Assortment planning for vertically differentiated products under a consider-then-choose model

Consider-then-choose models, borne out by empirical literature in marketing and psychology, note that customers follow a two-stage procedure to choose among alternatives. In this paper, we consider the assortment optimization problem of a retailer who manages a category of vertically differentiated products under customers’ consider-then-choose behavior. We characterize some structural results of the optimal assortment and find that the problem can be solved as the shortest path problem. Also, we develop an efficient algorithm to identify an optimal assortment.     

Polynomial algorithms for (integral) maximum two-flows in vertex edge-capacitated planar graphs

In this paper we study the maximum two-flow problem in vertex- and edge-capacitated undirected ST₂-planar graphs, that is, planar graphs where the vertices of each terminal pair are on the same face. For such graphs we provide an O(n) algorithm for finding a minimum two-cut and an O(n log n) algorithm for determining a maximum two-flow and show that the value of a maximum two-flow equals the value of a minimum two-cut. We further show that the flow obtained is half-integral and provide a characterization of edge and vertex capacitated ST₂-planar graphs that guarantees a maximum two-flow that is integral. By a simple variation of our maximum two-flow algorithm we then develop, for ST₂-planar graphs with vertex and edge capacities, an O(n log n) algorithm for determining an integral maximum two-flow of value not less than the value of a maximum two-flow minus one.     

Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace

We consider the problem of efficient integration of an n-variate polynomial with respect to the Gaussian measure in ℝⁿ and related problems of complex integration and optimization of a polynomial on the unit sphere. We identify a class of n-variate polynomials f for which the integral of any positive integer power f^p over the whole space is well approximated by a properly scaled integral over a random subspace of dimension O(log n). Consequently, the maximum of f on the unit sphere is well approximated by a properly scaled maximum on the unit sphere in a random subspace of dimension O(log n). We discuss connections with problems of combinatorial counting and applications to efficient approximation of a hafnian of a positive matrix.     

High resolution instrumentation system for fibre-Bragg grating aerospace sensors

A passive technique for high-resolution detection of the wavelength of peak reflection from fibre Bragg grating (FBG) sensors is presented. The approach, based on a de-convolution of the FBG spectrum and the spectrometer resolution, essentially overcomes the low spectral resolution (≈0.1 nm) associated with commercial spectrometers employing CCD detection. The performance of two algorithms, the Centroid Detection algorithm (CDA) and the least squares method (LSQ), are compared. The LSQ algorithm offers resolution enhancement of at least two orders of magnitude and is shown to be independent of the FBG intensity and bandwidth over a broad range.     

线性约束多目标规划的非单调信赖域算法

本文对线性约束多规划问题提出了一类非单调信赖域算法 ,该方法是可行点法与信赖域技巧的结合 .在一定的条件下证明了算法的全局收敛性 .并进行了数值试验 .     

The powers and pitfalls of algorithmic knowledge: a case study

This study examines one child's use of computational procedures over a period of 3 years in an urban elementary school where teachers were using a standards-based curriculum. From a sociocultural perspective, the use of standard algorithms to solve mathematical problems is viewed as a cultural tool that both enables and constrains particular practices. As this student appropriated and mastered procedures for addition, subtraction, multiplication and division, she could solve problems that involved fairly straightforward computations or where she could easily model the action to determine an appropriate computation. At the same time, her use of these algorithms, along with other readily available tools, such as her fingers or multiplication tables, constrained her ability to reflect on the tens-structure of the number system, an effect that had serious consequences for her overall mathematical achievement. The results of this study suggest that even when not directly introduced, algorithms have such strong currency that they can mediate more reform-oriented instruction.     

Markov games with incomplete information

We consider zero-sum Markov games with incomplete information. Here, the second player is never informed about the current state of the underlying Markov chain. The existence of a value and of optimal strategies for both players is shown. In particular, we present finite algorithms for computing optimal strategies for the informed and uninformed player. The algorithms are based on linear programming results.     

Two storage inventory model in a mixed environment

Multi-item inventory models with two storage facility and bulk release pattern are developed with linearly time dependent demand in a finite time horizon under crisp, stochastic and fuzzy-stochastic environments. Here different inventory parameters—holding costs, ordering costs, purchase costs, etc.—are assumed as probabilistic or fuzzy in nature. In particular cases stochastic and crisp models are derived. Models are formulated as profit maximization principle and three different approaches are proposed for solution. In the first approach, fuzzy extension principle is used to find membership function of the objective function and then it’s Graded Mean Integration Value (GMIV) for different optimistic levels are taken as equivalent stochastic objectives. Then the stochastic model is transformed to a constraint multi-objective programming problem using Stochastic Non-linear Programming (SNLP) technique. The multi-objective problems are transferred to single objective problems using Interactive Fuzzy Satisfising (IFS) technique. Finally, a Region Reducing Genetic Algorithm (RRGA) based on entropy has been developed and implemented to solve the single objective problems. In the second approach, the above GMIV (which is stochastic in nature) is optimized with some degree of probability and using SNLP technique model is transferred to an equivalent single objective crisp problem and solved using RRGA. In the third approach, objective function is optimized with some degree of possibility/necessity and following this approach model is transformed to an equivalent constrained stochastic programming problem. Then it is transformed to an equivalent single objective crisp problem using SNLP technique and solved via RRGA. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.     

Source-Region Electromagnetic Field in an Affinely Transformable AUBM

We derive expressions for the source–region electromagnetic field in an affinely transformable Axially Uniaxial Bianisotropic Medium (AUBM) by employing a technique originally developed by Fikioris for free space (i.e., vacuum). The obtained results may be used to determine the scattering response of an electrically small bianisotropic particle embedded in an affinely transformable AUBM. They can therefore be further used to homogenize a wide class of particulate composites.     

Assessing outcomes for dysphonic patients

This study was designed to evaluate a disease-specific outcome measure for patients with selected voice disorders and to relate this instrument to a standardized quality of life measurement. In addition, the study attempts to document the degree of handicap for dysphonia patients globally, between different vocal pathologies, and in comparison to other chronic diseases. In this prospective, observational study, 260 adult patients evaluated for alterations of voice completed a general quality of life measure (the Medical Outcomes Trust Short Form 36-Item[SF-36]) and a voice-specific instrument (Voice Handicap Index [VHI]) pretreatment.

The highest correlation was between the social functioning score of the SF-36and the total score of the VHI and the physical, emotional, and functional subscales (p < 0.001) of the VHI. Significant correlation was also obtained for the SF-36 domains mental health (p < 0.01), general health (p < 0.01), and role functioning emotional (p < 0.017) with the three VHI domains and the total VHI score. Patients had significantly lower scores than the general U.S. population in five of the eight domains of SF-36. Patients with vocal fold paralysis had the highest level of pretreatment disability as measured on both the VHI and SF-36 among voice patients. The patients with dysphonia had a lower level of physical functioning than the patients with chronic sinusitis (p < 0.01), reflecting a greater handicap. In addition, the dysphonia group had lower levels of social functioning than the angina (p < 0.01) and sciatica (p < 0.01) groups and a lower score for mental health than the angina group (p < 0.01).

The SF-36 correlates with the VHI in the domains of social functioning,mental health, and role functioning emotional. The baseline handicap for voice disorders represents a significant disability even in comparison to conditions such as angina pectoris, sciatica, and chronic sinusitis.