A cost model for deferred state life test plans with replacement

This paper presents a cost model for the deferred state life test plan, which is one of the lot-by-lot acceptance sampling plans by attributes. In most sampling plans, the decision to accept or reject a submitted lot depends only on the sampling test results of the lot concerned; other information will not be considered. Deferred state life test plan is a sampling plan which uses information about subsequent lots for making decisions to accept or reject the current lot. The objective of this paper is to evaluate the total test cost of using the deferred state life test plan to see whether the use of this life test plan can reduce the total cost of the sampling test. In order to calculate the expected total test cost of the deferred state life test plan, a cost model is developed for the deferred state life test plan with replacement. Also, a cost comparison is made between a deferred state life test plan and a comparable military standard sampling plan which offers the same level of producer's and consumer's protection. The results show that the deferred state life test plan consistently reduces the overall cost of sampling tests over a variety of test conditions.     

Design of Product Grading Procedures*

Consider a situation in which the items produced by a production process are sorted into two grades according to predetermined specifications and sold at two different prices. A loss is incurred by the producer when an item is classified into a grade and its quality does not meet the consumer's requirement of that grade. A loss in selling price is also incurred when an item is classified into a lower quality grade when it can meet the consumer's requirement of a higher grade. Consequently, the producer's profit is determined by sale prices and losses due to consumer dissatisfaction. The optimal grading specifications are determined to maximize the expected profit. Design of product grading procedures can be based on the performance variable of interest or a surrogate variable correlated with the performance variable. The practice of using correlated variables in product grading is common in industry. We develop product grading models for both the performance variable and a correlated variable.     

RISK AVERSION,WEALTH, AND BACKGROUND RISK

We use household survey data to construct a direct measure of absolute risk aversion based on the maximum price a consumer is willing to pay for a risky security. We relate this measure to consumer's endowments and attributes and to measures of background risk and liquidity constraints. We find that risk aversion is a decreasing function of the endowment—thus rejecting CARA preferences. We estimate the elasticity of risk aversion to consumption at about 0.7, below the unitary value predicted by CRRA utility. We also find that households' attributes are of little help in predicting their degree of risk aversion, which is characterized by massive unexplained heterogeneity. We show that the consumer's environment affects risk aversion. Individuals who are more likely to face income uncertainty or to become liquidity constrained exhibit a higher degree of absolute risk aversion, consistent with recent theories of attitudes toward risk in the presence of uninsurable risks. (JEL: D1, D8)     

LOCUS OF CONTROL,TRUST, AND DECISION MAKING*

A theoretical connection was proposed between certain social personality variables, namely locus of control (Internal or External) and trust (High and Low) and the formal decision-making model of Subjective Expected Utility (SEU). Rather than adopting the traditional definition of these variables as “generalized expectancies” for behavior of self and others, locus of control and trust were reconceptualized as intrapersonal tendencies to favor, prefer, or otherwise bias the subjective probabilities entering into a decision computation. S's high in external control orientation did not differ from internals overall, but external males were more risk averse under certain choice conditions (female-sex-role appropriate dilemma, probability-estimate form). Low-trust S's were also more risk averse than high-trust S's, overall. Low-trust males generated maximally risk-averse choice solutions under the choice condition of feminine role problem appropriateness and probability estimation. In general, female S's made choices that were more consistent with SEU-predicted solutions than males.     

Adversarial Risk Analysis with Incomplete Information: A Level‐k Approach

This article proposes, develops, and illustrates the application of level‐k game theory to adversarial risk analysis. Level‐k reasoning, which assumes that players play strategically but have bounded rationality, is useful for operationalizing a Bayesian approach to adversarial risk analysis. It can be applied in a broad class of settings, including settings with asynchronous play and partial but incomplete revelation of early moves. Its computational and elicitation requirements are modest. We illustrate the approach with an application to a simple defend‐attack model in which the defender's countermeasures are revealed with a probability less than one to the attacker before he decides on how or whether to attack.     

