Optimal Inspection of Imports to Prevent Invasive Pest Introduction

The United States imports more than 1 billion live plants annually—an important and growing pathway for introduction of damaging nonnative invertebrates and pathogens. Inspection of imports is one safeguard for reducing pest introductions, but capacity constraints limit inspection effort. We develop an optimal sampling strategy to minimize the costs of pest introductions from trade by posing inspection as an acceptance sampling problem that incorporates key features of the decision context, including (i) simultaneous inspection of many heterogeneous lots, (ii) a lot‐specific sampling effort, (iii) a budget constraint that limits total inspection effort, (iv) inspection error, and (v) an objective of minimizing cost from accepted defective units. We derive a formula for expected number of accepted infested units (expected slippage) given lot size, sample size, infestation rate, and detection rate, and we formulate and analyze the inspector's optimization problem of allocating a sampling budget among incoming lots to minimize the cost of slippage. We conduct an empirical analysis of live plant inspection, including estimation of plant infestation rates from historical data, and find that inspections optimally target the largest lots with the highest plant infestation rates, leaving some lots unsampled. We also consider that USDA‐APHIS, which administers inspections, may want to continue inspecting all lots at a baseline level; we find that allocating any additional capacity, beyond a comprehensive baseline inspection, to the largest lots with the highest infestation rates allows inspectors to meet the dual goals of minimizing the costs of slippage and maintaining baseline sampling without substantial compromise.     

The Economic Efficiency of Sampling Size: The Case of Beef Trim Revisited

A recent paper by Ferrier and Buzby provides a framework for selecting the sample size when testing a lot of beef trim for Escherichia coli O157:H7 that equates the averted costs of recalls and health damages from contaminated meats sold to consumers with the increased costs of testing while allowing for uncertainty about the underlying prevalence of contamination. Ferrier and Buzby conclude that the optimal sample size is larger than the current sample size. However, Ferrier and Buzby's optimization model has a number of errors, and their simulations failed to consider available evidence about the likelihood of the scenarios explored under the model. After correctly modeling microbial prevalence as dependent on portion size and selecting model inputs based on available evidence, the model suggests that the optimal sample size is zero under most plausible scenarios. It does not follow, however, that sampling beef trim for E. coli O157:H7, or food safety sampling more generally, should be abandoned. Sampling is not generally cost effective as a direct consumer safety control measure due to the extremely large sample sizes required to provide a high degree of confidence of detecting very low acceptable defect levels. Food safety verification sampling creates economic incentives for food producing firms to develop, implement, and maintain effective control measures that limit the probability and degree of noncompliance with regulatory limits or private contract specifications.     

The Economic Efficiency of Sampling Size: The Case of Beef Trim

The economically optimal sample size in a food safety test balances the marginal costs and marginal benefits of increasing the sample size. We provide a method for selecting the sample size when testing beef trim for Escherichia coli O157:H7 that equates the averted costs of recalls and health damages from contaminated meats sold to consumers with the increased costs of testing while allowing for uncertainty about the underlying prevalence rates of contamination. Using simulations, we show that, in most cases, the optimal sample size is larger than the current sample size of 60 and, in some cases, it exceeds 120. Moreover, lots with a lower prevalence rate have a higher expected damage because contamination is more difficult to detect. Our simulations indicate that these lots have a higher optimal sampling rate.     

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.     

Cost‐Effective Sampling and Analysis for Mycotoxins in a Cereal Batch

The presence of hazards (e.g., contaminants, pathogens) in food/feed, water, plants, or animals can lead to major economic losses related to human and animal health or the rejection of batches of food or feed. Monitoring these hazards is important but can lead to high costs. This study aimed to find the most cost‐effective sampling and analysis (S&A) plan in the cases of the mycotoxins deoxynivalenol (DON) in a wheat batch and aflatoxins (AFB₁) in a maize batch. An optimization model was constructed, maximizing the number of correct decisions for accepting/rejecting a batch of cereals, with a budget as major constraint. The decision variables were the choice of the analytical method: instrumental method (e.g., liquid chromatography combined with mass‐spectrometry (LC‐MS/MS)), enzyme‐linked‐immuno‐assay (ELISA), or lateral flow devices (LFD), the number of incremental samples collected from the batch, and the number of aliquots analyzed. S&A plans using ELISA showed to be slightly more cost effective than S&A plans using the other two analytical methods. However, for DON in wheat, the difference between the optimal S&A plans using the three different analytical methods was minimal. For AFB₁ in maize, the cost effectiveness of the S&A plan using instrumental methods or ELISA were comparable whereas the S&A plan considering onsite detection with LFDs was least cost effective. In case of nonofficial controls, which do not have to follow official regulations for sampling and analysis, onsite detection with ELISA for both AFB₁ in maize and DON in wheat, or with LFDs for DON in wheat, could provide cost‐effective alternatives.     

