Minimizing the makespan in a single machine scheduling problems with flexible and periodic maintenance

This paper deals with a single machine scheduling problems with availability constraints. The unavailability of machine results from periodic maintenance activities. In our research, a periodic maintenance consists of several maintenance periods. We consider a machine should stop to maintain after a periodic time interval or to change tools after a fixed amount of jobs processed simultaneously. Each maintenance period is scheduled after a periodic time interval. We study the problems under deterministic environment and flexible maintenance considerations. Preemptive operation is not allowed. In addition, we propose a more reasonable flexible model for the real production settings. The objective is to minimize the makespan. The proposed problem is NP-hard in the strong sense and some heuristic algorithms are provided. The purpose is to present an efficient and effective heuristic algorithm so that it will be straightforward and easy to implement. Computational results show that the proposed algorithm first fit decreasing (DFF) performs well.     

The polynomial Fourier transform with minimum mean square error for noisy data

In 2006, Naoki Saito proposed a Polyharmonic Local Fourier Transform (PHLFT) to decompose a signal f∈L²(Ω) into the sum of a polyharmonic componentu and a residualv, where Ω is a bounded and open domain in R^d. The solution presented in PHLFT in general does not have an error with minimal energy. In resolving this issue, we propose the least squares approximant to a given signal in L²([−1,1]) using the combination of a set of algebraic polynomials and a set of trigonometric polynomials. The maximum degree of the algebraic polynomials is chosen to be small and fixed. We show in this paper that the least squares approximant converges uniformly for a Hölder continuous function. Therefore Gibbs phenomenon will not occur around the boundary for such a function. We also show that the PHLFT converges uniformly and is a near least squares approximation in the sense that it is arbitrarily close to the least squares approximant in L² norm as the dimension of the approximation space increases. Our experiments show that the proposed method is robust in approximating a highly oscillating signal. Even when the signal is corrupted by noise, the method is still robust. The experiments also reveal that an optimum degree of the trigonometric polynomial is needed in order to attain the minimal l² error of the approximation when there is noise present in the data set. This optimum degree is shown to be determined by the intrinsic frequency of the signal. We also discuss the energy compaction of the solution vector and give an explanation to it.     

Model reduction for large-scale dynamical systems via equality constrained least squares

In this paper, we present a new method of model reduction for large-scale dynamical systems, which belongs to the SVD-Krylov based method category. It is a two-sided projection where one side reflects the Krylov part and the other side reflects the SVD (observability gramian) part. The reduced model matches the first r+i Markov parameters of the full order model, and the remaining ones approximate in a least squares sense without being explicitly computed, where r is the order of the reduced system, and i is a nonnegative integer such that 1≤i<r. The reduced system minimizes a weighted ?₂ error. By the definition of a shift operator, the proposed approximation is also obtained by solving an equality constrained least squares problem. Moreover, the method is generalized for moment matching at arbitrary interpolation points. Several numerical examples verify the effectiveness of the approach.     

Flexible working arrangements in context: An empirical investigation through self-organizing maps

This is one of the first studies to utilize Kohonen’s self-organizing maps on flexible work arrangements (FWAs), employee turnover and absenteeism within different national contexts and an array of organizational factors. While the majority of FWAs did not reduce significantly employee turnover or absenteeism, country and industry were significant contextual variables in FWA use: we deciphered six main country regions, where service and manufacturing organizations were important to FWA preferences. We found a curvilinear relationship between turnover and shift-work among manufacturing firms regardless of country: turnover decreases at low levels and increases at high levels of shift-work. We also found strong positive relationships between weekend work and turnover among manufacturing firms regardless of country and firms in the region comprising of Germany, Austria, Sweden, Finland, Denmark, Czech Republic and Belgium. Finally, we found consistently high concentration of organizations with low absenteeism throughout certain industries and countries: noteworthy are service organizations in the Netherlands and manufacturing organizations in Australia. The results demonstrate the contextuality of FWA use across countries and industries, and the usefulness of SOMs for research within human resource management.     

两两比较的TOPSIS法

TOPSIS法是一种常用的多目标决策方法,它以正负理想解作为统一的参照基准来比较方案的优劣.并不适用于常见的两两比较的决策行为.运用最小二乘法解决判别一致性问题,从而建立了两两比较的TOPSIS法,并进行了实例分析.     

求矩阵方程组的反对称最小二乘解的递推算法

讨论了矩阵方程组A_1XB_1=D_1,A_2XB_2=D_2反对称最小二乘解的递推算法,该算法不仅能够用于计算反对称最小二乘解,而且在选取特殊的初始矩阵时,算法能够求出矩阵方程组的极小范数反对称最小二乘解,以及对给定的矩阵进行最佳逼近的反对称解.     

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删失回归模型是一种很重要的模型,它在计量经济学中有着广泛的应用. 然而,它的变量选择问题在现今的参考文献中研究的比较少.本文提出了一个LASSO型变量选择和估计方法,称之为多样化惩罚$L_1$限制方法, 简称为DPLC. 另外,我们给出了非0回归系数估计的大样本渐近性质. 最后,大量的模拟研究表明了DPLC方法和一般的最优子集选择方法在变量选择和估计方面有着相同的能力.     

正交回归和一般最小二乘回归的几何误差分析

线性回归分析中,一般最小二乘回归的目标函数只考虑一个方向的扰动,采用基于几何距离的正交回归能克服固定单方向最优带来的拟合稳定性差的弊端。本文分析和比较了正交回归和一般最小二乘回归的误差,并定量地给出了两者的几何误差与原始数据的方差、相关系数之间的关系,指出正交回归的几何误差小于一般最小二乘回归,并且正交回归具有旋转不变性。最后,以平面直线拟合为例验证了这个结论。     

X‐tended target projection (XTP)—comparison with orthogonal partial least squares (OPLS) and PLS post‐processing by similarity transformation (PLS + ST)

Target projection (TP) also called target rotation (TR) was introduced to facilitate interpretation of latent‐variable regression models. Orthogonal partial least squares (OPLS) regression and PLS post‐processing by similarity transform (PLS + ST) represent two alternative algorithms for the same purpose. In addition, OPLS and PLS + ST provide components to explain systematic variation in X orthogonal to the response. We show, that for the same number of components, OPLS and PLS + ST provide score and loading vectors for the predictive latent variable that are the same as for TP except for a scaling factor. Furthermore, we show how the TP approach can be extended to become a hybrid of latent‐variable (LV) regression and exploratory LV analysis and thus embrace systematic variation in X unrelated to the response. Principal component analysis (PCA) of the residual variation after removal of the target component is here used to extract the orthogonal components, but X‐tended TP (XTP) permits other criteria for decomposition of the residual variation. If PCA is used for decomposing the orthogonal variation in XTP, the variance of the major orthogonal components obtained for OPLS and XTP is observed to be almost the same, showing the close relationship between the methods. The XTP approach is tested and compared with OPLS for a three‐component mixture analyzed by infrared spectroscopy and a multicomponent mixture measured by near infrared spectroscopy in a reactor. Copyright © 2008 John Wiley & Sons, Ltd.