混合整数线性模型方差分量的Bayes估计

本文研究了混合整数线性模型方差分量在无信息先验分布和有信息先验分布下Bayes估计，给出了混合整数线性模型方差分量无信息和：有信息先验分布下的极大后验估计和最佳Bayes估计。     

ρ混合、φ混合、ψ混合线性模型M估计的强相合性

研究了 ρ混合、φ混合、ψ混合样本线性模型中回归参数M估计的强相合性 ,在条件不变的情况下 ,获得与独立情形一样的M估计是强相合的充分条件 ,推广了文 [1 ]定理 2 .     

线性模型中φ混合误差下回归系数最小二乘估计的相合性

本文研究线性模型中φ－混合误差序列下回归系数最小二乘估计的相合性，分别对最小二乘估计为强相合和ｒ阶平均相合给出一些充分条件。     

混合线性模型M估计的强相合性

研究了混合样本线性模型中回归参数M估计的强相合性,在较弱的矩条件下,获得了M估计是强相合的充分条件,实质性地改进和推广了文[1]定理3.1.     

混合线性模型M估计的强相合性

研究了ρ~混合样本线性模型中回归参数M估计的强相合性, 在较弱的矩条件下, 获得了M估计是强相合的充分条件, 实质性地改进和推广了文［1］定理3.1.     

样本相关时线性模型中的ML_1N估计的强相合性

本文在样本为平稳强 φ-混合随机变量序列的条件下,证明了线性回归模型的最小一乘(简记为 ML_1N)估计的强相合性.     

样本相关时线性模型中的ML_1N估计的强相合性

本文在样本为平稳强 φ-混合随机变量序列的条件下,证明了线性回归模型的最小一乘(简记为 ML_1N)估计的强相合性.     

半参数混合效应模型中的估计及其强相合性

将Tao等(1999)提出的线性混合效应模型推广为半参数混合效应模型,给出了模型参数、回归函数和随机效应密度的估计,并研究了估计的强相合性及部分强相合速度.统计模拟表明我们给出的估计方法是可行的.     

线性模型中相依误差下回归系数最小二乘估计的相合性

文献[1]考虑了线性模型中误差序列{e_i}独立时,最小二乘估计(?)_n 的 r-阶矩的平均相合性.对{e_i}为鞅差序列,线性过程序列的情况,最近一些文献中得出了(?)_n 强相合的一些结果.在[1]的工作基础上,本文对{e_i}为 m-相依、*-混合、广义高斯等相依序列得出相应结果,给出了(?)_n 为 r-阶矩相合及强相合的一些充分条件.本文中相依序列的定义引自[2],[2]中给出了一些相依序列的实例,因而考虑相依误差下(?)_n 的相合性有一定的实用意义.考虑线性回归模型:     

混合样本线性模型M估计的强相合性

研究了混合样本线性模型中的M估计,在较弱的矩条件下,获得了M估计是强相合估计的充分条件.与相应结论比较,有了较大的实质性改进.     

整数线性规划投资组合模型的直接搜索算法求解

利用松弛最优邻近解临域整数点搜索法作过滤条件,建立求解整数规划的新方法——直接搜索算法,利用直接搜索算法并借助Matlab软件求解整数线性规划投资组合模型.数值结果表明了模型的建立与提出方法的有效性.     

Complexity of linear programming

The complexity of linear programming is discussed in the “integer” and “real number” models of computation. Even though the integer model is widely used in theoretical computer science, the real number model is more useful for estimating an algorithm's running time in actual computation.Although the ellipsoid algorithm is a polynomial-time algorithm in the integer model, we prove that it has unbounded complexity in the real number model. We conjecture that there exists no polynomial-time algorithm for the linear inequalities problem in the real number model. We also conjecture that linear inequalities are strictly harder than linear equalities in all “reasonable” models of computation.     

奥运会临时超市网点的优化设计

在对[1]提供的问卷调查数据进行处理的基础上,运用商圈理论,就2008北京奥运会比赛主场馆周边地区临时超市网点(MS)的设计问题,在满足购物需求、分布基本均衡和商业上赢利三大基本要求上,建立起整数线性规划数学模型,并得到较为理想的优化设计结果.     

