relatively insensitive to particular interpretive choices, or to acknowledge the differences in conclusions that would result from plausible alternative views of the world.     

Comparison of cancer slope factors using different statistical approaches.

The U.S. Environmental Protection Agency's cancer guidelines ( USEPA, 2005 ) present the default approach for the cancer slope factor (denoted here as s*) as the slope of the linear extrapolation to the origin, generally drawn from the 95% lower confidence limit on dose at the lowest prescribed risk level supported by the data. In the past, the cancer slope factor has been calculated as the upper 95% confidence limit on the coefficient (q*₁) of the linear term of the multistage model for the extra cancer risk over background. To what extent do the two approaches differ in practice? We addressed this issue by calculating s* and q*₁ for 102 data sets for 60 carcinogens using the constrained multistage model to fit the dose‐response data. We also examined how frequently the fitted dose‐response curves departed appreciably from linearity at low dose by comparing q₁, the coefficient of the linear term in the multistage polynomial, with a slope factor, s_c, derived from a point of departure based on the maximum liklihood estimate of the dose‐response. Another question we addressed is the extent to which s* exceeded s_c for various levels of extra risk. For the vast majority of chemicals, the prescribed default EPA methodology for the cancer slope factor provides values very similar to that obtained with the traditionally estimated q*₁. At 10% extra risk, q*₁/s* is greater than 0.3 for all except one data set; for 82% of the data sets, q*₁ is within 0.9 to 1.1 of s*. At the 10% response level, the interquartile range of the ratio, s*/s_c, is 1.4 to 2.0.     

On computer generation of balanced arrays

This paper provides an algebraic (and hence computing) procedure for generation of balanced arrays having two symbols, m rows, specified minimum and maximum column weights, arbitrary strength t≦m, and index set parameters μ^t₁, μ^t₂,…, μ^t_t. μ^t₀ is unspecified, and calculated as part of the algorithm, although the procedure for specifying it is straightforward and can be used if desired. Array generation is herein reduced to finding integral solutions to a linear programming problem. It is shown that the integral solutions of the system of equations comprise all balanced arrays with the given set of parameters.A computing algorithm is provided which constructs the system of equations to be solved; it has been interfaced with a standard linear programming package to provide some preliminary results.Additional algorithms whose development should result in substantial decreases in computing costs are discussed.