Optimal allocation in J-stage sampling with stratification from finite population

Summary  The known results of optimal allocation in two-stage simple random sampling with stratification from finite population are generalized for J-stages. The optimalization is treated by minimizing the cost function for given variance as well as by minimizing the variance for given cost. It turns out that for both cases the optimal values differ only for the first-stage units and are the same for all the subsequent. The general formula for minimum variance of the unbiased estimator of the population mean per element is given.     

Affordable dwelling-layout system design—A model for optimization

The systems nature of the residential land planning has been outlined and an optimization model for minimizing the cost of a layout has been presented earlier. In the present paper, a model for optimal design of the dwelling-layout system, consisting of the dwelling as well as the residential layout, has been developed. In this model, which is also a non-linear programming problem, maximizing the dwelling space has been taken as the objective function. Affordable cost and physical design standards such as density, public open space, circulation interval, have been taken as the constraints in the model. The problem has been solved using the geometric programming technique and the programme developed by the author. Using this model, a dwelling-layout system could be designed directly to achieve the maximum benefit i.e. maximum dwelling space, within the given affordable cost and fulfilling the given physical design standards mentioned above.     

Risk preference heterogeneity in group contests

We analyze the first model of a group contest with players that are heterogeneous in their risk preferences. In our model, individuals’ preferences are represented by a utility function exhibiting a generalized form of constant absolute risk aversion, allowing us to consider any combination of risk-averse, risk-neutral, and risk-loving players. We begin by proving equilibrium existence and uniqueness under both linear and convex investment costs. Then, we explore how the sorting of a compatible set of players by their risk attitudes into competing groups affects aggregate investment. With linear costs, a balanced sorting (i.e., minimizing the variance in risk attitudes across groups) always produces an aggregate investment level that is at least as high as an unbalanced sorting (i.e., maximizing the variance in risk attitudes across groups). Under convex costs, however, identifying which sorting is optimal is more nuanced and depends on preference and cost parameters.     

Simultaneous optimal estimation in linear mixed models

Simultaneous optimal estimation in linear mixed models is considered. A necessary and sufficient condition is presented for the least squares estimator of the fixed effects and the analysis of variance estimator of the variance components to be of uniformly minimum variance simultaneously in a general variance components model. That is, the matrix obtained by orthogonally projecting the covariance matrix onto the orthogonal complement space of the column space of the design matrix is symmetric, each eigenvalue of the matrix is a linear combinations of the variance components and the number of all distinct eigenvalues of the matrix is equal to the the number of the variance components. Under this condition, uniformly optimal unbiased tests and uniformly most accurate unbiased confidence intervals are constructed for the parameters of interest. A necessary and sufficient condition is also given for the equivalence of several common estimators of variance components. Two examples of their application are given.     

Optimum allocation in stratified sampling with replacement

In a stratified sample, when sampling is done with replacement in each stratum a better estimate of the population mean can be achieved by considering the distinct units only. An explicit expression for the variance for the mean, of a stratified sample based on the distinct units only, is obtained. Then the optimum allocation for the different stratum are obtained by minimizing this variance subject to (i) total sample size being fixed, or (ii) the expected number of distinct units being fixed. Neyman’s solutions are obtained as special cases. The solutions finally arrived at are algebraically complex, hence, numerical methods are applied. In all examples, the variance of the estimates obtained by this method are smaller than the variances obtained by Neyman’s allocation. A part of this work was supported by the Office of the Ordinance Research; U.S.A. Grant (DA-AROL(D)-31-124-G83) when the author was at University of California, Berkeley.     

Tests on the validity of static equilibrium models

This paper provides a framework to test the validity of static cost minimizing equilibrium assumptions that form the basis for much of the empirical literature on industrial production. The point of departure in our model is to allow the observed technology to be at a short-run equilibrium where firms minimize variable costs while being constrained by the utilization levels of quasi-fixed factors. The long-run equilibrium is then inferred by minimizing total costs with the optimal adjustment of quasi-fixed factor levels.We use results from the optimization problem to form tests with respect to quantities and prices. In the quantity space version, departures between the actual and the optimal long-run levels of quasi-fixed factors are tested for statistical significance. A significant non-zero departure implies the rejection of a static equilibrium specification. In the price space version, the test is cast as a comparison of the market price and the long-run shadow value of a quasi-fixed factor. Although the two versions would give identical results in the non-stochastic case, the rejection powers of these two tests are found to depend on the particular functional form chosen to represent the production process (i.e. cost function).In an application based on aggregate U.S. manufacturing where capital is taken to be quasi-fixed, we were able to reject the static equilibrium specification. These results cast doubt on the validity of a number of previous empirical studies.     

