一类灰色组合投资决策方法

以灰色系统理论和概率论为基础,探讨了含有区间灰数的组合投资决策问题,提出了具有交易费用的灰色组合投资模型的有效解及其临界最优解和均值白化最优解的概念.并且指出了这些概念所对应的投资偏好.利用分析方法和技巧,融合经典组合投资理论,构建了带有交易费用的灰色组合投资模型的熵权分析算法.为不确定型组合投资决策方法的研究提出了一条新思路.文中的算例说明了算法的可行性.     

活动长度有限制的多工序批量加工生产计划研究

当前的化工制造中,有很多工厂使用柔性制造设备,并采用批生产模式来组织生产.由于对设备进行准备和清理的成本比较大,加工的排序一般采用多批次加工同一种产品的活动（campaign）模式.在实际的生产中,由于需要保证产品质量和减少库存,应该考虑限制活动的最大长度.本文针对活动长度有限制的多工序批量加工问题进行研究,利用状态-任务-网络概念和层级模型方法,提出了修正的活动计划模型.该模型是基于混合整数线性规划模型,并且以供应网络内总生产成本和物流成本最小化作为目标函数.最后用一个算例来说明所构建模型的有效性.     

A Two-Warehouse Probabilistic Order-Level Inventory Model for Deteriorating Items

In this paper an order-level probabilistic inventory model for deteriorating items with two warehouses is developed. It is assumed that the production rate is infinite and shortages are allowed. The rates of deterioration of items in the two warehouses are different. Also, a single-warehouse version for deteriorating items is discussed. This paper also considers a two-warehouse model for non-deteriorating items. An illustrative example offers a comparative study of the optimum cost for varying shortage cost.     

Optimizing Response Functions of Media Exposure Distributions

The object of this paper is to show how to maximize the expected response of an advertising campaign, subject to a budget constraint. Four response functions are considered with closed-form solutions given for the resulting expected responses. These expected responses use only univariate marginal distributions and pairwise duplications, so they can be rapidly calculated compared with the usual cumbersome calculation based on the full frequency distribution. A simple heuristic solution to the formulated non-linear integer programming problem is given, resulting in big savings in computation time over the branch-and-bound technique, for example.     

A Game Theoretical Multiple Resource Interaction Approach to Resource Allocation in an Air Campaign

In this paper we propose a multiple resource interaction model in a game-theoretical framework to solve resource allocation problems in theater level military campaigns. An air raid campaign using SEAD aircraft and bombers against an enemy target defended by air defense units is considered as the basic platform. Conditions for the existence of saddle point in pure strategies is proved and explicit feedback strategies are obtained for a simplified model with linear attrition function limited by resource availability. An illustrative example demonstrates the key features.     

Determining the Optimum Stratum Boundaries Using Mathematical Programming

The method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation, is known as optimum stratification. In order to make the strata internally homogeneous, the strata are constructed in such a way that the strata variances should be as small as possible for the characteristic under study. In this paper the problem of determining optimum strata boundaries (OSB) is discussed when strata are formed based on a single auxiliary variable with a varying measurement cost per units across strata. The auxiliary variable considered in the problem is a size variable that holds a common model for a whole population. The OSB are achieved effectively by assuming a suitable distribution of the auxiliary variable and creating strata by cutting the range of the distribution at optimum points. The problem of finding the OSB, which minimizes the variance of the estimated population mean under a weighted stratified balanced sampling, is formulated as a mathematical programming problem (MPP). Treating the formulated MPP as a multistage decision problem, a solution procedure using dynamic programming technique is developed. A numerical example using a hospital population data is presented to illustrate the computational details of the solution procedure. A software program coded in JAVA is written to carry out the computation. The distribution of the auxiliary variable in this example is considered to be continuous with an exponential density function.     