Subjective Probabilities on Subjectively Unambiguous Events

This paper suggests a behavioral definition of (subjective) ambiguity in an abstract setting where objects of choice are Savage‐style acts. Then axioms are described that deliver probabilistic sophistication of preference on the set of unambiguous acts. In particular, both the domain and the values of the decision‐maker's probability measure are derived from preference. It is argued that the noted result also provides a decision‐theoretic foundation for the Knightian distinction between risk and ambiguity.     

Pre‐Orders for New To‐be‐Released Products Considering Consumer Loss Aversion

Advance selling through pre‐orders is a strategy to transfer inventory risk from a retailer to consumers. A newsvendor retailer can have three strategies to choose from: no advance selling allowed (NAS), moderate advance selling with a moderate discount for pre‐orders (MAS), and deep advance selling with a deep discount for pre‐orders (DAS). This research studies how a retailer could design an advance selling strategy to maximize her own profits. We find some interesting results. For example, there exist two thresholds for the selling season profit margin and two thresholds for consumer's expected valuation. For products with higher profit margin than the high threshold on profit margin, a retailer should always use DAS. For products with medium profit margin within the two thresholds, a retailer should adopt MAS if consumer's expected valuation is lower than the high threshold and use DAS otherwise. For products with lower profit margin than the low threshold, a retailer should use NAS, DAS, or MAS, respectively, if consumer's expected valuation is lower than the low threshold, higher than the high threshold, or between the two thresholds, respectively. Through sensitivity analyses, we also show the effects of multiple consumer characteristics on a retailer's optimal advance selling strategy.     

Consumer Trust in Food Safety—A Multidisciplinary Approach and Empirical Evidence from Taiwan

Food scandals that happened in recent years have increased consumers' risk perceptions of foods and decreased their trust in food safety. A better understanding of the consumer trust in food safety can improve the effectiveness of public policy and allow the development of the best practice in risk communication. This study proposes a research framework from a psychometric approach to investigate the relationships between the consumer's trust in food safety and the antecedents of risk perceptions of foods based on a reflexive modernization perspective and a cultural theory perspective in the hope of benefiting the future empirical study. The empirical results from a structural equation modeling analysis of Taiwan as a case in point reveal that this research framework based on a multidisciplinary perspective can be a valuable tool for a growing understanding of consumer trust in food safety. The antecedents in the psychometric research framework comprised reflexive modernization factors and cultural theory factors have all been supported in this study except the consumer's perception of pessimism toward food. Moreover, the empirical results of repeated measures analysis of variance give more detailed information to grasp empirical implications and to provide some suggestions to the actors and institutions involved in the food supply chain in Taiwan.     

Estimating Listeria monocytogenes Growth in Ready-to-Eat Chicken Salad Using a Challenge Test for Quantitative Microbial Risk Assessment

Currently, there is a growing preference for convenience food products, such as ready-to-eat (RTE) foods, associated with long refrigerated shelf-lives, not requiring a heat treatment prior to consumption. Because Listeria monocytogenes is able to grow at refrigeration temperatures, inconsistent temperatures during production, distribution, and at consumer's household may allow for the pathogen to thrive, reaching unsafe limits. L. monocytogenes is the causative agent of listeriosis, a rare but severe human illness, with high fatality rates, transmitted almost exclusively by food consumption. With the aim of assessing the quantitative microbial risk of L. monocytogenes in RTE chicken salads, a challenge test was performed. Salads were inoculated with a three-strain mixture of cold-adapted L. monocytogenes and stored at 4, 12, and 16 °C for eight days. Results revealed that the salad was able to support L. monocytogenes’ growth, even at refrigeration temperatures. The Baranyi primary model was fitted to microbiological data to estimate the pathogen's growth kinetic parameters. Temperature effect on the maximum specific growth rate (μ_max) was modeled using a square-root-type model. Storage temperature significantly influenced μ_max of L. monocytogenes (p < 0.05). These predicted growth models for L. monocytogenes were subsequently used to develop a quantitative microbial risk assessment, estimating a median number of 0.00008726 listeriosis cases per year linked to the consumption of these RTE salads. Sensitivity analysis considering different time–temperature scenarios indicated a very low median risk per portion (<−7 log), even if the assessed RTE chicken salad was kept in abuse storage conditions.     

