SAMPLE AVERAGE APPROXIMATION METHOD FOR A CLASS OF STOCHASTIC VARIATIONAL INEQUALITY PROBLEMS

This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.

A case study on sample average approximation method for stochastic supply chain network design problem

This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited in scale. We analyze the impact of uncertainty on demand based on actual large data from industrial companies.Deterministic equivalent model with nonanticipativity constraints, branch-and-fix coordination, sample average approximation(SAA) with Bayesian bootstrap, and Latin hypercube sampling were adopted to analyze stochastic demands. A computational study of supply chain network with front-ends in Europe and back-ends in Asia is presented to highlight the importance of stochastic factors in these problems and the efficiency of our proposed solution approach.

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting

In this paper, we study optimal recovery （reconstruction） of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞.

PointPCA:一种三维空间点云的特征提取算法

点云是一个庞大点的集合而且拥有重要的几何结构。由于其庞大的数据量,不可避免地就会在某些区域内出现一些相似点,这就使得在进行特征提取时提取到一些重复的信息,造成计算冗余,降低训练的准确率。针对上述问题,提出了一种新的神经网络——PointPCA,可以有效地解决上述问题;在PointPCA中,总共分为三个模块:a)采样模块,提出了一种average point sampling(APS)采样方法,可以有效地规避一些相似的点,得到一组近似代表这组点云的新的点集;b)特征提取模块,采用分组中的思想,对这组新的点的集合进行多尺度空间特征提取;c)拼接模块,将每一尺度提取的特征向量拼接到一起组合为一个特征向量。经过实验表明,PointPCA比PointNet在准确率方面提升了4.6%,比PointNet++提升了1.1%;而且在mIoU评估测试中也有不错的效果。

Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multiple dependent state sampling plan(MDSSP)concepts.Under accelerated conditions,the lifetime of a product follows the Weibull distribution with a known shape parameter,while the scale parameter can be determined using the acceleration factor(AF).The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive.An economic design of the proposed sampling plan was also considered for the ALT.A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number(ASN)and total cost of inspection(TC)under both producer’s and consumer’s risks.Numerical results are presented to support the AMDSSP for the ALT,while performance comparisons between the AMDSSP,the MDSSP and a single sampling plan(SSP)for the ALT are discussed.Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions.The AMDSSP also had a higher operating characteristic(OC)curve than both the existing sampling plans.Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

Flight Schedule Recovery under Uncertain Airport Capacity

Airlines adjust their flight schedules to satisfy more stringent airport capacity constraints caused by inclement weather or other unexpected disruptions.The problem will be more important and complicated if uncertain disruptions occur in hub airports.A two-stage stochastic programming model was established to deal with the realtime flight schedule recovery and passenger re-accommodation problem.The first-stage model represents the flight re-timing and re-fleeting decision in current time period when capacity information is deterministic,while the second-stage recourse model evaluates the passenger delay given the first-stage solutions when one future scenario is realized.Aiming at the large size of the problem and requirement for quick response,an algorithmic framework combining the sample average approximation and heuristic method was proposed.The computational results indicated of that the proposed method could obtain solutions with around 5% optimal gaps,and the computing time was linearly positive to the sample size.

A Projection and Contraction Method for P-Order Cone Constraint Stochastic Variational Inequality Problem

In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, further the rationality is given. When the underlying function is Lipschitz continuous, we acquire a projection and contraction algorithm to solve the approximation problem. In the end, the method is applied to some numerical experiments and the effectiveness of the algorithm is verified.

DETECTION OF INCIPIENT LOCALIZED GEAR FAULTS IN GEARBOX BY COMPLEX CONTINUOUS WAVELET TRANSFORM

As far as the vibration signal processing is concerned, composition ofvibration signal resulting from incipient localized faults in gearbox is too weak to be detected bytraditional detecting technology available now. The method, which includes two steps: vibrationsignal from gearbox is first processed by synchronous average sampling technique and then it isanalyzed by complex continuous wavelet transform to diagnose gear fault, is introduced. Twodifferent kinds of faults in the gearbox, i.e. shaft eccentricity and initial crack in tooth fillet,are detected and distinguished from each other successfully.

Dynamical intricacy and average sample complexity of amenable group actions

In 2018,Petersen and Wilson introduced the notion of dynamical intricacy and average sample complexity for dynamical systems of Z-action,based on the past works on the notion of intricacy in the research of brain network and probability theory.If one wants to take into account underlying system geometry in applications,more general group actions may need to be taken into consideration.In this paper,we consider this notion in the case of amenable group actions.We show that many basic properties in the Z-action case remain true.We also show that their suprema over covers or partitions are equal to the amenable topological entropy and the measure entropy,using the quasitiling technique in the theory of the amenable group.

Approximation of weak sense stationary stochastic processes from local averages

We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.

A two-stage skilled manpower planning model with demand uncertainty

Purpose-Human resources are one of the most important and effective elements for companies.In other words,employees are a competitive advantage.This issue is more vital in the supply chains and production systems,because of high need for manpower in the different specification.Therefore,manpower planning is an important,essential and complex task.The purpose of this paper is to present a manpower planning model for production departments.The authors consider workforce with individual and hierarchical skills with skill substitution in the planning.Assuming workforce demand as a factor of uncertainty,a two-stage stochastic model is proposed.Design/methodology/approach–To solve the proposed mixed-integer model in the real-world cases and large-scale problems,a Benders’decomposition algorithm is introduced.Some test instances are solved,with scenarios generated by Monte Carlo method.For some test instances,to find the number of suitable scenarios,the authors use the sample average approximation method and to generate scenarios,the authors use Latin hypercube sampling method.Findings–The results show a reasonable performance in terms of both quality and solution time.Finally,the paper concludes with some analysis of the results and suggestions for further research.Originality/value–Researchers have attracted to other uncertainty factors such as costs and products demand in the literature,and have little attention to workforce demand as an uncertainty factor.Furthermore,most of the time,researchers assume that there is no difference between the education level and skill,while they are not necessarily equivalent.Hence,this paper enters these elements into decision making.