Dynamic strategies for branch and bound

Some straightforward but unconventional strategies are proposed for implementing branch and bound methods. These include ‘shrinking’ the branch and bound tree and instituting ‘branch reversals’ by reference to the notion of the relative influence of particular branches in the current solution. An attractive feature of these strategies is their ease of implementation, and the fact that they free the solution process from its customary dependency on early branches created on the basis of inadequate information.     

Capital Usage in Adverse Situations: Applying Bourdieu’s Theory of Capital to Family Farm Businesses

The paper applies Pierre Bourdieu’s theory of capital to explore how farming family businesses respond to critical changes by using different forms of capital. The paper tells the story of three cases from the United Kingdom (UK): case one lost the entire farm business in the 2001 Foot and Mouth Disease (FMD) crisis; case two the family had to overcome the sudden death of the farmer; and in case three the farmer was diagnosed with a terminal illness. The results indicate that levels of economic capital are adversely affected, whilst social and symbolic capitals are important in assisting family members to cope and continue the business operations. The paper raises questions for future research and provides interesting findings for those involved with family business.     

Improved Linear Programming Models for Discriminant Analysis*

Discriminant analysis is an important tool for practical problem solving. Classical statistical applications have been joined recently by applications in the fields of management science and artificial intelligence. In a departure from the methodology of statistics, a series of proposals have appeared for capturing the goals of discriminant analysis in a collection of linear programming formulations. The evolution of these formulations has brought advances that have removed a number of initial shortcomings and deepened our understanding of how these models differ in essential ways from other familiar classes of LP formulations. We will demonstrate, however, that the full power of the LP discriminant analysis models has not been achieved, due to a previously undetected distortion that inhibits the quality of solutions generated. The purpose of this paper is to show how to eliminate this distortion and thereby increase the scope and flexibility of these models. We additionally show how these outcomes open the door to special model manipulations and simplifications, including the use of a successive goal method for establishing a series of conditional objectives to achieve improved discrimination.     

Prenatal Depression and Infant Temperament: The Moderating Role of Placental Gene Expression

Prior research has demonstrated the link between maternal depression during pregnancy (i.e., prenatal depression) and increased neurodevelopmental dysregulation in offspring. However, little is known about the roles of key hypothalamic–pituitary axis regulatory genes in the placenta modulating this association. This study will examine whether placental gene expression levels of 11β‐hydroxysteroid dehydrogenase type 2 (HSD11B2), glucocorticoid receptor (NR3C1), and mineralocorticoid receptor (NR3C2) can help elucidate the underlying mechanisms linking prenatal depression to infant temperament, particularly in infants with high negativity and low emotion regulation. Stored placenta tissues (N = 153) were used to quantify messenger ribonucleic acid levels of HSD11B2, NR3C1, and NR3C2. Assessments of prenatal depression and infant temperament at 6 months of age were ascertained via maternal report. Results found that prenatal depression was associated with increased Negative Affectivity (p < .05) after controlling for postnatal depression and psychosocial characteristics. Furthermore, the association between prenatal depression and Negative Affectivity was moderated by gene expression levels of HSD11B2, NR3C1, and NR3C2 such that greater gene expression significantly lessened the association between prenatal depression and Negative Affectivity. Our findings suggest that individual differences in placental gene expression may be used as an early marker of susceptibility or resilience to prenatal adversity.     

On correlation analysis of many‐to‐many observations: an alternative to Pearson's correlation coefficient and its application to an ecotoxicological study

Correlation studies are an important hypothesis‐generating and testing tool, and have a wide range of applications in many scientific fields. In ecological studies in particular, multiple environmental variables are often measured in an attempt to determine relationships between chemical, physical and biological factors. For example, one may wish to know whether and how soil properties correlate with plant physiology. Although correlation coefficients are widely used, their properties and limitations are often imperfectly understood. This is especially the case when one is interested in correlations between, say, trace element content in sediments and in marine organisms, where no one‐to‐one correspondence exists. We show that evaluating Pearson's correlation coefficient for either site‐specific means or composite samples results in biased estimates, and we propose an alternative estimator. We use simulation studies to demonstrate that our estimator generally has a much smaller bias and mean squared error. We further illustrate its use in a case study of the correlation between trace element content in sediments and in mussels in Lyttelton Harbour, New Zealand.     

PITFALLS OF ROUNDING IN DISCRETE MANAGEMENT DECISION PROBLEMS

A number of articles on managerial decision making have addressed the issue of whether or not to round a fractional solution to obtain a solution for a problem involving discrete alternatives. (An example is the problem in which the decision maker must select exactly one of several investment alternatives, but attaches no meaning to selecting two-thirds of one alternative and one-third of another.) Those articles which suggest that rounding can lead to undesirable answers are seemingly supported by the numerous “textbook examples” that purport to illustrate the dangers of rounding. However, the standard examples in which rounding fails to give a workable solution involve only a few rounding possibilities (usually two or four) and do not come from real world applications. Hence, it is questionable whether they provide any insight about what is likely to occur in a practical setting. This note fills a gap in previous discussions of rounding by providing two easily understood examples that dramatically portray the difficulties that rounding can encounter. The first example belongs to an important class of practical problems. We illustrate that rounding fails not only for this example, but also fails for all problems in its class. The second example is a unique “showcase” problem which can be summarized by a 5 times 5 cost matrix. This problem contains more than a million rounding alternatives, all of them infeasible! Following these examples, we present a “rounding paradox” and we show that its resolution gives analytical support to the conclusion that rounding will produce grave difficulties in a wide variety of practical situations.     

LIBERALIZING A DISTRIBUTION SYSTEM: THE EUROPEAN CAR MARKET

We quantify the competitive effects of liberalizing the selective and exclusive distribution system in the European car market, based on a model of oligopoly pricing with differentiated products. We consider two possible competitive effects from liberalization: (i) the creation of international intrabrand competition (cross‐border trade), which will result in a reduction of international price discrimination; and (ii) a possible cumulative effect arising from a strengthening of national intrabrand competition, which would result in reduced double marginalization. We find that the reduction in international price discrimination mainly redistributes consumer gains across countries; it has a positive but modest effect on total welfare. If liberalization also has the cumulative effect of reducing double marginalization, the welfare effects are much higher. Finally, we find that the effects of liberalization on the manufacturers' profits are either small or positive. This finding implies that international price discrimination, and softening competition through a double marginalization mechanism, should not be interpreted as main profit motives for the previous distribution system, but only as unintended side effects. Hence, the industry rationale for maintaining the previous distribution system should be sought in other areas. (JEL: F15, L42)