Landmarks in defense literature

Theory of Games and Economic Behaviour. By J. Von Neumann and O. Morgenstern. Princeton University Press, Princeton, NJ (1944)     

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.     

Determining optimal growth paths in logistics operations

This paper considers a logistics system modelled as a transportation problem with a linear cost structure and lower bounds on supply from each origin and to each destination. We provide an algorithm for obtaining the growth path of such a system, i. e., determining the optimum shipment patterns and supply levels from origins and to destinations, when the total volume handled in the system is increased. Extensions of the procedure for the case when the costs of supplying are convex and piecewise linear and for solving transportation problems that are not in “standard form” are discussed. A procedure is provided for determining optimal plant capacities when the market requirements have prespecified growth rates. A goal programming growth model where the minimum requirements are treated as goals rather than as absolute requirements is also formulated.     

Inventory control of by-products

The system to be controlled produces n products simultaneously in fixed proportions every time it is activated. Demands for the products in any period are components of an n dimensional vector random variable with known distribution function. Cases of excess demands backlogged and excess demands lost are considered. In the former the notion of k convexity can be generalized to guarantee relatively simple form for the optimal policy in an n decision problem. In the latter, this generalization was not successful although when there is no setup cost, a convexity argument can be used to show that the optimal policy has a simple form.     

Minimum-cost flows in convex-cost networks

An algorithm is given for solving minimum-cost flow problems where the shipping cost over an arc is a convex function of the number of units shipped along that arc. This provides a unified way of looking at many seemingly unrelated problems in different areas. In particular, it is shown how problems associated with electrical networks, with increasing the capacity of a network under a fixed budget, with Laplace equations, and with the Max-Flow Min-Cut Theorem may all be formulated into minimum-cost flow problems in convex-cost networks.     

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.