ERROR BOUNDS FOR CALCULATION OF THE GITTINS INDICES

For a wide class of semi-Markov decision processes the optimal policies are expressible in terms of the Gittins indices, which have been found useful in sequential clinical trials and pharmaceutical research planning. In general, the indices can be approximated via calibration based on dynamic programming of finite horizon. This paper provides some results on the accuracy of such approximations, and, in particular, gives the error bounds for some well known processes (Bernoulli reward processes, normal reward processes and exponential target processes).     

Agricultural management using the ADELAIS multiobjective linear programming software: A case application

This paper presents an application of the ADELAIS multiobjective linear programming software to farm planning problems in agricultural management. This application is illustrated on a Spanish farm case study initially presented by Romero, Amador and Barco as an application of compromise programming. The method employed here generates a sequence of efficient solutions using interactive utility assessment and satisfaction levels. A compromise solution among three conflicting objectives, i.e. seasonal labor, employment and business profitability, is finally obtained.     

漂移型线性规划理论及应用

到目前为止,有关灰色线性规划问题有不少研究,如灰色预测型线性规划^[1～6]灰色区间型线性规划^[7]等．本文在文献^[1～7]的基础上,针对漂移型线性规划问题,运用参数线性规划理论与方法,对其满意解及其性质等进行探研,并提出了一些新的结论,不仅为漂移型线性规划作了一些理论讨论,而且还以应用实例给予示范．     

一个地区能源规划模型

本文在综合考虑煤矿、电厂、铁路、输电线路的布局，以及电负荷中心、煤消费中心的分布和能源需求量等多因素复杂关系的基础上，提出了１９９０—２０００年内蒙古东部区能源规划模型。采用线性规划和混合整数规划方法在微型计算机上求解，得出数据结果和结论。     

渗透结构化设计思想的计算机语言教学

简要介绍了结构化设计的要点，提出了渗透结构化设计思想的计算机语言教学法，同时给出了在ＦｏｘＢＡＳＥ＋语言教学中如何渗入结构化设计思想     

A note on the admissibility of hammersley's estimator of an integer mean

Let X₁, X₂, …, X_n be identically, independently distributed N(i,1) random variables, where i = 0, ±1, ±2, … Hammersley (1950) showed that d = [X?_n], the nearest integer to the sample mean, is the maximum likelihood estimator of i. Khan (1973) showed that d is minimax and admissible with respect to zero-one loss. This note now proves a conjecture of Stein to the effect that in the class of integer-valued estimators d is minimax and admissible under squared-error loss.     

Duality and local sensitivity analysis in least squares,minimax, and least absolute values regressions

Abstract

This paper deals with the problem of local sensitivity analysis in regression, i.e., how sensitive the results of a regression model (objective function, parameters, and dual variables) are to changes in the data. We use a general formula for local sensitivities in optimization problems to calculate the sensitivities in three standard regression problems (least squares, minimax, and least absolute values). Closed formulas for all sensitivities are derived. Sensitivity contours are presented to help in assessing the sensitivity of each observation in the sample. The dual problems of the minimax and least absolute values are obtained and interpreted. The proposed sensitivity measures are shown to deal more effectively with the masking problem than the existing methods. The methods are illustrated by their application to some examples and graphical illustrations are given.     

基于模糊多分配的辽宁煤炭枢纽站选址研究

提出一种模糊多分配p枢纽站中位问题,其中运输成本定义为模糊变量,问题的目标函数是在给定的可信性水平下,最小化总的运输成本。对于梯形和正态运输成本,问题等价于确定的混合整数线性规划问题。在实证分析中,选取了辽宁省煤炭产业的相关面板数据,分析计算在不同可信度水平下煤炭运输枢纽站设立的数量和位置,再利用传统的优化方法(如分枝定界法)求解。经计算,这一模型和求解方法可以用来解决辽宁省煤炭运输的选址问题。     

Balanced treatment incomplete block designs through integer programming

An algorithm is presented to construct balanced treatment incomplete block (BTIB) designs using a linear integer programming approach. Construction of BTIB designs using the proposed approach is illustrated with an example. A list of efficient BTIB designs for 2 ? v ? 12, v + 1 ? b ? 50, 2 ? k ? min(10, v), r ? 10, r₀ ? 20 is provided. The proposed algorithm is implemented as part of an R package.     

Optimal sample coordination using controlled selection

Sample coordination maximizes or minimizes the overlap of two or more samples selected from overlapping populations. It can be applied to designs with simultaneous or sequential selection of samples. We propose a method for sample coordination in the former case. We consider the case where units are to be selected with maximum overlap using two designs with given unit inclusion probabilities. The degree of coordination is measured by the expected sample overlap, which is bounded above by a theoretical bound, called the absolute upper bound, and which depends on the unit inclusion probabilities. If the expected overlap equals the absolute upper bound, the sample coordination is maximal. Most of the methods given in the literature consider fixed marginal sampling designs, but in many cases, the absolute upper bound is not achieved. We propose to construct optimal sampling designs for given unit inclusion probabilities in order to realize maximal coordination. Our method is based on some theoretical conditions on joint selection probability of two samples and on the controlled selection method with linear programming implementation. The method can also be applied to minimize the sample overlap.