A comparison of approaches to exploit budget allocation data in cross-sectional maximum likelihood estimation of multi-attribute choice models

In this paper, four calibration approaches to exploit budget allocation data in maximum likelihood estimation of multi-attribute choice models are proposed. They differ on the implicit meaning of the dependent variable: (A) share of consumers according to the preferred alternative; (B) share of sales; (C) average share of consumer's budget; and (D) share of sales according to the preferred alternative. Differences between them can be conceived as depending on two circumstances: customer loyalty and customer selectivity. These are tested in the context of spatial consumer behavior, market response to hypermarket chains being represented as a function of their location strategies. Results show that different nuances on the definition of the dependent variable lead to slightly different relationships with the explanatory variables and to different predictive capabilities.     

Risk Communication,Values Clarification,and Vaccination Decisions

Many health‐related decisions require choosing between two options, each with risks and benefits. When presented with such tradeoffs, people often make choices that fail to align with scientific evidence or with their own values. This study tested whether risk communication and values clarification methods could help parents and guardians make evidence‐based, values‐congruent decisions about children's influenza vaccinations. In 2013–2014 we conducted an online 2×2 factorial experiment in which a diverse sample of U.S. parents and guardians (n = 407) were randomly assigned to view either standard information about influenza vaccines or risk communication using absolute and incremental risk formats. Participants were then either presented or not presented with an interactive values clarification interface with constrained sliders and dynamic visual feedback. Participants randomized to the risk communication condition combined with the values clarification interface were more likely to indicate intentions to vaccinate (β = 2.10, t(399) = 2.63, p < 0.01). The effect was particularly notable among participants who had previously demonstrated less interest in having their children vaccinated against influenza (β = –2.14, t(399) = –2.06, p < 0.05). When assessing vaccination status reported by participants who agreed to participate in a follow‐up study six months later (n = 116), vaccination intentions significantly predicted vaccination status (OR = 1.66, 95%CI (1.13, 2.44), p < 0.05) and rates of informed choice (OR = 1.51, 95%CI (1.07, 2.13), p < 0.012), although there were no direct effects of experimental factors on vaccination rates. Qualitative analysis suggested that logistical barriers impeded immunization rates. Risk communication and values clarification methods may contribute to increased vaccination intentions, which may, in turn, predict vaccination status if logistical barriers are also addressed.     

Distributionally Robust Optimization of Two‐Stage Lot‐Sizing Problems

This paper studies two‐stage lot‐sizing problems with uncertain demand, where lost sales, backlogging and no backlogging are all considered. To handle the ambiguity in the probability distribution of demand, distributionally robust models are established only based on mean‐covariance information about the distribution. Based on shortest path reformulations of lot‐sizing problems, we prove that robust solutions can be obtained by solving mixed 0‐1 conic quadratic programs (CQPs) with mean‐risk objective functions. An exact parametric optimization method is proposed by further reformulating the mixed 0‐1 CQPs as single‐parameter quadratic shortest path problems. Rather than enumerating all potential values of the parameter, which may be the super‐polynomial in the number of decision variables, we propose a branch‐and‐bound‐based interval search method to find the optimal parameter value. Polynomial time algorithms for parametric subproblems with both uncorrelated and partially correlated demand distributions are proposed. Computational results show that the proposed models greatly reduce the system cost variation at the cost of a relative smaller increase in expected system cost, and the proposed parametric optimization method is much more efficient than the CPLEX solver.     