基于供应链管理的一种采购算法研究

提出一种能在供应链管理环境下辅助功能性产品采购决策的方法。企业通过对价格和需求分布的分析,向一组供应商发送报价请求单RFQ(Request For Quote),相应地,供应商将会给出不同的报价反馈,这些报价反馈包含价格、交货数量、交货期等信息。企业在对这些供应商进行选择时,考虑了两个目标:每日的库存水平达到最优;同时使整个采购期内总成本最小。问题被描述为一个马尔科夫决策过程MDP(Markov decisionprocess),该过程能通过下一次所有随机状态的总期望效用值计算当前行为的效用。在求解该问题时,本文使用了动态规划方法。     

考虑寿命周期循环费用的预制混凝土结构可靠性优化设计

本文考虑建筑物从设计、生产、建造、使用、维修直到最终破坏整个寿命周期循环的费用变化过程,建立了一个基于可靠性的预制混凝土构件／结构的最小寿命周期费用优化设计决策模型。     

成本差异计算分析方法刍议

结合成本管理的实际情况，利用统计指数分析原理。对传统的成本差异分析内容与方法进行了分析、调整与完善。将变动成本差异与固定制造成本差异分析方法归一，同时将实际开支总额与标准开支总额之间的差额作为总差异．其分支差异有三个差异，即产量差异、用量差异和价格差异。在完善绝对数分析的基础上。补充了相对数分析内容。     

Economic design of a two-stage screening procedure with a prescribed outgoing quality

Summary An economic two-stage screening procedure based on screening and performance variables is proposed. A screening variable is used first to decide whether an item should be accepted, rejected, or undecided. The performance variable is then used to classify the undecided items. The two variables are assumed to have a bivariate normal distribution. A cost model is constructed which involves costs due to screening and performance inspections and misclassification errors. Optimal cutoff values on the screening variable minimizing the expected cost are obtained subject to the constraint that the outgoint quality exceeds a prespecified level. Methods of finding the optimal cutoff values are presented for both parameters-known and parameters-unknown cases.     

A note on Model Reference Adaptive System (MRAS) estimate with infinite variance

This paper discusses the estimation of a parameter in an autoregressive model with infinite variance. A recursive estimation procedure based on minimizing the prediction errors is provided. It is also shown that the model reference adaptive system estimate for an AR (1) model given in Aase (1983) is a special case.     

Optimal migration policies: an analytical approach. Part I

This paper explores the analytical features of population distribution or human settlement policies. It proposes a methodology for quantitative policy analysis and policy design based on optimal control and system theory. The paper consists of two parts. This part shows how policy models may be derived from demographic and demoeconomic or demometric models by adding a new dimension: the goals-means relationship of population distribution policy. It examines a large class of relevant policy models and demonstrates their relationship to the original Tinbergen Theory of Policy, which provides a paradigm for static and dynamic policy analysis. Problems of existence and of design of optimal population distribution policies are studied analytically. In designing optimal policies, use may be made of the minimizing properties of generalized inverses.     

考虑役龄阈值的最佳缓冲区库存维修策略研究

预防性维护PM对于生产系统有重要的作用。由于设备维护时会造成生产停滞,影响企业的经济效益,所以在生产线上下游设备之间建立库存缓冲区,保证生产的持续进行。考虑引入设备役龄阈值,构建费用模型和维护策略模型。以设备役龄阈值和缓冲区库存量为自变量,以最小化周期内总费用为目标,获得最佳的设备役龄阈值和缓冲区库存量。最后运用Matlab仿真软件进行了算例分析,验证了模型的有效性。     

A General Algorithm for Univariate Stratification

This paper presents a general algorithm for constructing strata in a population using  X , a univariate stratification variable known for all the units in the population. Stratum  h  consists of all the units with an  X  value in the interval   [ b _{h −1},  b_h )   . The stratum boundaries   { b_h }   are obtained by minimizing the anticipated sample size for estimating the population total of a survey variable  Y  with a given level of precision. The stratification criterion allows the presence of a take-none and of a take-all stratum. The sample is allocated to the strata using a general rule that features proportional allocation, Neyman allocation, and power allocation as special cases. The optimization can take into account a stratum-specific anticipated non-response and a model for the relationship between the stratification variable  X  and the survey variable  Y . A loglinear model with stratum-specific mortality for  Y  given  X  is presented in detail. Two numerical algorithms for determining the optimal stratum boundaries, attributable to Sethi and Kozak, are compared in a numerical study. Several examples illustrate the stratified designs that can be constructed with the proposed methodology. All the calculations presented in this paper were carried out with stratification , an R package that will be available on CRAN (Comprehensive R Archive Network).     

