Ship-pack optimization in a two-echelon distribution system

In large distribution systems, distribution centers (DC) deliver some merchandize to their retail stores in size-specific packages, also called ship-packs. These ship-packs include cases (e.g., cartons containing 24 or 48 units), inners (packages of 6 or 8 units) or eaches (individual units). For each Stock Keeping Unit (SKU), a retailer can decide which of these ship-pack options to use when replenishing its retail stores. Working with a major US retailer, we have developed a cost model that balances DC handling costs, store handling costs and inventory-related costs at both the DC and the stores, and therefore can help to determine the optimum warehouse ship-pack for each SKU. We implement our model for a sample of 529 SKUs, and show that by changing ship-pack size for about 30 SKUs, the retailer can reduce its total cost by 0.3% - 0.4%. Interestingly, we find that most of the cost savings occurs at the DC level.     

Structure of planar integral self‐affine tilings

For a self‐affine tile in $\mathbf {R}^2$ generated by an expanding matrix $A\in M_2(\mathbf {Z})$ and an integral consecutive collinear digit set ${\mathcal D}$, Leung and Lau [Trans. Amer. Math. Soc. 359 , 3337–3355 (2007).] provided a necessary and sufficient algebraic condition for it to be disklike. They also characterized the neighborhood structure of all disklike tiles in terms of the algebraic data A and ${\mathcal D}$. In this paper, we completely characterize the neighborhood structure of those non‐disklike tiles. While disklike tiles can only have either six or eight edge or vertex neighbors, non‐disklike tiles have much richer neighborhood structure. In particular, other than a finite set, a Cantor set, or a set containing a nontrivial continuum, neighbors can intersect in a union of a Cantor set and a countable set.     

Local superconvergence of the derivative for tensor‐product block FEM

In this article, we shall discuss local superconvergence of the derivative for tensor‐product block finite elements over uniform partition for three‐dimensional Poisson's equation on the basis of Liu and Zhu (Numer Methods Partial Differential Eq 25 (2009) 999–1008). Assume that odd m ≥ 3, x₀ is an inner locally symmetric point of uniform rectangular partition \begin{align*}\mathcal{T}_{h}\end{align*} and ρ(x₀,?Ω) means the distance between x₀ and boundary ?Ω. Combining the symmetry technique (Wahlbin, Springer, 1995; Schatz, Sloan, and Wahlbin, SIAM J Numer Anal 33 (1996), 505–521; Schatz, Math Comput 67 (1998), 877–899) with weak estimates for tensor‐product block finite elements of degree m ≥ 3 [see Liu and Zhu, Numer Methods Partial Differential Eq 25 (2009) 999–1008] and the finite element theory of Green function in ??³ presented in this article, we propose the \begin{align*}O(h^{m+3}|\ln h|^{\frac{4}{3}}+h^{2m+2}|\ln h|^{\frac{4}{3}}\rho(x_{0},\partial\Omega)^{-m})\end{align*} convergence of the derivatives for tensor‐product block finite elements of degree m ≥ 3 on x₀. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 457–475, 2012     

非对称线性方程组的二阶段分裂迭代法

本文针对非对称正定矩阵提出了一个收敛分裂, 给出了分裂收敛的充要条件. 在此基础上, 提出系数为非对称正定矩阵的线性方程组的二阶段算法, 并讨论了算法的收敛条件. 最后, 通过数值例子展示了算法的有效性.     

广义Carmichael数

设n是一个合数,Z_n表示模n的剩余类环,r(x)∈Z_n[x]是一个首一的k(>0)次不可约多项式。本文引入n是k阶摸r(x)的Carmichael数的定义,全体这样的数记为集C_(k,r)(x),由此给出k阶Carmichael数集:C_k={∪C_(k,r)(x)|r(x)过全体Z_n上的首一k次不可约多项式}。显然C_1表示通常的Carmichael数集。作者得到了n∈C_(k,r(x))的一个充要条件,进而得到n∈C_k的一个充要条件及n∈C_2的一个更易计算的充要条件,还证明了C_1(?)C_2以及|C_2|=∞。     

氧化锆增韧莫来石复相陶瓷的摩擦磨损行为与磨损机制

研究了氧化锆增韧莫来石得相陶瓷（ＺＴＭ）与氧化铝陶瓷摩擦副在室温至４００℃干摩擦下的摩擦磨损行为与机制。研究表明：ＺＴＭ陶瓷的磨损率随温度的升高而逐渐降低;室温下ＺＴＭ陶瓷的磨损机制以微观切削和微观断裂为主;随着温度的升高,ＺＴＭ陶瓷中的玻璃相具有微观润滑作用,其磨损机制转变为微观断裂和晶粒剥落为主;偶件氧化铝的磨损机制主要是脆性断裂及晶粒剥落。     

炼铝工业固体废料(赤泥)的物质组成与工程特性及其防治利用研究

据保守估算 ,我国每年排放的铝工业固体废料赤泥至少在 5 0 0万 t以上。由于赤泥对生态环境的严重危害 ,赤泥坝、赤泥库的安全已成为令人关注的环境问题。各类固体废弃物 (包括生活垃圾 )储存、处理和利用的研究不仅是当代环境科学的重要任务 ,亦是当代环境工程地质学、环境岩土工程学最重要、最迫切的研究任务之一。本文利用工程岩土学的有关理论和方法 ,系统地研究了赤泥的化学、矿物成分、不良工程特性及其形成变化机理 ,并在此基础上提出了赤泥的储存、加固 (处理 )和综合利用的原理和途径。     

求解二层规划问题的遗传算法

本文求解二层规划问题的遗传算法，给出了算法基本框架并对算法实现进行了研究．算法适用于各类线性和非线性二层规划问题．数值计算结果显示，该方法是可行和有效的．     

上市公司资本成本面板数据模型与实证分析

本文利用我国上市公司1997至2002年的有关财务数据,建立了我国上市公司资本成本面板数据模型,运用该模型分析了我国上市公司资本成本与财务杠杆、企业规模的关系.结果表明,财务杠杆的提升、企业规模的扩大将使资本成本下降.该结论对我国上市公司优化资本结构、提高企业价值具有一定的参考价值.