Impact of information sharing and lead time on bullwhip effect and on-hand inventory

This work analyzes a two echelon (warehouse–retailer) serial supply chain to study the impact of information sharing (IS) and lead time on bullwhip effect and on-hand inventory. The customer demand at the retailer is assumed to be an autoregressive (AR(1)) process. Both the echelons use a minimum mean squared error (MMSE) model for forecasting lead time demand (LTD), and follow an adaptive base-stock inventory policy to determine their respective order quantities. For the cases of without IS and inter as well as intra echelon IS, expressions for the bullwhip effect and on-hand inventory for the warehouse are obtained, considering deterministic lead-time. The results are compared with the previous research work and an easy analysis of the various bullwhip effect expressions under different scenarios, is done to understand the impact of IS on the bullwhip effect phenomenon. It is shown that some part of bullwhip effect will always remain even after sharing both inter as well as intra echelon information. Further, with the help of a numerical example it is shown that the lead time reduction is more beneficial in comparison to the sharing of information in terms of reduction in the bullwhip effect phenomenon.     

Superconvergence estimates of finite element methods for American options

In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. 39 (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and interpolation postprocessing analysis technique, we present sharp L ²-, L ^∞-norm error estimates and an H ¹-norm superconvergence estimate for this finite element method. As a by-product, the global superconvergence result can be used to generate an efficient a posteriori error estimator. This work was supported in part by the National Natural Science Foundation of China (10471103 and 10771158), the National Basic Research Program (2007CB814906), Social Science Foundation of the Ministry of Education of China (Numerical Methods for Convertible Bonds, 06JA630047), Tianjin Natural Science Foundation (07JCY-BJC14300), and Tianjin University of Finance and Economics.     

An optimal‐order estimate for MMOC‐MFEM approximations to porous medium flow

Mathematical models used to describe porous medium flow lead to coupled systems of time‐dependent partial differential equations. Standard methods tend to generate numerical solutions with nonphysical oscillations or numerical dispersion along with spurious grid‐orientation effect. The MMOC‐MFEM time‐stepping procedure, in which the modified method of characteristics (MMOC) is used to solve the transport equation and a mixed finite element method (MFEM) is used for the pressure equation, simulates porous medium flow accurately even if large spatial grids and time steps are used. In this article we prove an optimal‐order error estimate for a family of MMOC‐MFEM approximations. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Generalized partially linear mixed-effects models incorporating mismeasured covariates

In this article we consider a semiparametric generalized mixed-effects model, and propose combining local linear regression, and penalized quasilikelihood and local quasilikelihood techniques to estimate both population and individual parameters and nonparametric curves. The proposed estimators take into account the local correlation structure of the longitudinal data. We establish normality for the estimators of the parameter and asymptotic expansion for the estimators of the nonparametric part. For practical implementation, we propose an appropriate algorithm. We also consider the measurement error problem in covariates in our model, and suggest a strategy for adjusting the effects of measurement errors. We apply the proposed models and methods to study the relation between virologic and immunologic responses in AIDS clinical trials, in which virologic response is classified into binary variables. A dataset from an AIDS clinical study is analyzed.     

Global Error Bound for the Generalized Linear Complementarity Problem over a Polyhedral Cone

In this paper, the global error bound estimation for the generalized linear complementarity problem over a polyhedral cone (GLCP) is considered. To obtain a global error bound for the GLCP, we first develop some equivalent reformulations of the problem under milder conditions and then characterize the solution set of the GLCP. Based on this, an easily computable global error bound for the GLCP is established. The results obtained in this paper can be taken as an extension of the existing global error bound for the classical linear complementarity problems. This work was supported by the Research Grant Council of Hong Kong, a Chair Professor Fund of The Hong Kong Polytechnic University, the Natural Science Foundation of China (Grant No. 10771120) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.     

One-step 5-stage Hermite-Birkhoff-Taylor ODE solver of order 12

A one-step 5-stage Hermite-Birkhoff-Taylor method, HBT(12)5, of order 12 is constructed for solving nonstiff systems of differential equations y^′=f(t,y), y(t₀)=y₀, where y∈Rⁿ. The method uses derivatives y^′ to y⁽⁹⁾ as in Taylor methods combined with a 5-stage Runge-Kutta method. Forcing an expansion of the numerical solution to agree with a Taylor expansion of the true solution to order 12 leads to Taylor- and Runge-Kutta-type order conditions which are reorganized into Vandermonde-type linear systems whose solutions are the coefficients of the method. HBT(12)5 has a larger interval of absolute stability than Dormand-Prince DP(8, 7)13M and Taylor method T12 of order 12. The new method has also a smaller norm of principal error term than T12. It is superior to DP(8, 7)13M and T12 on the basis the number of steps, CPU time and maximum global error on common test problems. The formulae of HBT(12)5 are listed in an appendix.     

Error estimates in S P for cubature formulas exact for haar polynomials in the two-dimensional case

On the spaces S _p , an upper estimate is found for the norm of the error functional δ _N (f) of cubature formulas possessing the Haar d-property in the two-dimensional case. An asymptotic relation is proved for $ \left\| {\delta _N (f)} \right\|_{S_p^* } On the spaces S _p , an upper estimate is found for the norm of the error functional δ _N (f) of cubature formulas possessing the Haar d-property in the two-dimensional case. An asymptotic relation is proved for with the number of nodes N ∼ 2 ^d , where d → ∞. For N ∼ 2 ^d with d → ∞, it is shown that the norm of δ _N for the formulas under study has the best convergence rate, which is equal to N ^−1/p . Original Russian Text ? K.A. Kirillov, M.V. Noskov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 1, pp. 3–13.     

非线性抛物型积分微分方程非协调三角形Carey元的收敛性分析

将非协调三角形Carey元应用于二维空间中的非线性抛物型积分微分方程.通过一些新的特殊方法和技巧,给出了有限元解的最优L<'2>模和能量模误差估计.     

Simpson校正公式

给出了Simpson校正公式的截断误差,分析了复化Simpson校正公式的收敛阶.数值算例验证了理论分析的正确性.