Economic Process Management and Its Application on Bank Industry

A renewal equation approach is proposed to derive the multiple special-cause cost model for a system with two dependent subprocesses. The economic individual X control chart and simple cause-selecting control chart are thus constructed to monitor the two subprocesses. They may be used to maintain the whole process with minimum cost and effectively distinguish which component of the subprocesses is out of control. The economic design parameters of these two control charts can be determined by minimizing the cost model using a simple grid search method. An example of its application on controlling service quality in the bank industry is given to illustrate the design procedure and its application. It shows that these control charts may be used to control not only manufacturing dependent subprocesses but also service organisations with dependent subprocesses.     

Impact of treatment heterogeneity on drug resistance and supply chain costs

The efficacy of scarce drugs for many infectious diseases is threatened by the emergence and spread of resistance. Multiple studies show that available drugs should be used in a socially optimal way to contain drug resistance. This paper studies the tradeoff between risk of drug resistance and operational costs when using multiple drugs for a specific disease. Using a model for disease transmission and resistance spread, we show that treatment with multiple drugs, on a population level, results in better resistance-related health outcomes, but more interestingly, the marginal benefit decreases as the number of drugs used increases. We compare this benefit with the corresponding change in procurement and safety stock holding costs that result from higher drug variety in the supply chain. Using a large-scale simulation based on malaria transmission dynamics, we show that disease prevalence seems to be a less important factor when deciding the optimal width of drug assortment, compared to the duration of one episode of the disease and the price of the drug(s) used. Our analysis shows that under a wide variety of scenarios for disease prevalence and drug cost, it is optimal to simultaneously deploy multiple drugs in the population. If the drug price is high, large volume purchasing discounts are available, and disease prevalence is high, it may be optimal to use only one drug. Our model lends insights to policy makers into the socially optimal size of drug assortment for a given context.     

Optimal expenditures on police protection

The object of this paper is to propose an approach for operationalizing Rubin's (Minimizing Harm: a New Crime Policy for modern America, Westview Press, Boulder, CO, 1999) idea that minimizing harm is a solution to the crime policy conundrum. Harm is defined to be the total cost of damages due to crime plus the cost of police protection. Its minimization determines optimal expenditures for protection. This is an appropriate basis for specifying the optimal size of a police force, and provides a term of reference for actual policy decisions. Data for the states of the US are used to make the presentation more concrete and to clarify some of the problems that must be solved in actual applications of the method suggested. This does not eliminate the applicability of the approach to any other country or to the geo-political subdivisions within a country. The results obtained are of interest to policy makers dealing specifically with expenditures for police at local, regional or national levels or, more generally, with similar uses of public or private financial resources.     

随机需求和提前时间存储系统的建模与仿真

讨论了需求量、需求发生的间隔以及提前时间都为随机变量的一般随机存储系统。以平均库存总费用和缺货率为系统性能指标建立仿真模型，将二者加权平均得到策略的综合系数。在各种费用参数给定后，利用计算机仿真技术来选定最优存储策略。     

Logistics optimization through a social approach for food distribution

The management of supply chains is becoming more important in economic and social environments. Currently, the social sustainability is a factor that must be considered to design governmental strategies and policies. The objective of this research paper was to show, with a case study an approach to optimize distribution and delivery logistics of food in a social assistance program of school breakfast using mathematical models that include transportation distance, optimal locations, and vehicle routing through different clusters. By using qualitative variables like poverty levels, food insecurity and social exclusion, different clustering methods are proposed with the purpose of identifying the common characteristics in the studied population; and at the same time, reducing the distribution complexity. The results show an efficient approach to design a supply chain that includes economic and social factors. The new model developed in this paper can be used to plan social assistance governmental programs, to identify the specific needs and characteristics of the beneficiaries, minimizing the total cost of the distribution network logistics when delivering food for school meals.     

Model assisted survey sampling strategy in two phases

Postulating a super-population regression model connecting a size variable, a cheaply measurable variable and an expensively observable variable of interest, an asymptotically optimal double sampling strategy to estimate the survey population total of the third variable is specified. To render it practicable, unknown model-parameters in the optimal estimator are replaced by appropriate statistics. The resulting generalized regression estimator is then shown to have a model-cum-asymptotic design based expected square error equal to that of the asymptotically optimum estimator itself. An estimator for design variance of the estimator is also proposed.