On Extending Russell and Krajewski's Algorithm for Economic Purchase Order Quantities*

Russell and Krajewski presented an optimal purchase order quantity algorithm that considered the effect of the transportation rate structure for less-than-truckload (LTL) shipments. The authors applied the Russell and Krajewski algorithm to a variety of freight classes and lengths-of-haul. Anomalous cases were found in which the freight rate schedule, when used with the suggested algorithm, resulted in incorrect order size decisions. In this comment, the authors consider the impact of these anomalies on the optimal order quantity and associated total costs. A procedure is presented to adjust the Russell and Krajewski algorithm to arrive at the optimal purchase order quantity and the lowest total annual cost.     

The Effectiveness of Graphical Presentation for Information Extraction: A Cumulative Experimental Approach*

Three laboratory experiments were conducted to assess the relative strengths and weaknesses of bar, symbol, and line graphs for performing a variety of elementary information extraction tasks using two dependent variables, time and accuracy. The findings indicate that the degree of support provided by a particular graph format for a particular data extraction task depends on the matching of format and task in terms of their anchoring characteristics. Anchoring, in this context, refers to the phenomenon that specific and diverse parts of a graph are segmented by the reader to act as salient and relevant cues, or anchors, when different classes of information are to be extracted from the graph. A data extraction task has high x-value (y-value) anchoring if the x-axis (y-axis) component is represented in the question as either a given value or an unknown value. Conversely, a task has low x-value (y-value) anchoring if the x-axis (y-axis) component is not represented in the question as either a given value or as an unknown value. Data extraction accuracy was not significantly affected by presentation format. Bars provided the best time performance for data extraction tasks having high anchoring on both axes but were not appropriate for tasks having low anchoring on either the y axis or both the x and y axes. Line graphs tended to be worse in terms of time performance for tasks having high anchoring on both axes although they were as fast or better than other representations for tasks having low anchoring on both axes. Symbol plots appeared to possess anchoring characteristics associated with both bars and line graphs. Symbols (as with bars) tended to produce a time performance superior to that of line graphs for tasks having high anchoring on both axes; and (as with line graphs) symbols allowed faster results than bar graphs for tasks having low anchoring on either the y axis or both the x and y axes.     

Widening the gap: White ignorance,race relations and the consequences for Aboriginal people in Australia

White ignorance has a critical impact on race relations and is implicated in the maintenance of Aboriginal disadvantage. Addressing this ignorance is a largely overlooked capacity-building opportunity within Australia's non-Aboriginal population. It warrants consideration as a key component of strategies targeting Aboriginal disadvantage. Despite the established links between race relations and Aboriginal well-being, Aboriginal perspectives on non-Aboriginal people rarely feature in public discourse on “Aboriginal problems.” This paper draws on data from 180 in-depth interviews with 44 Aboriginal people in Darwin on the topic of White Australian people, culture and race relations. It reports Aboriginal perceptions of White Australian ignorance across areas of great symbolic and practical significance to Aboriginal people's lives. Their experience is that most White Australians are ignorant of the history of colonisation and the complexities of its aftermath. They are ignorant of Aboriginal law, cultures and languages, and of the extent of their own ignorance. The call to address White ignorance subverts assumptions about whose ignorance and capacity must be dealt with in order to progress national goals of reconciliation, address Aboriginal disadvantage and achieve justice and equality for Aboriginal people.     

Lattice and Schröder paths with periodic boundaries

We consider paths in the plane with (1,0$1,0$), (0,1$0,1$), and (a,b$a,b$)-steps that start at the origin, end at height n$n$, and stay strictly to the left of a given non-decreasing right boundary. We show that if the boundary is periodic and has slope at most b/a$b/a$, then the ordinary generating function for the number of such paths ending at height n   is algebraic. Our argument is in two parts. We use a simple combinatorial decomposition to obtain an Appell relation or “umbral” generating function, in which the power zⁿ$z^n$ is replaced by a power series of the form zⁿ_φn(z),$z^n{\phi }_n(z),$ where _φn(0)=1.${\phi }_n(0)=1.$ Then we convert (in an explicit way) the umbral generating function to an ordinary generating function by solving a system of linear equations and a polynomial equation. This conversion implies that the ordinary generating function is algebraic. We give several concrete examples, including an alternative way to solve the tennis ball problem.     

Cluster designs to assess the prevalence of acute malnutrition by lot quality assurance sampling: a validation study by computer simulation

Summary.  Traditional lot quality assurance sampling (LQAS) methods require simple random sampling to guarantee valid results. However, cluster sampling has been proposed to reduce the number of random starting points. This study uses simulations to examine the classification error of two such designs, a 67×3 (67 clusters of three observations) and a 33×6 (33 clusters of six observations) sampling scheme to assess the prevalence of global acute malnutrition (GAM). Further, we explore the use of a 67×3 sequential sampling scheme for LQAS classification of GAM prevalence. Results indicate that, for independent clusters with moderate intracluster correlation for the GAM outcome, the three sampling designs maintain approximate validity for LQAS analysis. Sequential sampling can substantially reduce the average sample size that is required for data collection. The presence of intercluster correlation can impact dramatically the classification error that is associated with LQAS analysis.     

Testing for symmetry in multivariate distributions

Using the empirical characteristic function, a Cramér–von Mises test for reflected symmetry about an unspecified point is derived for multivariate distributions. The test statistic is based on an empirical process for which the weak convergence is established. The null properties of the test are studied as well as its power and local power. Estimators for the unknown symmetric point are previously proposed. Their consistency and asymptotical normality are proved by studying the weak convergence of some multidimensional empirical process. A simulation experiment shows that the estimators of the symmetric point are good, and that the test performs well on the examples tested. The new test is compared to the one derived in [N. Henze, B. Klar, S.G. Meintanis, Invariant tests for symmetry about an unspecified point based on empirical characteristic function, J. Multivariate. Anal. 87 (2003) 275–297].     

The Effects of Minimum Wage Increases on Retail Employment and Hours: New Evidence from Monthly CPS Data

Proponents of state and federal minimum wage increases argue that past minimum wage hikes have not adversely affected retail employment. However, the existing empirical evidence is mixed. This study uses monthly data from the 1979–2004 Current Population Survey to provide new estimates of the effect of minimum wage increases on retail employment and hours worked. The findings suggest evidence of modest adverse effects. A 10% increase in the minimum wage is associated with a 1% decline in retail trade employment and usual weekly hours worked. Larger negative employment and hours effects are observed for the least experienced workers in the retail sector. These results are robust across a number of specifications, but are sensitive to controls for state time trends.