Tolerance Factors in Multiple and Multivariate Linear Regressions

In this article, an improved method of computing tolerance factors for constructing tolerance regions in a multivariate linear regression model is proposed. The method is based on a chi-square approximation to the distribution of a linear function of noncentral chi-square variables and simulation. The merits of the proposed approach and the usual simulation method considered in Lee and Mathew (2004 Lee , Y. , Mathew , T. ( 2004 ). Tolerance regions in multivariate linear regression . Journal of Statistical Planning Inference 126 : 253 – 271 . [Google Scholar]) are evaluated using Monte Carlo simulation. The study indicates that the proposed approach is stable and accurate even for small samples, and better than available methods. For constructing two-sided tolerance intervals in multiple linear regression, coverage level adjusted one-sided tolerance factors are shown to be better than available approximate tolerance factors. The results based on the coverage level adjusted one-sided tolerance factors are as good as the ones based on the exact two-sided tolerance factors in many cases.     

On approximating the central and noncentral multivariate gamma distributions

In this paper a finite series approximation involving Laguerre polynomials is derived for central and noncentral multivariate gamma distributions. It is shown that if one approximates the density of any k nonnegative continuous random variables by a finite series of Laguerre polynomials up to the (n₁, …, n_k)th degree, then all the mixed moments up to the order (n₁, …, n_k) of the approximated distribution equal to the mixed moments up to the same order of the random variables. Some numerical results are given for the bivariate central and noncentral multivariate gamma distributions to indicate the usefulness of the approximations.     

Analysis of generalized linear mixed models via a stochastic approximation algorithm with Markov chain Monte-Carlo method

In recent years much effort has been devoted to maximum likelihood estimation of generalized linear mixed models. Most of the existing methods use the EM algorithm, with various techniques in handling the intractable E-step. In this paper, a new implementation of a stochastic approximation algorithm with Markov chain Monte Carlo method is investigated. The proposed algorithm is computationally straightforward and its convergence is guaranteed. A simulation and three real data sets, including the challenging salamander data, are used to illustrate the procedure and to compare it with some existing methods. The results indicate that the proposed algorithm is an attractive alternative for problems with a large number of random effects or with high dimensional intractable integrals in the likelihood function.     

预知两种信息带准备时间的平行机半在线排序

本文研究了P2,rj/sum & max/Cmax问题,即预知所有工件加工时间总和sum和最大工件加工时间max的两台处理器的带准备时间的半在线问题,并给出了竞争比为6/5的最优半在线算法.     

随机需求下基于“自营+外包”模式的配送中心选址-配送问题研究

针对顾客需求量不确定情况下末端配送中心选址及提前备货问题，提出了基于“自营+外包”配送模式的配送中心选址-配送问题。以自营配送中心的固定运行成本、提前备货成本和各种场景下的自营配送成本、外包配送成本以及缺货损失成本的期望值之和最小化为目标，建立了两阶段连续型随机规划模型。第一阶段确定自营配送中心的选址位置和各个配送中心的提前备货量；第二阶段确定各种场景下的自营配送货运量、外包配送货运量和客户点的缺货量等，使总成本期望值达到最小。基于Monte Carlo抽样理论设计了求解模型的样本均值近似方法；以及求解大规模问题L-shaped分解算法。通过模拟算例验证了两阶段随机规划模型的优越性和样本均值近似方法的有效性；并对自营配送中心固定运行成本、单位商品的自营配送成本和外包配送成本等进行灵敏度分析，得到了不同参数对应的最优配送策略，结果表明，正常情况下“自营+外包”配送模式是企业的最佳选择。本文同时将配送中心选址和提前备货量作为随机规划模型的第一阶段决策变量，可以帮助企业降低物流成本、提高顾客的满意度。     

Likelihood Inference for Discretely Observed Nonlinear Diffusions

This paper is concerned with the Bayesian estimation of nonlinear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis‐Hastings algorithm, in conjunction with the Euler‐Maruyama discretization scheme, are used to sample the posterior distribution of the latent data and the model parameters. Techniques for computing the likelihood function, the marginal likelihood, and diagnostic measures (all based on the MCMC output) are developed. Examples using simulated and real data are presented and discussed in detail.     

Deterministic Approximation of Stochastic Evolution in Games

This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The processes are Markov chains, and the approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long‐run behavior of the discrete stochastic process, for large populations, and its deterministic flow approximation. In particular, we provide probabilistic bounds on exit times from and visitation rates to neighborhoods of attractors to the deterministic flow. We sharpen these results in the special case of ergodic processes.     

Coordinated Contract Decisions in a Make‐to‐Order Manufacturing Supply Chain: A Stochastic Programming Approach

One of the important objectives of supply chain S&OP (Sales and Operations Planning) is the profitable alignment of customer demand with supply chain capabilities through the coordinated planning of sales, production, distribution, and procurement. In the make‐to‐order manufacturing context considered in this paper, sales plans cover both contract and spot sales, and procurement plans require the selection of supplier contracts. S&OP decisions also involve the allocation of capacity to support sales plans. This article studies the coordinated contract selection and capacity allocation problem, in a three‐tier manufacturing supply chain, with the objective to maximize the manufacturer's profitability. Using a modeling approach based on stochastic programming with recourse, we show how these S&OP decisions can be made taking into account economic, market, supply, and system uncertainties. The research is based on a real business case in the Oriented Strand Board (OSB) industry. The computational results show that the proposed approach provides realistic and robust solutions. For the case considered, the planning method elaborated yields significant performance improvements over the solutions obtained from the mixed integer programming model previously suggested for S&OP.     

Accuracy of Numerical Solutions Using the Euler Equation Residuals

This paper is concerned with asymptotic properties on the accuracy of numerical solutions. It is shown that the approximation error of the policy function is of the same order of magnitude as the size of the Euler equation residuals. Moreover, for bounding this approximation error the most relevant parameters are the discount factor and the curvature of the return function. These findings provide theoretical foundations for the construction of tests to assess the performance of alternative computational methods.