Book reviews

Use of Force: The Practise of States by A. Mark Weisburd, Penn: Penn State Press, University Park, 1997, ISBN 0-271-01679-5 (hbk), $65.00/£58.00, ISBN 0-271-01680-9 (pbk), $25.00/£22.50

Late Breaking Foreign Policy: the News Media's Influence on Peace Operations by Warren P. Strobel, Washington DC: United States Insititute of Peace Press, 1997, ISBN 1-878379-68-2 (hbk), £23.25, ISBN 1-878379-67-4 (pbk)

The Reluctant Sheriff: The United States After the Cold War by Richard N. Haass, New York: Council on Foreign Relations, 1997, 148pp, index, ISBN 0-87609-201-6 (hbk), $24.95

The UN, Peace and Force edited by Michael Pugh, London: Frank Cass, 1997, ISBN 0-7146-4795-4 (hbk), £29.50, ISBN 0-7146-4320-3 (pbk), £15.00

Confidence-Building in South East Asia by Malcolm Chalmers, Oxford: Westview Press, 1996, ISBN 1-85143-116-0 (pbk), £19.95

Britain's Strategic Nuclear Deterrent: From Before the V-Bomber to Beyond Trident by Robert H. Paterson, London: Frank Cass, 1997, ISBN 0-7146470-3 (hbk), £35.00, ISBN 0-7146-4297-5 (pbk) £18.00

OSS in China: Prelude to Cold War by Maochun Yu, London: Yale University Press, 1997, ISBN 0 300 06698-8 (hbk), £25.00

Preventing Violent Conflicts: A Strategy for Preventive Diplomacy by Michael S. Lund, Washington DC: US Institute of Peace Press, 1996, ISBN 1-878379-52-6 (pbk), £11.75     

Damage calculations for unreliable warheads

For large numbers of perfectly reliable, optimally targeted warheads the square-root law approximates the expected fraction damage achieved on an area target. In this paper a more exact expression is derived for this damage fraction which Holds for all numbers of warheads. This expression is shown to converge to the square-root law when a large number of warheads are fired. The more exact expression is used in a procedure to calculate expected damage when warheads are unreliable, and this procedure is shown to be superior to a modified square-root approximation which has been used previously.     

Duality for quasi-concave programs with application to economics

A duality theory is developed for mathematical programs with strictly quasi-concave objective functions to be maximized over a convex set. This work broadens the duality theory of Rockafellar and Peterson from concave (convex) functions to quasi-concave (quasi-convex) functions. The theory is closely related to the utility theory in economics. An example from economic planning is examined and the solution to the dual program is shown to have the properties normally associated with market prices.     

Computational results with a branch-and-bound algorithm for the general knapsack problem

In this paper, a branch-and-bound procedure is presented for treating the general knapsack problem. The fundamental notion of the procedure involves a variation of traditional branching strategies as well as the incorporation of penalties in order to improve bounds. Substantial computational experience has been obtained, the results of which would indicate the feasibility of the procedure for problems of large size.     

The simplex method for integral multicommodity networks

The simplex method is interpreted as a labeling procedure for certain classes of multicommodity flow problems in a manner similar to that for single commodity networks. As opposed to general multicommodity algorithms, no explicit matrix inversion is required; all simplex operations are performed graph-theoretically.     

A differential equation model of search for randomly arriving and departing targets

In this paper we analyze optimal search strategies in an environment in which multiple, independent targets arrive and depart at random. The analysis revolves around a continuous time differential equation model which captures the time dependent nature of the search process. We explore the impact on optimal strategies of nonzero travel times between regions as well as differing target arrival rates. We derive simple closed form expressions for determining if only one region should be searched.     

An F approximation for two-parameter weibull and log-normal tolerance bounds based on possibly censored data

An approximation suggested in Mann, Schafer and Singpurwalla [18] for obtaining small-sample tolerance bounds based on possibly censored two-parameter Weibull and lognormal samples is investigated. The tolerance bounds obtained are those that effectively make most efficient use of sample data. Values based on the approximation are compared with some available exact values and shown to be in surprisingly good agreement, even in certain cases in which sample sizes are very small or censoring is extensive. Ranges over which error in the approximation is less than about 1 or 2 percent are determined. The investigation of the precision of the approximation extends results of Lawless [8], who considered large-sample maximum-likelihood estimates of parameters as the basis for approximate 95 percent Weibull tolerance bounds obtained by the general approach described in [18]. For Weibull (or extreme-value) data the approximation is particularly useful when sample sizes are moderately large (more than 25), but not large enough (well over 100 for severely censored data) for asymptotic normality of estimators to apply. For such cases simplified efficient linear estimates or maximum-likelihood estimates may be used to obtain the approximate tolerance bounds. For lognormal censored data, best linear unbiased estimates may be used, or any efficient unbiased estimators for which variances and covariances are known as functions of the square of the distribution variance.     

A bayesian approach to evaluating military investments in product improvement and testing

Two issues of frequent importance in new product development are product improvement and reliability testing. A question often faced by the developer is: Should the product be distributed in its present state, or should it be improved further and/or tested before distribution? A more useful statement of the question might be: What levels of investment in further improvement and testing are economically permissible? Products for which this question is relevant may vary widely in type and intended use. This paper presents a model for determining these levels for one such product—an equipment modification procedure. The model presented makes use of present value analysis to compare cost streams and of Bayesian statistics to relate the costs to various outcomes under conditions of uncertainty. The model is applied to an actual military problem and a method is described for examining the sensitivity of the results to changes in the prior probabilities and discount rate.