Lowering Inventory Systems Costs by Using Regression-Derived Estimators of Demand Variability*

Scientific techniques for inventory management typically are applied to systems containing many items. Such techniques require an estimation of the demand variance (and mean) of each item from historical data. This research demonstrates a significant potential for improvement in system cost performance from using least-squares regression fits of a variance-to-mean functional relation instead of the standard statistical variance estimate. Even when there is a moderate degree of heterogeneity among items and when the form of the variance-to-mean relation is misspecified, substantial cost savings may be realized. The cost of statistical uncertainty may be reduced by half. The research also provides evidence that system cost is fairly insensitive to the number of items used to fit the regression. This paper provides the underlying reason why a regression-derived variance estimator yields lower cost: it is less variable than the usual individual item variance estimator.     

Characterization of Unacceptable Solutions in LP Discriminant Analysis*

Many linear programming models have been proposed for performing discriminant analysis. Partial characterizations for unacceptable solutions have been presented and new models proposed to circumvent these problems. In this paper those conditions leading to unacceptable solutions for all two-group models are characterized.     

Inference in a Binary Response Model with Applications to Data Analysis*

Standard errors of the coefficients of a logistic regression (a binary response model) based on the asymptotic formula are compared to those obtained from the bootstrap through Monte Carlo simulations. The computer intensive bootstrap method, a nonparametric alternative to the asymptotic estimate, overestimates the true value of the standard errors while the asymptotic formula underestimates it. However, for small samples the bootstrap estimates are substantially closer to the true value than their counterpart derived from the asymptotic formula. The methodology is discussed using two illustrative data sets. The first example deals with a logistic model explaining the log-odds of passing the ERA amendment by the 1982 deadline as a function of percent of women legislators and the percent vote for Reagan. In the second example, the probability that an ingot is ready to roll is modelled using heating time and soaking time as explanatory variables. The results agree with those obtained from the simulations. The value of the study to better decision making through accurate statistical inference is discussed.     

A Warning Zone Method for the Multiperiod Cost Variance Investigation Problem

This paper develops a warning zone approach to make variance investigation decisions for a multiperiod process. The assumed cost generation process varies between an in-control and out-of-control state. These states cannot be directly observed, but must be inferred from the reported cost variances. Using the warning zone method of inference, the manager investigates the process whenever an upper threshold is exceeded or a lower threshold is exceeded for two consecutive periods. A four-state Markov chain models the resulting decision process. Steady state probabilities are derived for this chain and are used to obtain explicit formulas for the effectiveness and efficiency of the decision process. These formulas permit computation of the cost savings attainable by the warning zone method. Compared to other decision rules, the warning zone method is much simpler than the theoretically optimal Bayesian revision method, but uses more information than the Markovian control limit method. Numerical comparison of results shows that the warning zone method usually captures most of the available cost savings, even in cases where the Markovian control limit method does not perform well.     

A Bayesian Approach for Analyzing Results of Vehicle Collision Tests

Certain motor vehicle safety standards stipulate a collision test speed and a set of performance criteria that vehicles must satisfy during or after the collision test. For example, Federal Motor Vehicle Safety Standard 301 requires a 30 mile per hour (mph) barrier collision and specifies a certain maximum allowable limit on the total spillage of fuel. Vehicle designs are required to meet this standard; however, when collision tests are conducted at speeds higher than the standard, vehicles do not always satisfy the performance criteria. This paper develops a mathematical model for estimating the probability of meeting the standard by using a Bayesian framework to incorporate engineering judgment with collision test results. The model is based on the idea that there are random features to a vehicle's ability to meet performance standards in a collision, especially at such elevated speeds. Example calculations are included to illustrate the estimation of the probability of meeting the standard and to compare it with a maximum likelihood approach.     

A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy

This paper deals with a single server Poisson arrival queue with two phases of heterogeneous service along with a Bernoulli schedule vacation model, where after two successive phases service the server either goes for a vacation with probability p (0≤p≤1) or may continue to serve the next unit, if any, with probability q(=1−p). Further the concept of multiple vacation policy is also introduced here. We obtained the queue size distributions at a departure epoch and at a random epoch, Laplace Stieltjes Transform of the waiting time distribution and busy period distribution along with some mean performance measures. Finally we discuss some statistical inference related issues.     

A NEW CLASS OF MODELS FOR THE DISCRIMINANT PROBLEM

Discriminant analysis is relevant to business decision making in a variety of contexts, such as when one decides to make or buy a specified component, fund a venture project, or hire a particular person. Potential applications in artificial intelligence, particularly in the area of pattern recognition, have further underscored the importance of the field. A recent innovation in discriminant analysis is provided by special linear programming (LP) models, which offer attractive alternatives to classical statistical approaches. The scope of application in which discriminant analysis can be advantageously employed is broadened by the flexibility to tailor parameters in the LP approaches to reflect diverse goals and by the power to explore the sensitivity of these parameters. In spite of the promise of the LP formulations, however, limitations to their effectiveness have been uncovered in certain settings. A recent advance involving a normalization construct removes some of the limitations but entails solving the LP model twice (to allow for different signs of a normalization constant) and does not yield equivalent solutions for different rotations of the problem data. This paper introduces a new model and a new class of normalizations that remedy both remaining limitations, making it possible to take advantage of the modeling capabilities of the LP formulations without the attendant shortcomings encountered by earlier investigations. Our development shows by empirical testing and illustrative analysis that the quality of solutions from LP discriminant approaches is more favorable (relative to the classical model) than previously supposed.     

A Variable Selection Criterion in the Linear Programming Approaches to Discriminant Analysis*

There are numerous variable selection rules in classical discriminant analysis. These rules enable a researcher to distinguish significant variables from nonsignificant ones and thus provide a parsimonious classification model based solely on significant variables. Prominent among such rules are the forward and backward stepwise variable selection criteria employed in statistical software packages such as Statistical Package for the Social Sciences and BMDP Statistical Software. No such criterion currently exists for linear programming (LP) approaches to discriminant analysis. In this paper, a criterion is developed to distinguish significant from nonsignificant variables for use in LP models. This criterion is based on the “jackknife” methodology. Examples are presented to illustrate implementation of the proposed criterion.     

Open Order Rescheduling in Job Shops with Demand Uncertainty: A Simulation Study

This paper addresses the problem of open order rescheduling in a job shop. Results are reported of experiments conducted in a simulation model of an 8-machine job shop. Four different order updating policies are examined. The due-date process is modeled to include several realistic features about the pattern of due-date variability. These features are parameterized and tested at several levels. Tardiness results indicate that open order rescheduling is beneficial only when allowances are loosely set. The results indicate that inventory performance is improved by order rescheduling, particularly in cases when due dates are revised to earlier times than originally forecast.     

美国竞选财政制度初探

美国竞选财政制度是美国政治制度中争议最多的问题之一。由于利益集团政策参与的需求和竞选人竞选的需要 ,美国的竞选捐赠日益加剧 ,捐赠规模日趋膨胀 ,并在一定程度上导致了决策过程中利益代表性的偏差。由此 ,美国早期的法律就对利益集团的竞选捐赠进行限制 ,2 0世纪 4 0年代以来 ,美国关于竞选财政制度改革的立法不断。但改革遇到利益需求和关于合宪性问题等种种障碍 ,步履维艰。美国政治中的这一两难状况是其政治体制所使然 ,有关竞选财政制度改革的争论仍将继续下去。