Robust optimization of uncertain multistage inventory systems with inexact data in decision rules

In production-inventory problems customer demand is often subject to uncertainty. Therefore, it is challenging to design production plans that satisfy both demand and a set of constraints on e.g. production capacity and required inventory levels. Adjustable robust optimization (ARO) is a technique to solve these dynamic (multistage) production-inventory problems. In ARO, the decision in each stage is a function of the data on the realizations of the uncertain demand gathered from the previous periods. These data, however, are often inaccurate; there is much evidence in the information management literature that data quality in inventory systems is often poor. Reliance on data “as is” may then lead to poor performance of “data-driven” methods such as ARO. In this paper, we remedy this weakness of ARO by introducing a model that treats past data itself as an uncertain model parameter. We show that computational tractability of the robust counterparts associated with this extension of ARO is still maintained. The benefits of the new model are demonstrated by a numerical test case of a well-studied production-inventory problem. Our approach is also applicable to other ARO models outside the realm of production-inventory planning.     

Computational thinking and constructionism: creating difference equations in spreadsheets

The invention of the computer has led to the establishment of a new research paradigm, computation, which has recently become more and more popular in scientific exploration. However, computation is not well represented in high school and university curricula in science and engineering, although it applies to a wide range of disciplines beyond computer science and software engineering. In light of the increasing need to provide students with computational education, this paper presents a novel way to develop computational thinking among students. The proposed approach is based on the implementation of Papert's theory of constructionism in electronic spreadsheets. In this approach, students build their knowledge while constructing the difference equation that describes a physical (or engineering) phenomenon, based on specific cases investigated in the spreadsheet. The method does not require the students to write code or perform complex calculations in the spreadsheet and makes it possible to teach advanced subjects at a relatively early stage. The method is demonstrated through contents taken from the secondary and tertiary curricula in mechanics and electromagnetism.     

Robust Mean-Squared Error Estimation of Multiple Signals in Linear Systems Affected by Model and Noise Uncertainties

This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in which the second order statistics of the noise vectors (i.e., their covariance matrices) are also subjected to uncertainty. We seek a robust mean-squared error estimator immuned against both sources of uncertainty. We show that the optimal robust mean-squared error estimator has a special form represented by an elementary block circulant matrix, and moreover when the uncertainty sets are ellipsoidal-like, the problem of finding the optimal estimator matrix can be reduced to solving an explicit semidefinite programming problem, whose size is independent of N. The research was partially supported by BSF grant #2002038     

Copolymerization of acrylonitrile. III. Copolymerization with α-cyanocinnamamide

Acrylonitrile was copolymerized in solution with α-cyanocinnamamide up to low conversions. The conventional scheme of copolymerization fitted this copolymer. The basic properties, such as solubility, viscosity, and thermal behavior, of the copolymer prepared in bulk and in solution were determined.     

Research Methodology in the Management Sciences: Formalism or Empiricism

This paper analyses the major problems confronted in research on management problems. That management science can neither be completely formal nor completely empirical is emphasized. The conclusion reached is that a subtle interplay between the two is essential: factual and theoretical positions which are mutually compatible must be established in the development of useful problem solving algorithms. This condition suggests that the most powerful managerial algorithms are heuristic and computer-based.     

On the detectability of forbidden lines

We show that the traditional interpretation of the non-detection of forbidden lines in dense natural plasmas is based on a misunderstanding. The central intensity of the line, taken to be a measure of detectability, is shown to have a maximum as a function of electron density and to be a linear function of electron density in tenuous plasmas.     

Extension of some results for channel capacity using a generalized information measure

A new formulation for the channel capacity problem is derived by using the duality theory of convex programming. The simple nature of this dual representation is suitable for computational purposes. The results are derived in a unified way by formulating the channel capacity problem as a special case of a general class of concave programming problems involving a generalized information measure recently introduced by Burbea and Rao [10].Research supported by National Science Foundation Grant No. ECS-8604354.     

Vibrational spectra of Matrix isolated binary and mixed cadmium dihalides

The Raman spectra CdX₂ and CdXY (X, Y = Cl, Br, I) molecules isolated in solid krypton at 20°K are reported together with the matrix isolation infrared spectrum of CdX₂ and CdXY (X, Y = Br, I) molecules. Isotopic effects and force constants are discussed and several irregularities in them are interpreted as possible indications of slightly bent structures. The bending vibration frequency of CdClI as well as several bands assigned to dimers are also reported.