Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem

In the binary single constraint Knapsack Problem, denoted KP, we are given a knapsack of fixed capacity c and a set of n items. Each item j, j = 1,...,n, has an associated size or weight w_j and a profit p_j. The goal is to determine whether or not item j, j = 1,...,n, should be included in the knapsack. The objective is to maximize the total profit without exceeding the capacity c of the knapsack. In this paper, we study the sensitivity of the optimum of the KP to perturbations of either the profit or the weight of an item. We give approximate and exact interval limits for both cases (profit and weight) and propose several polynomial time algorithms able to reach these interval limits. The performance of the proposed algorithms are evaluated on a large number of problem instances.     

Quantitative Estimates of Risk for Noncancer Endpoints

While quantitative estimates of risk have been a standard practice in cancer risk assessment for many years, no similar practice is evident in noncancer risk assessment. We use two recent examples involving methylmercury and arsenic to illustrate the negative impact of this discrepancy on risk communication and cost-benefit analysis. We argue for a more balanced treatment of cancer and noncancer risks and suggest an approach for reaching this goal.     

Priority Setting for the Distribution of Localized Hazard Protection

We address the problem of distributing safety-enhancing devices across a region, where each identical device provides for only local protection of the population. The devices protect nonidentical sectors of the population. The sectors of population are exposed to nonidentical intensities of hazard. A method for the screening and prioritizing of needs for the protective devices is described. An approach of risk-benefit-cost analysis under uncertainty is recommended as follows. Measures of hazard intensity and population exposure are identified. Exogenous parameters that influence assessments of risks, benefits, and costs are identified. Uncertainties of the exogenous parameters are propagated by interval analysis. Several tiers of the plausibility of need for protection are identified. The tiers are useful in setting priorities for the distribution of the safety devices. The method is demonstrated in an engineering application to roadway lighting, but has implications for disaster preparedness, anti-terrorism, transportation safety, and other arenas of public safety.     

制造业设备维护与管理的相对有效性评估

在设备维护与管理的评估中引入数据包络分析,以此为核心构建了设备维护与管理相对有效性的评估方法。该方法在系统功能建模的基础上,全面分析了设备维护与管理作为服务系统的投入与产出构成,以数据包络分析为计算模型完成了设备维护与管理有效性的评估。该方法满足了设备维护与管理评估全面性和客观性的要求,其有效性和可信度通过在某石化企业的应用得到了验证。     

Risk Modeling, Assessment, and Management of Lahar Flow Threat

The 1991 eruption of Mount Pinatubo in the Philippines is considered one of the most violent and destructive volcanic activities in the 20th century. Lahar is the Indonesian term for volcanic ash, and lahar flows resulting from the massive amount of volcanic materials deposited on the mountain's slope posed continued post-eruption threats to the surrounding areas, destroying lives, homes, agricultural products, and infrastructures. Risks of lahar flows were identified immediately after the eruption, with scientific data provided by the Philippine Institute of Volcanology, the U.S. Geological Survey, and other research institutions. However, competing political, economic, and social agendas subordinated the importance of scientific information to policy making. Using systemic risk analysis and management, this article addresses the issues of multiple objectives and the effective integration of scientific techniques into the decision-making process. It provides a modeling framework for identifying, prioritizing, and evaluating policies for managing risk. The major considerations are: (1) applying a holistic approach to risk analysis through hierarchical holographic modeling, (2) applying statistical methods to gain insight into the problem of uncertainty in risk assessment, (3) using multiobjective trade-off analysis to address the issue of multiple decisionmakers and stakeholders in the decision-making process, (4) using the conditional expected value of extreme events to complement and supplement the expected value in quantifying risk, and (5) assessing the impacts of multistage decisions. Numerical examples based on ex post data are formulated to illustrate applications to various problems. The resulting framework from this study can serve as a general baseline model for assessing and managing risks of natural disasters, which the Philippines' lead agency-the National Disaster Coordinating Council (NDCC)-and other related organizations can use for their decision-making processes.     

On the Effect of Probability Distributions of Input Variables in Public Health Risk Assessment

A central part of probabilistic public health risk assessment is the selection of probability distributions for the uncertain input variables. In this paper, we apply the first-order reliability method (FORM)^(1–3) as a probabilistic tool to assess the effect of probability distributions of the input random variables on the probability that risk exceeds a threshold level (termed the probability of failure) and on the relevant probabilistic sensitivities. The analysis was applied to a case study given by Thompson et al. ⁽⁴⁾ on cancer risk caused by the ingestion of benzene contaminated soil. Normal, lognormal, and uniform distributions were used in the analysis. The results show that the selection of a probability distribution function for the uncertain variables in this case study had a moderate impact on the probability that values would fall above a given threshold risk when the threshold risk is at the 50th percentile of the original distribution given by Thompson et al. ⁽⁴⁾ The impact was much greater when the threshold risk level was at the 95th percentile. The impact on uncertainty sensitivity, however, showed a reversed trend, where the impact was more appreciable for the 50th percentile of the original distribution of risk given by Thompson et al. ⁴ than for the 95th percentile. Nevertheless, the choice of distribution shape did not alter the order of probabilistic sensitivity of the basic uncertain variables.     

Two phase parametric and probabilistic NPV calculations, with possible deferral of disposal of UK nuclear waste as an example

This paper illustrates the value of several particular features of a first phase parametric approach to discounted cash flow (DCF) decision analysis when significant uncertainty is involved. It also illustrates the value of second phase probabilistic approaches to selected parameters for five quite different example reasons. The most controversial example reason concerns the discount rate. The particular example used to illustrate both phases may stimulate general interest because of the important issues involved, but it is argued that the two phase approach as a whole has a wide range of applications for decisions large and small.     

基于MCMC稳态模拟的贝叶斯经验费率厘定信用模型

B黨lmann-Straub model is one of the most famous applications of the Bayesian method for the experience rate making.However,by the traditional B黨lmann-Straub model one cannot get the unbiased posterior estimation of the parameters when there is not sufficient prior information for the structural parameters;What's more,the difficult of computing high dimension numeration limits the application of Bayesian method.This paper introduces the Markov chain Monte Carlo simulaton method based on the Gibbs sampling after analyzing the structure of the B黨lmann-Straub model and sets up the Bayesian credibility model for estimating the predictive risk premium.Also by using the results of the numeration analysis,this paper proves that from this model one can get the posterior distributions of the parameters dynamically and the posterior estimation of the censoring parameters in the situation that exists unknown parameters,as well as improve the precision of the numeration,which can be helpful to find the heterogeneity of the premium.     

基于方差分析的资本结构决策模型

本文利用统计学原理与风险决策分析方法,提出了资本结构决策新的方差分析方法和矩阵模型.与原有的基于概率分析的方法比较,本文建立的模型方法克服和舍弃了模糊性和难操作性,有效地权衡了风险与收益,使资本结构决策模型更富可操作性和广泛适用性,能够为企业最优资本结构决策提供一定的决策依据.