Ensuring responsive capacity: How to contract with backup suppliers

Firms that source from offshore plants frequently perceive the lack of reliability and flexibility to be among the major drawbacks of their strategy. To mitigate against imminent mismatches of uncertain supply and demand, establishing capacity hedges in the form of responsive backup suppliers is a way out that many firms follow. This article analyzes how firms should contract with backup suppliers, inducing the latter to install responsive capacity. We show that supply options are appropriate to achieve sourcing channel coordination under forced compliance, whereas any firm commitment contract imposes a deadweight loss on the system. Whereas price-only contracts are unable to coordinate the sourcing channel under voluntary compliance, utilization-dependent price-only contracts are. Under the former contract, a price-focused strategy on the part of the manufacturer turns out to diminish the system’s service level and possibly has negative implications on installed backup capacity, and not least on the manufacturer’s profit.     

多元线性模型参数的部分压缩估计

考虑多元线性回归模型Y=XB ε,其中E(Vec(ε))=0,Cov(Vec(ε))=∑In,当设计阵X呈病态时,模型参数的LS估计不再是一个优良估计,为此,提出了一种部分压缩估计,并分析了其性质.     

The difficulty of “length × width”: Is a square the unit of measurement?

In individual interviews, 220 students in grades 4, 6, 8, and 9 were given one task, and 72 eighth graders were given three tasks to answer two questions: (a) Is a square the unit of measurement for an area for students in grades 4-8? and (b) Does a square have a space-covering characteristic for students in grade 8? The answers to both questions were No (except for eighth (and ninth) graders in advanced sections of mathematics). The difficulty of “length × width” is explained in light of Piaget's theory, and educational implications are discussed.     

Generalized mix functions and orthogonal equitable rectangles

Ristenpart and Rogaway defined “mix” functions, which are used to mix inputs from two sets of equal size, and produce outputs from the same two sets, in an optimal way. These functions have a cryptographic application in the context of extending the domain of a block cipher. It was observed that mix functions could be constructed from orthogonal latin squares. In this article, we give a simple, scalable construction for mix functions. We also consider a generalization of mix functions, in which the two sets need not be of equal size. These generalized mix functions turn out to be equivalent to an interesting type of combinatorial design which has not previously been studied. We term these “orthogonal equitable rectangles” and we construct them for all possible parameter situations, with a small number of exceptions and possible exceptions. Research supported by NSERC discovery grant 203114-06.     

Superposition Method in Thermal-Stress Problems for Rectangular Plates

The classical two-dimensional biharmonic problem for a rectangular domain is considered. Some historical aspects of the problem are elucidated. The superposition method turns out to be efficient in solving thermoelastic-equilibrium problems in a rectangle. The relationship between the mathematical and engineering approaches to these problems is studied. A few typical examples are given __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 101–117, September 2005.     

矩形结构垂直腔顶发射激光器的偏振特性

为了获得高功率的偏振激光,对矩形结构的980nm大口径顶发射垂直腔面发射激光器(VCSEL)进行了研究。实验结果显示,对于400μm×80μm出光口径的矩形VCSEL器件,在工作电流内,水平偏振光和竖直偏振光共同存在,并且水平偏振光一直占据主导地位;而且水平偏振光的光谱相对于竖直偏振光有蓝移。这些现象和理论模型的分析结果非常吻合,证明矩形结构能很好的稳定大口径VCSEL的偏振方向。最后测得矩形VCSEL在水平方向和竖直方向的远场发散角分别为6.9°和10.2°。     

一种基于梯度的直线段检测算法

针对传统直线段检测算法计算量大、鲁棒性差的不足,本文提出了一种在数字图像中检测直线段的算法.图像梯度对于检测图像中的边缘结构具有重要意义,算法首先求取图像梯度的模值和方向;然后根据梯度模值伪排序结果采用梯度区域增长方法扩张方向一致的邻域像素,得到的连通像素区域作为直线段候选区域;最后用外接矩形描述候选区域,其长轴和短轴可作为直线段判定标准,满足判定标准的长轴就是所求的直线段,并用MATLAB对图像进行仿真实验.结果表明:本文算法耗时8.87 s检测出了108条直线段,与传统算法相比,不但耗时降低了17％,而且检测出的直线段增加了16％.