On Variational Bayes Estimation and Variational Information Criteria for Linear Regression Models

Variational Bayes (VB) estimation is a fast alternative to Markov Chain Monte Carlo for performing approximate Baesian inference. This procedure can be an efficient and effective means of analyzing large datasets. However, VB estimation is often criticised, typically on empirical grounds, for being unable to produce valid statistical inferences. In this article we refute this criticism for one of the simplest models where Bayesian inference is not analytically tractable, that is, the Bayesian linear model (for a particular choice of priors). We prove that under mild regularity conditions, VB based estimators enjoy some desirable frequentist properties such as consistency and can be used to obtain asymptotically valid standard errors. In addition to these results we introduce two VB information criteria: the variational Akaike information criterion and the variational Bayesian information criterion. We show that variational Akaike information criterion is asymptotically equivalent to the frequentist Akaike information criterion and that the variational Bayesian information criterion is first order equivalent to the Bayesian information criterion in linear regression. These results motivate the potential use of the variational information criteria for more complex models. We support our theoretical results with numerical examples.     

基于失效情景的应急设施选址评估指标体系与模型

突发事件具有巨大的破坏性、不确定性,应急设施有可能失效,本文研究基于失效情景的应急设施选址评估指标体系与评估模型。首先基于定义的失效情景研究应急设施选址评估指标。构建全局性、可靠性、时效性、均衡性、经济性评估指标。可靠性作为重要评估指标有助于提高应急设施对需求区域的物资保障程度,保证系统的稳定性,采用多重覆盖率刻画。然后,设计具有不同侧重评估目标的一般情景评估指标体系、设施失效情景评估指标体系以及多区域情景评估指标体系。最后,由于应急设施选址评估具有多影响因素特征,涉及输入和输出多个指标的测度,选取处理多输入\多输出问题具有优势的评估方法—数据包络法,对应急设施选址的合理性进行评估。实例验证评估指标体系的实用性和有效性。     

Sample size determination for estimating multivariate process capability indices based on lower confidence limits

With the advent of modern technology, manufacturing processes have become very sophisticated; a single quality characteristic can no longer reflect a product's quality. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, several new multivariate capability (NMC) indices, such as NMC _p and NMC _pm , have been developed over the past few years. However, the sample size determination for multivariate process capability indices has not been thoroughly considered in previous studies. Generally, the larger the sample size, the more accurate an estimation will be. However, too large a sample size may result in excessive costs. Hence, the trade-off between sample size and precision in estimation is a critical issue. In this paper, the lower confidence limits of NMC _p and NMC _pm indices are used to determine the appropriate sample size. Moreover, a procedure for conducting the multivariate process capability study is provided. Finally, two numerical examples are given to demonstrate that the proper determination of sample size for multivariate process indices can achieve a good balance between sampling costs and estimation precision.     

Supply Chain Management of Fresh Products with Producer Transportation*

This article considers a class of fresh‐product supply chains in which products need to be transported by the upstream producer from a production base to a distant retail market. Due to high perishablility a portion of the products being shipped may decay during transportation, and therefore, become unsaleable. We consider a supply chain consisting of a single producer and a single distributor, and investigate two commonly adopted business models: (i) In the “pull” model, the distributor places an order, then the producer determines the shipping quantity, taking into account potential product decay during transportation, and transports the products to the destination market of the distributor; (ii) In the “push” model, the producer ships a batch of products to a distant wholesale market, and then the distributor purchases and resells to end customers. By considering a price‐sensitive end‐customer demand, we investigate the optimal decisions for supply chain members, including order quantity, shipping quantity, and retail price. Our research shows that both the producer and distributor (and thus the supply chain) will perform better if the pull model is adopted. To improve the supply chain performance, we propose a fixed inventory‐plus factor (FIPF) strategy, in which the producer announces a pre‐determined inventory‐plus factor and the distributor compensates the producer for any surplus inventory that would otherwise be wasted. We show that this strategy is a Pareto improvement over the pull and push models for both parties. Finally, numerical experiments are conducted, which reveal some interesting managerial insights on the comparison between different business models.     

Retail Strategies for Extended Warranty Sales and Impact on Manufacturer Base Warranties

Consider two competing manufacturers selling their products through the same retailer. If this retailer derives profits from extended warranty sales, the manufacturers face a dilemma in setting their base warranties. Although they have incentive to increase their warranties to make their products attractive to consumers, the retailer might prefer selling lower‐warranty products to enhance extended warranties sales. We develop a stylized model to determine and analyze optimal manufacturer and retailer strategies in this setting. Consistent with the ongoing decline in warranties for products that are sold through independent retailers, we show that these interactions exert downward pressure on manufacturer warranties. Rather than pitching the extended warranty at the checkout after customers have selected a certain product, we find that retailers can often benefit from inducing simultaneous consideration of product and extended warranty characteristics, for example by posting extended warranty information right on the product shelf.     