INSIGHTS ON SERVICE SYSTEM DESIGN FROM A NORMAL APPROXIMATION TO ERLANG'S DELAY FORMULA

We show how a simple normal approximation to Erlang's delay formula can be used to analyze capacity and staffing problems in service systems that can be modeled as M/M/s queues. The numbers of servers, s, needed in an M/M/s queueing system to assure a probability of delay of, at most, p can be well approximated by s ≅ p + z_***I-p+, where z_1-p, is the (1 - p)th percentile of the standard normal distribution and ρ, the presented load on the system, is the ratio of Λ, the customer arrival rate, to μ, the service rate. We examine the accuracy of this approximation over a set of parameters typical of service operations ranging from police patrol, through telemarketing to automatic teller machines, and we demonstrate that it tends to slightly underestimate the number of servers actually needed to hit the delay probability target—adding one server to the number suggested by the above formula typically gives the exact result. More importantly, the structure of the approximation promotes operational insight by explicitly linking the number of servers with server utilization and the customer service level. Using a scenario based on an actual teleservicing operation, we show how operations managers and designers can quickly obtain insights about the trade-offs between system size, system utilization and customer service. We argue that this little used approach deserves a prominent role in the operations analyst's and operations manager's toolbags.     

Supply chain coordination through cooperative advertising with reference price effect

Cooperative advertising, which usually occurs in a vertical supply chain, is typically a cost sharing and promotion mechanism for the manufacturer to affect retail performance. Research in the literature, however, rarely considers the important phenomenon that advertising has a positive effect on the consumer's reference price. In fact, when a consumer makes a decision to buy a product or not, a reference price is usually in his mind and plays a determinant role. Taking into account the impact of advertising on the reference price, this paper proposes a dynamic cooperative advertising model for a manufacturer–retailer supply chain and analyzes how the reference price effect would influence the decisions of all the channel members. In our model, both the consumer's goodwill and reference price for the product are assumed to be influenced by the advertising and are modeled in differential dynamic equations. In addition, the advertising level, the consumer's goodwill and the reference price are all assumed to have positive effect on sales. Utilizing differential game theory, this paper formulates the optimal decisions of the manufacturer and the retailer in two different game scenarios: Stackelberg game and cooperative game. Also, this paper proposes a new mechanism to coordinate the supply chain in which both the manufacturer and the retailer share each other's advertising costs.     

On Optimal Rules of Persuasion

A speaker wishes to persuade a listener to accept a certain request. The conditions under which the request is justified, from the listener's point of view, depend on the values of two aspects. The values of the aspects are known only to the speaker and the listener can check the value of at most one. A mechanism specifies a set of messages that the speaker can send and a rule that determines the listener's response, namely, which aspect he checks and whether he accepts or rejects the speaker's request. We study mechanisms that maximize the probability that the listener accepts the request when it is justified and rejects the request when it is unjustified, given that the speaker maximizes the probability that his request is accepted. We show that a simple optimal mechanism exists and can be found by solving a linear programming problem in which the set of constraints is derived from what we call the L‐principle.     

Social Indeterminacy

An extension of Condorcet's paradox by McGarvey (1953) asserts that for every asymmetric relation R on a finite set of candidates there is a strict‐preferences voter profile that has the relation R as its strict simple majority relation. We prove that McGarvey's theorem can be extended to arbitrary neutral monotone social welfare functions that can be described by a strong simple game G if the voting power of each individual, measured by the Shapley–Shubik power index, is sufficiently small. Our proof is based on an extension to another classic result concerning the majority rule. Condorcet studied an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is p>1/2. Condorcet's jury theorem asserts that if the number of voters tends to infinity then the probability that the first candidate will be elected tends to one. We prove that this assertion extends to a sequence of arbitrary monotone strong simple games if and only if the maximum voting power for all individuals tends to zero.     

