Order consolidation for hierarchical product lines

We consider the batch production of hierarchical product lines in raw material industry where the whole or parts of multiple customer orders may be consolidated and processed in the same batch if their product specifications are compatible. The objective of the problem is to find maximum possible number of batches completely filled up to their capacity. The compatibility relationship among product specifications is represented by a graph called the compatibility graph. If the compatibility graph is an arbitrary graph, the problem is proven to be NP-hard and belongs to Max SNP-hard class. We develop an optimum algorithm for an important subclass of the problem where the graph is a quasi-threshold graph which in fact is the case for producing hierarchical product lines that are often found in raw materials industry.     

Flood Catastrophe Model for Designing Optimal Flood Insurance Program: Estimating Location‐Specific Premiums in the Netherlands

As flood risks grow worldwide, a well‐designed insurance program engaging various stakeholders becomes a vital instrument in flood risk management. The main challenge concerns the applicability of standard approaches for calculating insurance premiums of rare catastrophic losses. This article focuses on the design of a flood‐loss‐sharing program involving private insurance based on location‐specific exposures. The analysis is guided by a developed integrated catastrophe risk management (ICRM) model consisting of a GIS‐based flood model and a stochastic optimization procedure with respect to location‐specific risk exposures. To achieve the stability and robustness of the program towards floods with various recurrences, the ICRM uses stochastic optimization procedure, which relies on quantile‐related risk functions of a systemic insolvency involving overpayments and underpayments of the stakeholders. Two alternative ways of calculating insurance premiums are compared: the robust derived with the ICRM and the traditional average annual loss approach. The applicability of the proposed model is illustrated in a case study of a Rotterdam area outside the main flood protection system in the Netherlands. Our numerical experiments demonstrate essential advantages of the robust premiums, namely, that they: (1) guarantee the program's solvency under all relevant flood scenarios rather than one average event; (2) establish a tradeoff between the security of the program and the welfare of locations; and (3) decrease the need for other risk transfer and risk reduction measures.     

On the Complex Quantification of Risk: Systems‐Based Perspective on Terrorism

This article highlights the complexity of the quantification of the multidimensional risk function, develops five systems‐based premises on quantifying the risk of terrorism to a threatened system, and advocates the quantification of vulnerability and resilience through the states of the system. The five premises are: (i) There exists interdependence between a specific threat to a system by terrorist networks and the states of the targeted system, as represented through the system's vulnerability, resilience, and criticality‐impact. (ii) A specific threat, its probability, its timing, the states of the targeted system, and the probability of consequences can be interdependent. (iii) The two questions in the risk assessment process: “What is the likelihood?” and “What are the consequences?” can be interdependent. (iv) Risk management policy options can reduce both the likelihood of a threat to a targeted system and the associated likelihood of consequences by changing the states (including both vulnerability and resilience) of the system. (v) The quantification of risk to a vulnerable system from a specific threat must be built on a systemic and repeatable modeling process, by recognizing that the states of the system constitute an essential step to construct quantitative metrics of the consequences based on intelligence gathering, expert evidence, and other qualitative information. The fact that the states of all systems are functions of time (among other variables) makes the time frame pivotal in each component of the process of risk assessment, management, and communication. Thus, risk to a system, caused by an initiating event (e.g., a threat) is a multidimensional function of the specific threat, its probability and time frame, the states of the system (representing vulnerability and resilience), and the probabilistic multidimensional consequences.     

Nonparametric Instrumental Regression

The focus of this paper is the nonparametric estimation of an instrumental regression function ϕ defined by conditional moment restrictions that stem from a structural econometric model E[Y−ϕ(Z)|W]=0, and involve endogenous variables Y and Z and instruments W. The function ϕ is the solution of an ill‐posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyzes identification and overidentification of this model, and presents asymptotic properties of the estimated nonparametric instrumental regression function.     

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.     

Marginal methods for clustered longitudinal binary data with incomplete covariates

Many analyses for incomplete longitudinal data are directed to examining the impact of covariates on the marginal mean responses. We consider the setting in which longitudinal responses are collected from individuals nested within clusters. We discuss methods for assessing covariate effects on the mean and association parameters when covariates are incompletely observed. Weighted first and second order estimating equations are constructed to obtain consistent estimates of mean and association parameters when covariates are missing at random. Empirical studies demonstrate that estimators from the proposed method have negligible finite sample biases in moderate samples. An application to the National Alzheimer's Coordinating Center (NACC) Uniform Data Set (UDS) demonstrates the utility of the proposed method.     

On three and four vicious walkers

We establish a reflection principle for three lattice walkers and use this principle to reduce the enumeration of configurations of three vicious walkers to the enumeration of configurations of two vicious walkers. More precisely, the reflection principle leads to a bijection between three walks (L₁, L₂, L₃) such that L₂ intersects both L₁ and L₃ and three walks (L₁, L₂, L₃) such that L₁ intersects L₃. Hence we find a combinatorial interpretation of the formula for the generating function for the number of configurations of three vicious walkers, originally derived by Bousquet-Mélou by using the kernel method, and independently by Gessel by using tableaux and symmetric functions. This answers a question posed by Gessel and Bousquet-Mélou. We also find a reflection principle for four vicious walks that leads to a combinatorial interpretation of a formula derived from Gessel's theorem.     

洛必答法则使用技巧及注意事项浅析

洛必答法则是求解极限的一个非常重要的方法,一般教材的编写,只是着重例题类型的分类专门讨论,在技巧的讨论上着墨较少,文章则从洛必答法则使用技巧以及注意事项方面针对一些实例做出浅析.     

家庭医生签约服务下社区居民就医选择的相关因素研究

为了解南京市浦口区居民就医选择现状,分析影响就医选择的相关因素,以浦口区11个社区卫生服务中心为调查地点,普查与等容抽样相结合方式纳入调查对象2301人。问卷调查收集其人口学特征、就医选择以及医疗相关行为等信息;多因素Logistic回归分析浦口区居民就医选择的相关影响因素。结果显示,调查对象中1883人(81.9%)表示可以接受以家庭医生为核心的基层首诊,1525人(66.3%)选择首先去基层医疗机构就诊。Logistic回归分析结果显示,到最近医疗机构所需时间、年龄、慢性病、是否签约家庭医生是居民接受以家庭医生为核心的基层首诊的相关因素;影响居民就医选择的相关因素则包括到最近医疗机构所需时间、年龄、文化程度、家庭人均月收入、是否签约家庭医生。浦口区居民选择基层医疗机构首诊的构成比相对较高;签约家庭医生有助于促进社区居民对基层首诊的选择与接受度;60岁及以上老年人与慢病患者对基层首诊的需求度更高,提示签约家庭医生的推广工作应重点关注这两类人群。