Multi-phase Algorithms for Throughput Maximization for Real-Time Scheduling

We consider the problem of off-line throughput maximization for job scheduling on one or more machines, where each job has a release time, a deadline and a profit. Most of the versions of the problem discussed here were already treated by Bar-Noy et al. (Proc. 31st ACM STOC, 1999, pp. 622–631; http://www.eng.tau.ac.il/amotz/). Our main contribution is to provide algorithms that do not use linear programming, are simple and much faster than the corresponding ones proposed in Bar-Noy et al. (ibid., 1999), while either having the same quality of approximation or improving it. More precisely, compared to the results of in Bar-Noy et al. (ibid., 1999), our pseudo-polynomial algorithm for multiple unrelated machines and all of our strongly-polynomial algorithms have better performance ratios, all of our algorithms run much faster, are combinatorial in nature and avoid linear programming. Finally, we show that algorithms with better performance ratios than 2 are possible if the stretch factors of the jobs are bounded; a straightforward consequence of this result is an improvement of the ratio of an optimal solution of the integer programming formulation of the JISP2 problem (see Spieksma, Journal of Scheduling, vol. 2, pp. 215–227, 1999) to its linear programming relaxation.     

Growth of tuber crops and almost sure band for quantiles

Some tuber crops are governed by memoryless property of exponential distribution leading to a mixture distribution with heavy tail. Quantile-based estimators may then be appropriate than mean as a measure of central tendency. We prove almost sure representation theorems for sample quantiles in a general setup of U statistics, under slightly stronger assumption than assuming the existence of a continuously differentiable distribution function F for the kernel h. We obtain almost sure (a.s.) upper and lower estimate for F^{? 1}(p), p ∈ (0, 1) as a band for p varying. As an application, dataset arising from two varieties of potato cultivation are analyzed.     

Estimation of multiple gamma scale-parameters: bayes estimation subject to uniform domination

Simultaneous estimation of p gamma scale-parameters is considered under squared-error loss. The problem of minimizing, subject to uniform risk domination, the Bayes risk (or more generally the posterior expected loss) against certain conjugate or mixtures of conjugate priors is considered. Rather surprisingly, it is shown that the minimization can be done conditionally, thus avoiding variational arguments. Relative savings loss (and a posterior version thereof) are found, and it is found that in the most favorable situations, Bayesian robustness can be achieved without sacrificing substantial subjective Bayesian gains.     

An economic inspection interval for control of defective items in a hot rolling mill

The article addresses a real-life problem on determining the optimum sampling interval for control of defective items in a hot rolling mill. Having observed that the pattern of appearance of mill defects indicates a geometric process failure mechanism, an economic model is developed in line with the method suggested by Taguchi and critically examined by Nayebpour & Woodall. An expression for the expected loss per product as a function of the sampling interval is derived and the optimum interval is obtained by minimizing this loss function. The practical issues involved in this exercise, such as estimation of various cost components, are also discussed and the effect of erroneous estimation of cost components is studied through a sensitivity analysis.     

Community and anti-poverty targeting

The standard theory of anti-poverty targeting assumes individual incomes cannot be observed, but statistical properties of income distribution in broadly defined groups are known. ‘Indicator targeting’ rules are then derived for the forms of transfers conditioned on group membership of individuals. In this literature the motivating notion of a ‘group’ is purely statistical, even when it is groups such as localities and ethnicities. We focus instead on groups which are ‘communities’, meaning thereby collections of individuals who have access to community-specific public goods, from which non-members are excluded. Such differential access constitutes a source of inequality among poor individuals belonging to different communities, which is not captured by monetary earnings. We show that this formulation of what constitutes a group changes many of the basic results of the indicator targeting literature. Optimal targeting for poverty alleviation leads to seemingly paradoxical rules, such as targeting transfers to the community that is richer. Total wealth of non-poor members of a community and its distribution both become relevant for specifying optimal indicator targeting rules. In addition, a poverty measure that is sensitive to the community identities of poor individuals, yet defined on nominal incomes, may be incompatible with some of the basic axioms in the standard literature on poverty measurement.     

A new approach to default priors and robust bayes methodology

Following the developments in DasGupta et al. (2000), the authors propose and explore a new method for constructing proper default priors and a method for selecting a Bayes estimate from a family. Their results are based on asymptotic expansions of certain marginal correlations. For ease of exposition, most results are presented for location families and squared error loss only. The default prior methodology amounts, ultimately, to the minimization of Fisher information, and hence, Bickel's prior works out as the default prior if the location parameter is bounded. As for the selected Bayes estimate, it corresponds to ‘Gaussian tilting’ of an initial reference prior.     

Transitivity and fuzzy preferences

The authors would like to thank a referee at Social Choice and Welfare for insightful comments.