The relationship between decision variables and penalty cost parameter in (Q,R) inventory models

This paper is concerned with the optimum decision variables found using order quantity, reorder point (Q, R) inventory models. It examines whether the optimum variables (Q* and R*) are necessarily monotonic functions of the backorder cost parameter (or equivalently of the performance objective). For a general class of models it is proved that R* must increase as the performance objective is raised, and an inequality condition is derived which governs how Q* will change. Probability distributions of lead time demand are cited or found for which Q* increases, Q* decreases, and Q* is independent of increases in performance objectives or backorder cost parameter.     

Values for optimum reject allowances

Industrial situations exist where it is necessary to estimate the optimum number of parts to start through a manufacturing process in order to obtain a given number of completed good items. The solution to this problem is not straightforward when the expected number of rejects from the process is a random variable and when there are alternative penalties associated with producing too many or too few items. This paper discusses various aspects of this problem as well as some of the proposed solutions to it. In addition, tables of optimum reject allowances based on a comprehensive model are presented.     

Book reviews

Exporting Democracy: Fulfilling America's Destiny. By Joshua Muravchik, American Enterprise Institute (1991) ISSN 0–8447–3734–8. $12.95.

Generals in the Palacio. By Roderick Ai Camp. Oxford University Press, (1992), ISBN 0–19–507300–2, £45.

L'Armement en France. Genèse, Ampleur et Coût d'une Industrie By François Chesnais and Claude Serfati, Editions Nathan, Collection Economie/Sciences Sociales, Paris (1992), ISBN 2–09–190086–9.

The Têt Offensive. Intelligence Failure in War. By James Wirtz, Cornell University Press, New York (1991), ISBN 0–8014–2486–0. $38.50.

Restructuring of arms producton in Western Europe. Edited by Michael Brzoska and Peter Lock. Oxford University Press, Oxford (1992), ISBN 0–1982–9147–7. £25.00.

What is Proper Soldiering? A study of new perspectives for the future uses of the Armed Forces of the 1990s. By Michael Harbottle. The Centre for International Peacebuilding, Chipping Norton (1992), £3.50.

The Strategic Defence Initiative By Edward Reiss, Cambridge University Press, Cambridge (1992), ISBN 0–521–41097–5. £30.00.     

采用空气轴承的大行程快速刀具伺服系统

随着对结构化超精密部件需要的不断增加,出现了加工具有高的表面光洁度以及形状精度的非旋转对称镜片的新技术。根据现有的快速刀具伺服系统,研制出了最大行程为16mm的新型快速刀具伺服系统(图1)。以前的快速刀具伺服系统采用了弹性导向机构,而现在的快速刀具伺服系统则采用了空气轴承,并且用了一个高频直线电机来驱动这个系统。由于采用了一个新的功率放大器,使得这个系统能够最高达到100Hz的频率以及1mm的振动幅度。这篇文章给出了这种新型快速刀具伺服系统的技术细节。     

Estimating value in a uniform auction

Consider an auction in which increasing bids are made in sequence on an object whose value θ is known to each bidder. Suppose n bids are received, and the distribution of each bid is conditionally uniform. More specifically, suppose the first bid X₁ is uniformly distributed on [0, θ], and the i^th bid is uniformly distributed on [X_i?1, θ] for i = 2, …?, n. A scenario in which this auction model is appropriate is described. We assume that the value θ is un known to the statistician and must be esimated from the sample X₁, X₂, …?, X_n. The best linear unbiased estimate of θ is derived. The invariance of the estimation problem under scale transformations in noted, and the best invariant estimation problem under scale transformations is noted, and the best invariant estimate of θ under loss L(θ, a) = [(a/θ) ? 1]² is derived. It is shown that this best invariant estimate has uniformly smaller mean-squared error than the best linear unbiased estimate, and the ratio of the mean-squared errors is estimated from simulation experiments. A Bayesian formulation of the estimation problem is also considered, and a class of Bayes estimates is explicitly derived.     

Refined prediction for linear regression models

Adequate prediction of a response variable using a multiple linear regression model is shown in this article to be related to the presence of multicollinearities among the predictor variables. If strong multicollinearities are present in the data, this information can be used to determine when prediction is likely to be accurate. A region of prediction, R, is proposed as a guide for prediction purposes. This region is related to a prediction interval when the matrix of predictor variables is of full column rank, but it can also be used when the sample is undersized. The Gorman-Toman ten-variable data is used to illustrate the effectiveness of the region R.     

A note on the “value” of bounds on EVPI in stochastic programming

The existing literature concentrates on determining sharp upper bounds for EVPI in stochastic programming problems. This seems to be a problem without an application. Lower bounds, which we view as having an important application, are only the incidental subject of study and in the few instances that are available are obtained at an extremely high cost. In order to suggest a rethinking of the course of this research, we analyze the need for bounds on EVPI in the context of its significance in decision problems.