A model for optimal stopping in advertisement

In this work we propose a model for optimal advertisement in new product diffusion based on the Bass model and assuming that the effect of the environmental pressure in the diffusion of the product is subject to a stochastic dependence. The optimal stopping problem is reduced to a free boundary problem which is analyzed and solved numerically, in order to determine an optimal stopping rule for the advertisement campaign. The numerical solution is obtained through a policy iteration like contraction scheme, the convergence properties of which are studied in detail. Furthermore, the expected time until the optimal stopping of the campaign is estimated. Finally, a combined optimal stopping and control problem for the optimization of the advertisement effectiveness is also proposed and solved numerically. Our results are expected to provide useful guidelines for campaign managers, for the choice of effectiveness and duration of an advertisement campaign.     

On a Replacement Problem of a Cumulative Damage Model

Items are assumed to fail only by degradation. An appropriate stochastic model of such items is a cumulative process in which an item can fail only when the total amount of damage exceeds a prespecified failure level. This paper introduces a replacement policy in which an item is replaced at a certain level of damage before failure or at failure, whichever occurs first. The optimum replacement level of damage which will minimize the total expected cost per unit of time for an infinite time span is obtained. A numerical example is also presented. The total expected cost for a finite time span is also discussed.     

Optimal economic production quantity policy for imperfect process with imperfect repair and maintenance

This study integrates maintenance and production programs with the economic production quantity (EPQ) model for an imperfect process involving a deteriorating production system with increasing hazard rate: imperfect repair and rework upon failure (out of control state). The imperfect repair performs some restorations and restores the system to an operating state (in-control state), but leaves its failure until perfect preventive maintenance (PM) is performed. There are two types of PM, namely imperfect PM and perfect PM. The probability that perfect PM is performed depends on the number of imperfect maintenance operations performed since the last renewal cycle. Mathematical formulas are obtained for deriving the expected total cost. For the EPQ model, the optimum run time, which minimizes the total cost, is discussed. Various special cases are considered, including the maintenance learning effect. Finally, a numerical example is presented to illustrate the effects of PM, setup, breakdown and holding costs.     

An example of simulation optimisation using a neural network metamodel: finding the optimum number of kanbans in a manufacturing system

A method of finding the optimum solution for a stochastic discrete-event system is described. A simulation model of the system is first built and then used to train a neural network metamodel. The optimisation process consists of using the metamodel to find an approximate optimum solution. This solution is then used by the simulation as the starting point in a more precise search for an optimum. The approach is demonstrated with an example that finds the optimum number of kanbans needed to control a manufacturing system.     

Optimal design in axial motion for several frequency constraints

Governing equations for the optimal design of a rod with tip mass subject to several constraints on natural frequency are developed. The relation of this mass distribution to the globally optimum design for lowest frequency is discussed. A numerical example for two frequencies is presented. Some continuity results concerning the optimal mass distribution are presented.     

Multiproduct,Three-Stage Production Inventory Systems

This paper deals with production systems with three stages in series and producing multiple products. A method of determining a near optimal production plan taking into consideration the demands, the production rates, the set-up costs and all the relevant inventory carrying costs is discussed. This heuristic approach gives the method of determining the production batch quantities and the sequence in which the different products are to be taken up in a production cycle. A numerical example is also included. The results obtained for 21 test problems by the use of the heuristic are compared with the exact optimum values, and the power of the heuristic is demonstrated.     

物业管理招标中的层次关联比选

应用层次分析法确定影响物业管理投标书总体方案的各因素间权重 ,根据灰色关联理论建立了对投标书进行总体综合评价并排序优选的数学模型 ,给出了计算实例 .     

基于模糊机会约束规划的最优产量决策

研究了模糊环境下,双寡头市场中两企业的最优产量决策问题。在四种博弈结构下,结合Cournot模型、Stackelberg模型以及模糊可能性理论,建立了模糊机会约束规划模型来确定两企业的最优产量水平。最后通过一个算例说明,基于市场的最大收益,最优决策应为两企业均为追随者。     

需求和采购价格均为时变的易变质物品EOQ模型

基于需求和采购价格均为时变的EOQ模型,进一步考虑物品的变质对库存系统的影响,建立了相应的EOQ模型,并证明了在给定条件下,计划期内的库存总成本是关于服务水平的凸函数.并应用数学软件MATLAB,对该模型进行仿真计算和主要参数的灵敏度分析,结果表明,该模型存在最优解且各主要参数对最优库存控制有不同程度的影响.     