A Three‐step Method for Choosing the Number of Bootstrap Repetitions

This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, confidence regions, hypothesis tests, p‐values, and bias correction. For each of these problems, the paper provides a three‐step method for choosing B to achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval length, test's critical value, test's p‐value, or bias‐corrected estimate based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B=∞. The results apply quite generally to parametric, semiparametric, and nonparametric models with independent and dependent data. The results apply to the standard nonparametric iid bootstrap, moving block bootstraps for time series data, parametric and semiparametric bootstraps, and bootstraps for regression models based on bootstrapping residuals. Monte Carlo simulations show that the proposed methods work very well.     

Perceptions and Expected Immediate Reactions to Severe Storm Displays

The National Weather Service has adopted warning polygons that more specifically indicate the risk area than its previous county‐wide warnings. However, these polygons are not defined in terms of numerical strike probabilities (p_s). To better understand people's interpretations of warning polygons, 167 participants were shown 23 hypothetical scenarios in one of three information conditions—polygon‐only (Condition A), polygon + tornadic storm cell (Condition B), and polygon + tornadic storm cell + flanking nontornadic storm cells (Condition C). Participants judged each polygon's p_s and reported the likelihood of taking nine different response actions. The polygon‐only condition replicated the results of previous studies; p_s was highest at the polygon's centroid and declined in all directions from there. The two conditions displaying storm cells differed from the polygon‐only condition only in having p_s just as high at the polygon's edge nearest the storm cell as at its centroid. Overall, p_s values were positively correlated with expectations of continuing normal activities, seeking information from social sources, seeking shelter, and evacuating by car. These results indicate that participants make more appropriate p_s judgments when polygons are presented in their natural context of radar displays than when they are presented in isolation. However, the fact that p_s judgments had moderately positive correlations with both sheltering (a generally appropriate response) and evacuation (a generally inappropriate response) suggests that experiment participants experience the same ambivalence about these two protective actions as people threatened by actual tornadoes.     

Methodology for Determining the Appropriateness of a Linear Dose‐Response Function

Microbial food safety risk assessment models can often at times be simplified by eliminating the need to integrate a complex dose‐response relationship across a distribution of exposure doses. This is possible if exposure pathways lead to pathogens at exposure that consistently have a small probability of causing illness. In this situation, the probability of illness will follow an approximately linear function of dose. Consequently, the predicted probability of illness per serving across all exposures is linear with respect to the expected value of dose. The majority of dose‐response functions are approximately linear when the dose is low. Nevertheless, what constitutes “low” is dependent on the parameters of the dose‐response function for a particular pathogen. In this study, a method is proposed to determine an upper bound of the exposure distribution for which the use of a linear dose‐response function is acceptable. If this upper bound is substantially larger than the expected value of exposure doses, then a linear approximation for probability of illness is reasonable. If conditions are appropriate for using the linear dose‐response approximation, for example, the expected value for exposure doses is two to three logs₁₀ smaller than the upper bound of the linear portion of the dose‐response function, then predicting the risk‐reducing effectiveness of a proposed policy is trivial. Simple examples illustrate how this approximation can be used to inform policy decisions and improve an analyst's understanding of risk.     

Probability of Causation and the Attributable Proportion Risk

A uranium miner who smokes develops lung cancer: what is the probability that radiation, rather than tobacco, caused it? This paper briefly explains the principles and limits of probability models for which this question makes sense, and then shows how principles of risk accounting can be applied to obtain a solution to the general problem of attributing risk in the presence of joint, possibly interacting, causes. A procedure for calculating each factor's “share” in a jointly caused risk is proposed, and shown to be a generalization of the “probability of causation” concept. Problems of implementation and interpretation for the proposed attribution procedure are discussed, and illustrative error bounds are derived for a simple decision rule, in which probability of causation or attributable risk share calculations are made using aggregate data as a proxy for unknown individual data.