Measuring trends in child well-being: an evidence-based approach

This paper first reviews the goals of the founding documents of the social indicators and quality-of-life movements of the 1960s and 1970s. It next describes the current state of knowledge with respect to the founding goals of this field. The focus then turns to the topic of measuring changes in child and youth well-being in the United States over the past few decades. In particular, the evidence-based approach used in the construction of the recently developed composite Child and Youth Well-Being Index (CWI) is described. Some findings from the CWI regarding changes in child and youth well-being in the period 1975–2004 are reported. Trends in the CWI then are compared with data on trends in subjective well-being of high school seniors – similarities of trends in these two series provide validating support for the interpretation of the CWI as an index of changes in the quality-of-life of children and youth. Using data on some additional indicator series, most of which were initiated in the 1990s, an Expanded CWI is then described. The qualitative pattern of change in the expanded CWI is shown to be similar to that of the basic CWI, except that the expanded CWI shows a more pronounced decline in the early-1990s and a slower rate of improvement into the early-2000s. The paper concludes with some possible directions for future work. Revision of a paper presented at the Measuring Child Well-Being: The Pros and Cons of Composite Indices Session, American Statistical Association Annual Meeting, Minneapolis, MN, August 7–11, 2005. We thank Kristin Moore for useful comments. The research on the Child and Youth Well-Being Index reported herein was supported by a grant from the Foundation for Child Development.     

Indicators and Indices of Child Well-being: A Brief American History

This paper traces the history of indicators and indices of child well-being from its origins in the social indicator movement of the 1970s through recent developments in the field. Initial work calling for comprehensive sets of indicators of child well-being and later recommendations for indicator improvement are detailed. Products that resulted from these recommendations, such as comprehensive indicator reports and online resources are described. The development of child well-being indices is shown to parallel the history of indicators. The contributions of state and international indicator and index projects are included as well. Important aspects of child well-being indicator development are uncovered through documenting its history, including the need to focus on subjective as well as objective measures of well-being, and the need to develop indicators for the multiple ecological contexts of children’s lives, but to separate measures of context from measures of child outcomes. A rough consensus emerges across the history of indicator efforts on the critical domains of child well-being: physical, psychological, cognitive, social, and economic well-being. Recent recognition of the importance of indicators of positive development is noted. This paper was funded by the KIDS COUNT project of the Annie E. Casey Foundation.     

Longitudinal Analysis of Inhibitors of Manufacturer Delivery Performance

This article examines demand, manufacturing, and supply factors proposed to inhibit manufacturer delivery execution. Extant research proposes many factors expected to harm delivery performance. Prior cross‐sectional empirical research examines such factors at the plant level, generally finding factors arising from dynamic complexity to be significant, but factors arising from detail complexity to be insignificant. Little empirical research examines the factors using product‐level operating data, which arguably makes more sense for analyzing how supply chain complexity factors inhibit delivery. For purposes of research triangulation, we use longitudinal product‐level data from MRP systems to examine whether the factors inhibit internal manufacturing on time job rates and three customer‐oriented measures of delivery performance: product line item fill rates, average delivery lead times, and average tardiness. Our econometric models pool product line item data across division plants and within distinct product families, using a proprietary monthly dataset on over 100 product line items from the environmental controls manufacturing division of a Fortune 100 conglomerate. The data summarize customer ordering events of over 900 customers and supply chain activities of over 80 suppliers. The study contributes academically by finding significant detail complexity inhibitors of delivery that prior studies found insignificant. The findings demonstrate the need for empirical research using data disaggregated below the plant‐level unit of analysis, as they illustrate how some factors previously found insignificant indeed are significant when considered at the product‐level unit of analysis. Managers can use the findings to understand better which drivers and inhibitors of delivery performance are important.     

Assessing Antecedents of Socially Responsible Supplier Selection in Three Global Supply Chain Contexts

A number of highly publicized, controversial lapses in social responsibility within global supply chains have forced managers and scholars to reexamine long‐held perspectives on supplier selection. Extending Carter and Jennings’ department‐level study of purchasing social responsibility, our research assesses the role of supply managers’ ethical intentions and three key antecedents that drive socially responsible supplier selection. Comparing evidence from firms operating in China, the United States, and the United Arab Emirates, we identify three key drivers of supply managers’ ethical intentions and examine both their direct and indirect impacts on socially responsible supplier selection. We find differential support for the predictor relationships on supply manager ethical intentions across national contexts and mediated versus nonmediated models. These observations bear important implications for firms conducting global supply management.     

Role of Random Capacity Risk and the Retailer in Decentralized Supply Chains with Competing Suppliers

This research considers a supply chain under the following conditions: (i) two heterogeneous suppliers are in competition, (ii) supply capacity is random and pricing is endogenous, (iii) consumer demand, with and without an intermediate retailer, is price dependent. Specifically, we examine how uncertainty in supply capacity affects optimal ordering and pricing decisions, supplier and retailer profits, and the incentives to reduce such uncertainty. When two suppliers sell through a monopolistic retailer, supply uncertainty not only affects the retailer's diversification strategy for replenishment, but also changes the suppliers’ wholesale price competition and the incentive for reducing capacity uncertainty. In this dual‐sourcing model, we show that the benefit of reducing capacity uncertainty depends on the cost heterogeneity between the suppliers. In addition, we show that a supplier does not necessarily benefit from capacity variability reduction. We contrast this incentive misalignment with findings from the single‐supplier case and a supplier‐duopoly case where both suppliers sell directly to market without the monopolistic retailer. In the latter single‐supplier and duopoly cases, we prove that the unreliable supplier always benefits from reducing capacity variability. These results highlight the role of the retailer's diversification strategy in distorting a supplier's incentive for reducing capacity uncertainty under supplier price competition.