Optimal two-stage production-inventory policy with whole lot and split lots

This paper deals with the problem of determining the optimal lot sizes for a two-stage production-inventory system. The first stage has a large lot to be processed in a single batch and is called the ‘whole lot’; this is split in the second stage into smaller lots of equal size called ‘split lots’. The lot in stage 1 is inspected for its conformity to standards before it is passed on to stage 2. We use a single sampling attribute plan for inspection and examine the consequences of rejecting or accepting the lot. The rejected lots are 100 % inspected and defectives are eliminated..The accepted lots contain defectives in the uninspected part which are identified during stage 2 processing. We have combined these aspects of inspection with the usual inventory costs and developed a model to determine the optimal sizes of the whole lot and split lots     

基于可控提前期的随机寄售库存模型

本文通过假定需求提前期为随机且可控的,将寄售库存（Consignment Stock,CS）模型拓展到随机情形。本文首先将库存成本分为与财务相关的成本和与储存相关的成本两部分,得出CS方式下买卖双方的联合期望总成本公式,然后将订货量、订货点、提前期、运送次数作为决策变量,求得系统的最优参数设置及最小总成本。文章最后提出一个算法,并通过仿真的形式表明无论在确定还是随机环境中,CS方式的总成本都可能优于集成化库存方式。     

An optimal set-up policy for control charts

A model of a production process, using an unscheduled set-up policy and utilizing fraction-defective control charts to control current production is developed taking into consideration all the costs; namely cost of sampling, cost of not detecting a change in the process, cost of a false indication of change, and the cost of re-adjusting detected changes. The model is based on the concept of the expected time between detection of changes calling for set-ups. It is shown that the combination of unscheduled set-ups and control charts can be utilized in an optimal way if those combinations of sample size, sampling interval and extent of control limits from process average will be used that provide the minimum expected total cost per unit of time. The costs when a production process with unscheduled set-up is controlled by using the appropriate optimal control charts is compared to the cost of a production process using scheduled set-ups at optimum intervals in conjunction with its appropriate control charts. This comparison indicates the criteria for selecting production processes with scheduled set-ups using optimal set-up intervals over unscheduled set-ups. Suggestions are made to evaluate the optimal process set-up strategy and the accompanying decision parameters, for any specific cost data, by use of computer enumeration.     

Long‐Term Debt and Optimal Policy in the Fiscal Theory of the Price Level

The fiscal theory says that the price level is determined by the ratio of nominal debt to the present value of real primary surpluses. I analyze long‐term debt and optimal policy in the fiscal theory. I find that the maturity structure of the debt matters. For example, it determines whether news of future deficits implies current inflation or future inflation. When long‐term debt is present, the government can trade current inflation for future inflation by debt operations; this tradeoff is not present if the government rolls over short‐term debt. The maturity structure of outstanding debt acts as a “budget constraint” determining which periods' price levels the government can affect by debt variation alone. In addition, debt policy—the expected pattern of future state‐contingent debt sales, repurchases and redemptions—matters crucially for the effects of a debt operation. I solve for optimal debt policies to minimize the variance of inflation. I find cases in which long‐term debt helps to stabilize inflation. I also find that the optimal policy produces time series that are similar to U.S. surplus and debt time series. To understand the data, I must assume that debt policy offsets the inflationary impact of cyclical surplus shocks, rather than causing price level disturbances by policy‐induced shocks. Shifting the objective from price level variance to inflation variance, the optimal policy produces much less volatile inflation at the cost of a unit root in the price level; this is consistent with the stabilization of U.S. inflation after the gold standard was abandoned.     

Analysis of a batch machine fed by an unreliable discrete machine

This paper analyses the behaviour of a manufacturing line consisting of two machines in series where the first machine processes lots one at a time, and is subject to failure and takes a random amount of time to repair when it fails, and the second machine is a perfectly reliable batch machine. A control limit policy is adopted to determine lot sizes for the batch machine. When the batch machine completes processing, if the number of lots in the buffer is greater than or equal to the critical number (Q?), all the lots in the buffer are loaded immediately, otherwise the batch machine waits until Q lots are accumulated. An embedded discrete time Markov-chain approach is proposed, and recursive approaches are developed to derive necessary performance measures. A numerical example explains how to obtain the optimal value of a critical number minimizing the cost functions.     

