An overview of inventory systems with several demand classes

In this chapter we discuss inventory systems where several demand classes may be distinguished. In particular, we focus on single-location inventory systems and we analyse the use of a so-called critical level policy. With this policy some inventory is reserved for high-priority demand. A number of practical examples where several demand classes naturally arise are presented, and the implications and modelling of the critical level policy in distribution systems are discussed. Finally, an overview of the literature on inventory systems with several demand classes is given

An overview of inventory systems with several demand classes

In this chapter we discuss inventory systems whereseveral demand classes may be distinguished. In particular, we focus on single-location inventory systems and we analyse the use of a so-called critical level policy. With this policy some inventory is reserved for high-priority demand. A number of practical examples whereseveral demand classes naturally arise are presented, and the implications and modelling of the critical level policy in distribution systems are discussed. Finally, an overview of theliterature on inventory systems with several demand classes is given.rationing;Inventory;demand classes;critical level

The Limitations of Optimization from Samples

In this paper we consider the following question: can we optimize objective functions from the training data we use to learn them? We formalize this question through a novel framework we call optimization from samples (OPS). In OPS, we are given sampled values of a function drawn from some distribution and the objective is to optimize the function under some constraint. While there are interesting classes of functions that can be optimized from samples, our main result is an impossibility. We show that there are classes of functions which are statistically learnable and optimizable, but for which no reasonable approximation for optimization from samples is achievable. In particular, our main result shows that there is no constant factor approximation for maximizing coverage functions under a cardinality constraint using polynomially-many samples drawn from any distribution. We also show tight approximation guarantees for maximization under a cardinality constraint of several interesting classes of functions including unit-demand, additive, and general monotone submodular functions, as well as a constant factor approximation for monotone submodular functions with bounded curvature

Optimal algorithms for global optimization in case of unknown Lipschitz constant

We consider a family of function classes which allow functions with several minima and which demand only Lipschitz continuity for smoothness. We present an algorithm almost optimal for each of these classes

Accelerated Training for Massive Classification via Dynamic Class Selection

Massive classification, a classification task defined over a vast number of classes (hundreds of thousands or even millions), has become an essential part of many real-world systems, such as face recognition. Existing methods, including the deep networks that achieved remarkable success in recent years, were mostly devised for problems with a moderate number of classes. They would meet with substantial difficulties, e.g. excessive memory demand and computational cost, when applied to massive problems. We present a new method to tackle this problem. This method can efficiently and accurately identify a small number of "active classes" for each mini-batch, based on a set of dynamic class hierarchies constructed on the fly. We also develop an adaptive allocation scheme thereon, which leads to a better tradeoff between performance and cost. On several large-scale benchmarks, our method significantly reduces the training cost and memory demand, while maintaining competitive performance.Comment: 8 pages, 6 figures, AAAI 201

BIBS: A Lecture Webcasting System

The Berkeley Internet Broadcasting System (BIBS) is a lecture webcasting system developed and operated by the Berkeley Multimedia Research Center. The system offers live remote viewing and on-demand replay of course lectures using streaming audio and video over the Internet. During the Fall 2000 semester 14 classes were webcast, including several large lower division classes, with a total enrollment of over 4,000 students. Lectures were played over 15,000 times per month during the semester. The primary use of the webcasts is to study for examinations. Students report they watch BIBS lectures because they did not understand material presented in lecture, because they wanted to review what the instructor said about selected topics, because they missed a lecture, and/or because they had difficulty understanding the speaker (e.g., non-native English speakers). Analysis of various survey data suggests that more than 50% of the students enrolled in some large classes view lectures and that as many as 75% of the lectures are played by members of the Berkeley community. Faculty attitudes vary about the virtues of lecture webcasting. Some question the use of this technology while others believe it is a valuable aid to education. Further study is required to accurately assess the pedagogical impact that lecture webcasts have on student learning

Efficiency in Bulgaria's schools : a nonparametric study

In Eastern European countries in large social sectors such as education, inefficiency and technical deficiencies are the legacy of the old command economy. The authors examine the technical efficiency of classroom use (defined as the number of classes per classroom in one transitional economy -- Bulgaria. They examine the concept of efficiency in 199 urban and rural municipalities, using data envelopment analysis to generate efficiency scores. Those scores -- discussed in terms of frequency and regional distribution -- are then regressed on several socioeconomic variables. The researchers find significant relationships between the efficiency scores, on the one hand, and, on the other, the proportion of students in the population under age 20 (demand indicator), the number of teachers (variable input), the percentage of the municipal budget spent on education, and the degree of urbanization. Efficiency in the use of classrooms (in terms of classes) varies considerably among municipalities, and the efficiency is highest in the capital city of Sofia. To the extent that some variation in efficiency reflects demand or demographic factos, there is little that policy can do to change the pattern. But some changes in municipal policy could increase the efficiency of classroom use without jeopardizing the fundamental learning objective. In some rural areas, for example, where there are few students and classroom utilization is low, it may be possible to consolidate several grades into multigrade classes and reduce the size of the teaching (and nonteaching) staff, while maintaining the quality of learning and maximizing the use of such fixed inputs as classrooms. To the extent that it is possible to use such classrooms more efficiently, savings could be generated in the municipalities that need them most: in demographically sparse, poor municipalities with a weak economic base. Those savings could then be reallocated to other educational essentials, such as equipment and materials.Teaching and Learning,Primary Education,Public Health Promotion,Health Monitoring&Evaluation,Environmental Economics&Policies,Environmental Economics&Policies,Teaching and Learning,Health Monitoring&Evaluation,Primary Education,Curriculum&Instruction