AN ANALYSIS OF THE DYNAMIC THEORY OF THE MULTI—PRODUCT FIRM USING THE CALCULUS OF VARIATIONS

The purpose of this paper is to present the theory of the multi-product firm in situations where the revenue function depends not only on the rate of output but also on changes in the rate of output, and, similarly, where the cost function depends on changes in the rate of factor utilization as well as the rate of their utilization. Since the analysis will utilize the calculus of variations, a general introduction to this technique is also presented. The model analyzed assumes perfect foresight and knowledge concerning the revenue, cost, and production functions, and the calculus of variations is used to derive the conditions for an extremum. The first section presents the mathematical model and the model of the firm, and the optimality conditions are discussed in the second section.     

An integrated production and inventory model for a whole manufacturing supply chain involving reverse logistics with finite horizon period

This paper proposes a model and solution method for coordinating integrated production and inventory cycles in a whole manufacturing supply chain involving reverse logistics for multiple items with finite horizon period. A whole manufacturing supply chain involving reverse logistic consists of tier-2 suppliers supplying raw materials to tier-1 suppliers, tier-1 suppliers producing parts, a manufacturer which manufactures and assembles parts from tier-1 suppliers into finished products, distributors distributing finished products to retailers, retailers selling products to end customers and a third party which collects the used finished products from end customers, dissembles collected products into parts, and feed the parts back to the supply chain. In this system, we consider a finite horizon period. A mathematical model for representing the behaviors of the system is developed. Solution methods based on decentralized and a combination of decentralized and centralized decision making process, referred to as the semi-centralized decision making process, are proposed to solve the model while the centralized decision making process is solved by a mixed integer nonlinear programming method. A numerical example is used to demonstrate the model and the solutions based on the three types of the coordination.     

Examining Localized Patterns of Air Quality Perception in Texas: A Spatial and Statistical Analysis

Environmental and human health issues associated with outdoor air pollution, such as ozone, sulfur dioxide, and other pollutants in metropolitan regions, are an area of growing concern for both policy officials and the general public. Increasing attention from the news media, new health data, and public debate over the effectiveness of clean air regulations have raised the importance of air quality in the public consciousness. While public perceptions of air quality have been studied thoroughly dating back to the 1960s, little empirical research has been conducted to explain the spatial aspects of these perceptions, particularly at the local level. Although recent studies suggest characteristics of local setting are important in shaping perceptions of air quality, the roles of proximity, neighborhood characteristics, and location have not been clarified. This study seeks to improve understanding of the major factors shaping public perceptions of air quality by examining the spatial pattern of local risk perception, the role of socioeconomic characteristics in forming these perceptions, and the relationship between perceived and scientifically measured air pollution. First, we map the spatial pattern of local air quality perceptions using Geographic Information Systems (GIS) across the Dallas and Houston metropolitan areas. Next, we explain these perceptions through local contextual factors using both bivariate correlations and multivariate regression analysis. Results indicate that perceptions of air quality in the study areas are not significantly correlated with air quality based on readings of air monitoring stations. Instead, perceptions appear to be influenced by setting (urban vs. rural), state identification, access to information, and socioeconomic characteristics such as age, race, and political identification. We discuss the implications of the findings and provide direction on how further research can provide a deeper understanding of the local contextual factors influencing public perceptions.     

Birth outcome, not pregnancy process: Reply to van der Veen

In a recent article (Frisbie. Forbes. and Pullum 1996) we documented racial/ethnic differences in birth outcomes according to a more fine-grained classification than has typically been employed in the demographic literature. In his commentary, van der Veen focuses on the measurement of one of the dimensions of that classification, maturity of the infant. as proxied by the fetal growth ratio. The crux of the critique is easily seen in van der Veen's statement that “all of my disagreements with Frisbie et al. 's method arise from their particular use of a postnatal standard for the assessment of intrauterine growth.” Our critic misunderstands our objective: He fails to realize our interest in birth outcome, not pregnancy process, and does not perceive that our intent was to extend the research extant in both the demographic and public-health literatures in which patently postnatal (i.e., ex utero) measures are taken as outcomes interesting in their own right and/or as risk factors for infant mortality and infant and childhood morbidity. Specifically, he does recognize that we purposefully expanded our focus to include moderately compromised births to determine if they were at higher risk than the normal births with whom they are conventionally categorized. Our discussion draws on research cited in the original article, on studies cited by our critic, and on a few more recent investigations. Although we have never argued that ours is the only, or even the best, approach in all cases, we try to clarify the rationale for, and adduce additional empirical evidence of, the utility of the method we used.     

Drug dependency and HIV testing among state prisoners

HIV and drug use are higher among prisoners than the general US population. This study examines drug dependency/use and differences between prisoners who volunteered for HIV testing and those who did not in a less densely populated state. It was hypothesized that prisoners who volunteered for an HIV test were engaged in more drug use and other risky behaviors than those who did not. Survey data were collected from 600 randomly selected inmates (567 males and 33 females) from 15 state prisons. Subjects were male (95%), white (63%), never married (43%), and 44% volunteered for an HIV test since entering prison. Ninety-two percent of inmates met DSM criteria for drug dependence in their lifetime. Those who volunteered for HIV testing were 2.6 times more likely to ever have used PCP; 1.5 times more likely to ever have used cocaine; 1.4 times more likely to ever have had a problem with drugs; 1.3 times more likely to have used opiates, and 1.6 times more likely to report having been sexually or physically abused. Implications for interventions are discussed.     

An Investigation of Measures of Modern and Old-Fashioned Sexism

Working from the Principle of Beneficence we make the case that there is a need for adequate measures of sexism in men and women. Swim, Aikin, Hall and Hunter (1995) suggest that modern sexism represents a constellation of beliefs in which individuals: (a) disavow women's present-day discrimination; (b) reject women's demands for political and economic power; and (c) disapprove of policies designed to promote gender equality. To assess this construct, Swim et al. (1995) developed the Modern Sexism Scale (MSS), and to date, few studies have assessed its reliability and factor structure. Using data from 187 Canadian participants, confirmatory factor analysis was used to assess the unidimensionality of the MSS and Swim and associates' (1995) Old-Fashioned Sexism Scale (OFSS). Results do not support Swim et al.'s conceptualization of modern sexism as a unidimensional construct; however, the OFSS fit a unidimensional model. The implications of these findings are discussed.