Coordinating replenishments in a supply chain with quality control considerations

We study the impact of coordinated replenishment, a popular supply chain initiative, on a quality control system. We use the (Q, S) policy to manage a two-item inventory control system. If the items are jointly replenished, the number ordered for each item varies from lot to lot. As the number varies, the sampling plan will also be changed. Companies have to determine sampling plans to minimize quality cost when the order is mixed with several items and the number of each item varies from order to order. Management's primary concern is to determine the optimal sampling sizes and acceptance numbers for all items in an order.     

Salmonella Prevalence Alone Is Not a Good Indicator of Poultry Food Safety

Salmonella is a leading cause of foodborne illness (i.e., salmonellosis) outbreaks, which on occasion are attributed to ground turkey. The poultry industry uses Salmonella prevalence as an indicator of food safety. However, Salmonella prevalence is only one of several factors that determine risk of salmonellosis. Consequently, a model for predicting risk of salmonellosis from individual lots of ground turkey as a function of Salmonella prevalence and other risk factors was developed. Data for Salmonella contamination (prevalence, number, and serotype) of ground turkey were collected at meal preparation. Scenario analysis was used to evaluate effects of model variables on risk of salmonellosis. Epidemiological data were used to simulate Salmonella serotype virulence in a dose‐response model that was based on human outbreak and feeding trial data. Salmonella prevalence was 26% (n = 100) per 25 g of ground turkey, whereas Salmonella number ranged from 0 to 1.603 with a median of 0.185 log per 25 g. Risk of salmonellosis (total arbitrary units (AU) per lot) was affected (p ≤ 0.05) by Salmonella prevalence, number, and virulence, by incidence and extent of undercooking, and by food consumption behavior and host resistance but was not (p > 0.05) affected by serving size, serving size distribution, or total bacterial load of ground turkey when all other risk factors were held constant. When other risk factors were not held constant, Salmonella prevalence was not correlated (r = ?0.39; p = 0.21) with risk of salmonellosis. Thus, Salmonella prevalence alone was not a good indicator of poultry food safety because other factors were found to alter risk of salmonellosis. In conclusion, a more holistic approach to poultry food safety, such as the process risk model developed in the present study, is needed to better protect public health from foodborne pathogens like Salmonella.     

Optimal Resource Allocation for Defense of Targets Based on Differing Measures of Attractiveness

This article describes the results of applying a rigorous computational model to the problem of the optimal defensive resource allocation among potential terrorist targets. In particular, our study explores how the optimal budget allocation depends on the cost effectiveness of security investments, the defender's valuations of the various targets, and the extent of the defender's uncertainty about the attacker's target valuations. We use expected property damage, expected fatalities, and two metrics of critical infrastructure (airports and bridges) as our measures of target attractiveness. Our results show that the cost effectiveness of security investment has a large impact on the optimal budget allocation. Also, different measures of target attractiveness yield different optimal budget allocations, emphasizing the importance of developing more realistic terrorist objective functions for use in budget allocation decisions for homeland security.     

运输成本对批量敏感时的供应链批量协调策略比较研究

以一个多周期、随机客户需求和单位产品运输成本对批量敏感的供应链为研究对象,建立了由生产商负责产品运输时,供应链分散决策情形下的最佳批量模型,并提出了基于批量折扣和改由批发商负责产品运输的供应链批量协调策略.研究结果表明:当由生产商负责产品运输时,单位产品运输成本对批量越不敏感,生产商的最佳生产批量越小,与批发商要求的短周期、小批量订货越接近;如果改由批发商负责产品运输,批发商的最佳订货批量更接近于生产商的最佳生产批量.最后,通过数例分析发现,对生产商来讲,当单位产品运输成本对批量不太敏感时,批量折扣政策优于改由批发商负责产品运输的策略,但当单位产品运输成本对批量较敏感时,后者优于前者.     