An integer fixed-charge multicommodity flow (FCMF) model for train unit scheduling

An integer fixed-charge multicommodity flow (FCMF) model is used as the first part of a two-phase approach for train unit scheduling, and solved by an exact branch- and-price method. To strengthen knapsack constraints and deal with complicated scenarios arisen in the integer linear program (ILP) from the integer FCMF model, preprocessing is used by computing convex hulls of sets of points representing all possible train formations utilizing multiple unit types.     

Minimum node covers and 2-bicritical graphs

The problem of finding a minimum cardinality set of nodes in a graph which meet every edge is of considerable theoretical as well as practical interest. Because of the difficulty of this problem, a linear relaxation of an integer programming model is sometimes used as a heuristic. In fact Nemhauser and Trotter showed that any variables which receive integer values in an optimal solution to the relaxation can retain the same values in an optimal solution to the integer program. We define 2-bicritical graphs and give several characterizations of them. One characterization is that they are precisely the graphs for which an optimal solution to the linear relaxation will have no integer valued variables. Then we show that almost all graphs are 2-bicritical and hence the linear relaxation almost never helps for large random graphs.This research was supported in part by the National Research Council of Canada.     

An optimal solution to a three echelon supply chain network with multi-product and multi-period

Recently, Kadadevaramath et al. (2012) [1] presented a mathematical model for optimizing a three echelon supply chain network. Their model is an integer linear programming (ILP) model. In order to solve it, they developed five algorithms; four of them are based on a particle swarm optimization (PSO) method and the other is a genetic algorithm (GA). In this paper, we develop a more general mathematical model that contains the model developed by Kadadevaramath et al. (2012) [1]. Furthermore, we show that all instances proved in Kadadevaramath et al. (2012) [1] can easily be solved optimally by any integer linear programming solver.     

Multi-step methods for choosing the best set of variables in regression analysis

In a recent article (Konno and Yamamoto in ISE 07-01, Department of Industrial and Systems Engineering, Chuo University, February 2007), one of the authors formulated the problem of choosing the best set of explanatory variables from a large number of candidate variables in a linear regression model as a mixed 0–1 integer linear programming problem and showed that it can be solved by the state-of-the-art integer programming software.     

A linear programming embedded genetic algorithm for an integrated cell formation and lot sizing considering product quality

Production lot sizing models are often used to decide the best lot size to minimize operation cost, inventory cost, and setup cost. Cellular manufacturing analyses mainly address how machines should be grouped and parts be produced. In this paper, a mathematical programming model is developed following an integrated approach for cell configuration and lot sizing in a dynamic manufacturing environment. The model development also considers the impact of lot sizes on product quality. Solution of the mathematical model is to minimize both production and quality related costs. The proposed model, with nonlinear terms and integer variables, cannot be solved for real size problems efficiently due to its NP-complexity. To solve the model for practical purposes, a linear programming embedded genetic algorithm was developed. The algorithm searches over the integer variables and for each integer solution visited the corresponding values of the continuous variables are determined by solving a linear programming subproblem using the simplex algorithm. Numerical examples showed that the proposed method is efficient and effective in searching for near optimal solutions.     

Cutting plane method for multiple objective stochastic integer linear programming

This paper grapples with the problem of incorporating integer variables in the constraints of a multiple objective stochastic linear program (MOSLP). After representing uncertain aspirations of the decision maker by converting the original problem into a deterministic multiple objective integer linear program (MOILP), a cutting plane technique may be used to compute all the efficient solutions of the last model leaving the decision maker to choose a solution according to his preferences. A numerical example is also included for illustration.     

A new robust mixed integer-valued model in DEA

The mixed integer linear programming (MILP) models are proposed to estimate the performance of decision making units (DMUs) including both integer and real values in data envelopment analysis (DEA). There are several studies to propose MILPs in the literature of DEA; however, they have some major shortcomings unfortunately. This study firstly mentioned the shortcomings in the previous researches and secondly suggests a robust MILP based on the Kourosh and Arash Method (KAM). The proposed linear model, integer-KAM (IKAM), has almost all capabilities of the linear KAM and significantly removes the shortcomings in the current MILPs. For instance, IKAM benchmarks and ranks all technically efficient and inefficient DMUs at the same time. It detects outliers, and estimates the production frontier significantly. A numerical example of 39 Spanish airports with four integer inputs and three outputs including two integer values and a real value also represents the validity of the statements.