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.     

A price leadership method for solving the inspector's non-constant-sum game

An inspector's game is a non-constant-sum two-person game in which one player has promised to perform a certain duty and the other player is allowed to inspect and verify occasionally that the duty has indeed been performed. A solution to a variant of such a game is given in this paper, based on the assumption that the inspector can announce his mixed strategy in advance, if he so wishes, whereas the other player, who has already given his promise, cannot threaten by explicitly saying that he will not keep his word.     

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

War, Culture and the Media: Representations of the Military in 20th Century Britain. Edited by Ian Stewart and Susan L. Carruthers, Trowbridge: Flicks Books, (1996), ISBN 0-948911-86-7 (pbk), £14.95.

The Future of Europe. By Peter Coffey, Aldershot: Edward Elgar, (1995), ISBN 1-85278-586-1 (hardback), £39.95, ISBN 1-85278-587-X (pbk), £12.95.

Global Dangers: Changing Dimensions of International Security. Edited by Sean M. Lynn-Jones, Steven E. Miller, London: the MIT Press, (1996), ISBN O-262-62097-9 (pbk), £13.50;.

New Studies in Post-Cold War Security. Edited by K.R. Dark, Aldershot: Dartmouth Publishing Company, (1996), ISBN 1-85521-728-7 (hardback), £42.50.

Enlarging NATO - The Russian Factor. By Richard L. Kugler with Marianna V. Kozintseva, Santa Monica, CA: National Defense Research Institute and Rand Corporation, (1996), ISBN 0-8330-2357-8, $20.00.     

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.