Application of the knapsack model for budgeting

The budget problem of selecting projects (or activities) with known values (or payoffs) and associated costs, subject to a prescribed maximum budget, is akin to the knapsack problem, which is well documented in the literature. The optimal solution to maximise the total value of selected projects for a given budget constraint can readily be obtained. In practice, budgets are often somewhat flexible, or subject to possible changes, so that an optimal solution for a given budget value may not remain optimal when the budget is modified. It is, therefore, sensible in many situations to consider a budget range, instead of a single budget value. In addition to their original objective of maximising the total value of selected projects, decision makers are often concerned to get ‘value for money’, indicated by the ratio of payoff to cost. This paper examines how these questions can be tackled through the introduction of a stability index, to guide project selection within a defined budget range, and the use of a portfolio diagram, to help in the ranking of projects with respect to the stated twin objectives.     

RATIONALIZATION OF THE SUPPLIER BASE IN THE PRESENCE OF YIELD UNCERTAINTY

An important aspect of supply chain management is the optimal configuration of the supplier base. We develop a model to determine optimal lot sizes and the optimal number of suppliers when the yield of the product delivered from each supplier is random. While small orders from a large number of suppliers can reduce yield uncertainty, fixed costs associated with each supplier provide a penalty for having too many suppliers. This is the key tradeoff addressed by our model. We look at the cases when the suppliers are identical as well as nonidentical.     

Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions

The paper considers the classical single-period inventory model, also known as the Newsboy Problem, with the demand normally distributed and fully observed in successive inventory cycles. The extent of applicability of such a model to inventory management depends upon demand estimation. Appropriate estimators for the optimal order quantity and the maximum expected profit are developed. The statistical properties of the two estimators are explored for both small and large samples, analytically and through Monte-Carlo simulations. For small samples, both estimators are biased. The form of distribution of the optimal order quantity estimator depends upon the critical fractile, while the distribution of the maximum expected profit estimator is always left-skewed. Small samples properties of the estimators indicate that, when the critical fractile is set over a half, the optimal order quantity is underestimated and the maximum expected profit is overestimated with probability over 50%, whereas the probability of overestimating both quantities exceeds again 50% when the critical fractile is below a half. For large samples, based on the asymptotic properties of the two estimators, confidence intervals are derived for the corresponding true population values. The validity of confidence intervals using small samples is tested by developing appropriate Monte-Carlo simulations. In small samples, these intervals attain acceptable confidence levels, but with high unit shortage cost, for the case of maximum expected profit, significant reductions in their precision and stability are observed.     

Joint inventory and technology selection decisions

In some manufacturing systems, the type of production technology selected dictates the lot size, or sets an upper limit on it. In this paper, we formulate a model in which the lot sizing decision has to be made at the technology selection stage. Furthermore, the cost of the technology depends on the lot size it can produce. The problem is addressed under two different assumptions about demand. First demand is assumed to be constant. A closed-form expression for the optimal lot size is derived for this case. Second, demand is assumed to be linearly decreasing. Using an accurate approximation to the total cost function, a closed-form expression for the optimal lot size is derived. We illustrate the models with numerical examples.     

AN ECONOMIC PRODUCTION QUANTITY MODEL WITH LEARNING AND FORGETTING CONSIDERATIONS

The focus of this work is on the effects of learning on economic production quantity in batch production systems. We assumed that both unit variable manufacturing time and setup time follow a learning curve. We modified the classical Economic Production Quantity model to incorporate these two types of learning phenomena. We also incorporated the forgetting effect in our model so that a fraction of the learning is lost between consecutive lots. We developed a dynamic program to obtain the optimal solution to the problem. We investigated the nonincreasing lot size property and used it to improve the efficiency of our dynamic program. We consider a special case of the model in which all lot sizes are assumed equal. After theoretical treatment, we carried out a computational study of the effect of assuming equal lot sizes on the optimal solutions. The results of our examples strongly indicate that the assumption of equal lot sizes not only simplifies the determination of the optimal solutions, but also provides close approximations to the optimal solutions.     

Optimal Cost Sampling for Decision Making with Multiple Regression Models

This paper develops an explicit relationship between sample size, sampling error, and related costs for the application of multiple regression models in observational studies. Graphs and formulas for determining optimal sample sizes and related factors are provided to facilitate the application of the derived models. These graphs reveal that, in most cases, the imprecision of estimates and minimum total cost are relatively insensitive to increases in sample size beyond n=20. Because of the intrinsic variation of the regression model, even if larger samples are optimal, the relative change in the total cost function is small when the cost of imprecision is a quadratic function. A model-utility approach, however, may impose a lower bound on sample size that requires the sample size be larger than indicated by the estimation or cost-minimization approaches. Graphs are provided to illustrate lower-bound conditions on sample size. Optimal sample size in view of all considerations is obtained by the maximin criterion, the maximum of the minimum sample size for all approaches.