Book reviews

British Military History: a Supplement to Robin Higham's Guide to the Sources.. Edited by Gerald Jordan. Garland, New York (1988), xii + 586 pp., $75.00

Red Duster at War. By John Slader. William Kimber, London (1988), 352 pp., £15.50

Armed Services and Society. By Martin Edmonds. Leicester University Press, Leicester (1988), 226 pp., £25.00     

Aggregating assignment constraints

This article shows how simple systems of linear equations with {0,1} variables can be aggregated into a single linear equation whose {0,1} solutions are identical to the solutions of the original system. Structures of the original systems are exploited to keep the aggregator's integer coefficients from becoming unnecessarily large. The results have potential application in integer programming and information theory, especially for problems that contain assignment-type constraints along with other constraints. Several unresolved questions of a number-theoretic nature are mentioned at the conclusion of the article.     

On finding spanning eulerian subgraphs

In this article, we examine the problem of producing a spanning Eulerian subgraph in an undirected graph. After the ?-completeness of the general problem is established, we present polynomial-time algorithms for both the maximization and minimization versions where instances are defined on a restricted class of graphs referred to as series-parallel. Some novelties in the minimization case are discussed, as are heuristic ideas.     

Quadratic forms in spherical random variables: Generalized noncentral x2 distribution

Let X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi-square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitting probabilities.     

A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

Bayes adaptive control of two-echelon inventory systems i: development for a special case of one-station lower echelon and monte carlo evaluation

Bayes adaptive control policies are developed in the present paper for the special case of a one-station lower echelon: a Poisson distribution of demand, whose mean is assumed to have a prior gamma distribution. The cost structure is of a common type. The ordering policy for the upper echelon, which minimizes expected cost, is replaced by a new type of policy, called Bayes prediction policy. This policy does not require tedious computations, of the sort required by dynamic programming solutions. The characteristics of the policies are studied by Monte Carlo simulation, and supplemented by further theoretical development.     

A comparative study of demand forecasting techniques for military helicopter spare parts

This paper deals with techniques applicable to predicting spare parts demand for military helicopters. The military helicopter is a distinct weapons system, whose unique configuration may preclude the direct application of forecasting techniques which have proved successful for other weapon systems. Furthermore, although the military helicopter has become extremely important tactically in modern warfare, it has received scant attention in terms of research concerning its supply support. Specifically, this paper summarizes research done to measure and compare the forecasting accuracy of six mathematical models, as they were applied to three prominent military helicopters. In addition, the paper describes attempts that were made to define, where possible, the conditions under which a specific forecasting technique might be applicable. In general, it is shown that the most accurate set of helicopter spare parts demand forecasts are produced by a second order polynomial exponential smoothing model. This model is observed to have most accurately described the highly volatile, and upward-trended demand time series which were the subject of the study.     

Interception in a network

This paper presents an algorithm for determining where to place intercepting units in order to maximize the probability of preventing an opposing force from proceeding from one particular node in an undirected network to another. The usual gaming assumptions are invoked; namely, the strategy for placing the units is known to the opponent and he will choose a path through the network which, based on this knowledge, maximizes his probability of successful traverse. As given quantities, the model requires a list of the arcs and nodes of the network, the number of intercepting units available to stop the opposing force, and the probabilities for stopping the opposition at the arcs and nodes as functions of the number of intercepting units placed there. From these quantities, the algorithm calculates the probabilities for placing the unit at the arcs and nodes when one intercepting unit is available, and the expected numbers of units to place at the arcs and nodes when multiple intercepting units are available.