Non-linear model parameter estimation–estimating a feasible parameter set with respect to model use

This article deals with non-linear model parameter estimation from experimental data. As for non-linear models a rigorous identifiability analysis is difficult to perform, parameter estimation is performed in such a way that uncertainty in the estimated parameter values is represented by the range of model use results when the model is used for a certain purpose. Using this approach, the article presents a simulation study where the objective is to discover whether the estimation of model parameters can be improved, so that a small enough range of model use results is obtained. The results of the study indicate that from plant measurements available for the estimation of model parameters, it is possible to extract data that are important for the estimation of model parameters relative to a certain model use. If these data are improved by a proper measurement campaign (e.g. proper choice of measured variables, better accuracy, higher measurement frequency) it is to be expected that a valid model for a certain model use will be obtained. The simulation study is performed for an activated sludge model from wastewater treatment, while the estimation of model parameters is done by Monte Carlo simulation.     

Intervention analysis to identify significant exposures in pulsing advertising campaigns: an operative procedure

The purpose of this paper is to develop an operational method to detect the most effective exposures in the context of a given pulsing advertising campaign. For most effective, are intended those exposures that produce a statistically significant increase in the level of a response variable, either temporarily or permanently. The method consists in specifying an intervention model for the response variable, where the significant exposures are selected on the basis of a probabilistic criterion, and is empirically evaluated by using brandlevel data from five advertising tracking studies that also include the actual spending schedules. Given a pulsing advertising campaign, the proposed method serves both as an a-posteriori improvement of the campaign itself and as an a-priori additional information for programming future scheduling. Mathematics Subject Classification: 62M10.     

矿井布局问题

本研究了“撒网式”全面钻探过程中如何尽可能多地利用旧井而节约开支的问题,在两种距离和一定的误差意义下,运用图论、线性规划等方法建立了多个数学模型,并提出了相应的算法,对于所给的数值例子,利用计算机进行计算,得到了矿井最佳布局方案。     

Spatial Regression Models,Response Surfaces,and Process Optimization

Abstract

Spatial regression models are developed as a complementary alternative to second-order polynomial response surfaces in the context of process optimization. These models provide estimates of design variable effects and smooth, data-faithful approximations to the unknown response function over the design space. The predicted response surfaces are driven by the covariance structures of the models. Several structures, isotropic and anisotropic, are considered and connections with thin plate splines are reviewed. Estimation of covariance parameters is achieved via maximum likelihood and residual maximum likelihood. A feature of the spatial regression approach is the visually appealing graphical summaries that are produced. These allow rapid and intuitive identification of process windows on the design space for which the response achieves target performance. Relevant design issues are briefly discussed and spatial designs, such as the packing designs available in Gosset, are suggested as a suitable design complement. The spatial regression models also perform well with no global design, for example with data obtained from series of designs on the same space of design variables. The approach is illustrated with an example involving the optimization of components in a DNA amplification assay. A Monte Carlo comparison of the spatial models with both thin plate splines and second-order polynomial response surfaces for a scenario motivated by the example is also given. This shows superior performance of the spatial models to the second-order polynomials with respect to both prediction over the complete design space and for cross-validation prediction error in the region of the optimum. An anisotropic spatial regression model performs best for a high noise case and both this model and the thin plate spline for a low noise case. Spatial regression is recommended for construction of response surfaces in all process optimization applications.     

多用户多准则随机系统最优与最优收费

针对固定交通需求量和出行者的时间价值为离散分布的多准则随机交通均衡,分别研究了依费用度量和依时间度量的多用户多准则随机系统最优和最优收费问题.分别建立了基于费用和基于时间的随机系统最优的最优化模型,阐述了该模型解的唯一性条件及等价的变分不等式问题.运用变分不等式方法,研究了一阶最优收费的可行性,即能否依边际定价原则,通过收取与出行者类别无关的道路收费使多用户多准则随机均衡流与随机系统最优流一致.一阶最优收费不适用于依时间度量的随机系统最优情况,因而建立了一个最优化模型来得到此时的非歧视性道路收费.最后给出了具体算例.