Book Reviews

Strategic Air Defense. Edited by Stephen J. Cimbala. Scholarly Resources, Wilmington, DE (1989), ISBN 0–8420–2285–6, $40.00

NATO's Defence of the North. Brassey's Atlantic Commentaries No. 1. Edited by Eric Grove. Brassey's, London (1989), ISBN 0–08–037339–9, £7.50

Maritime Strategy and the Balance of Power: Britain and America in the Twentieth Century. Edited by John B. Hattendorf and Robert S. Jordan. Macmillan, London (1989), ISBN 0–333–43789–6, £45.00

Superpowers at Sea: an Assessment of the Naval Arms Race. By Richard Fieldhouse and Shunji Taoka. SIPRI, Oxford (1989), ISBN 0–19–829135–3

Security at Sea: Naval Arms Control. Edited by Richard Fieldhouse. Oxford University Press, Oxford (1990), ISBN 0–19–829130–2, £25.00

Strategy in the Southern Oceans: a South American View. By Virginia Gamba‐Stonehouse. Pinter, London (1989), ISBN 0–86187–017–4, £30.00

The Defence Industrial Base and the West. Edited by D. G. Haglund. Routledge, London (1989), ISBN 0–415–00923–5, £30.00

Defense and Détente: US and West German Perspectives on Defense Policy. Edited by Joseph I. Coffey and Klaus von Schubert. Westview Press, Boulder, CO, ISBN 0–8133–7722–6, $36.50     

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.     

Optimal dispatching strategies for vehicles having exponentially distributed trip times

A transportation system has N vehicles with no capacity constraint which take passengers from a depot to various destinations and return to the depot. The trip times are considered to be independent and identically distributed random variables. The dispatch strategy at the depot is to dispatch immediately, or to hold any returning vehicles with the objective of minimizing the average wait per passenger at the depot, if passengers arrive at a uniform rate. Optimal control strategies and resulting waits are determined in the special case of exponentially distributed trip time for various N up to N = 15. For N ? 1, the nature of the solution is always to keep a reservoir of vehicles in the depot, and to decrease (increase) the time headway between dispatches as the size of the reservoir gets larger (smaller). For sufficiently large N, one can approximate the number of vehicles in the reservoir by a continuum and obtain analytic experession for the optimal dispatch rate as a function of the number of vehicles in the reservoir. For the optimal strategy, it is shown that the average number of vehicles in the depot is of order N^1/3. These limit properties are expected to be quite insensitive to the actual trip time distribution, but the convergence of the exact properties to the continuum approximation as N → ∞ is very slow.     

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.     

The random order service G/M/m queue

The waiting time in the random order service G/M/m queue is studied. For the Laplace transform we obtain a simpler representation than previously available. For the moments, an explicit recursive algorithm is given and carried out numrically for some cases. This gives rise to the conjecture that the waiting-time distributio can be approximated by the one for M/M/m after a suitable change of scale.     

A versatile scheme for ranking the extreme points of an assignment polytope

A cutting plane scheme embedded in an implicit enumeration framework is proposed for ranking the extreme points of linear assignment problems. This method is capable of ranking any desired number of extreme points at each possible objective function value. The technique overcomes storage difficulties by being able to perform the ranking at any particular objective function value independently of other objective values. Computational experience on some test problems is provided.     

A note on first passage times in birth and death and nonnegative diffusion processes

Consider a birth and death process starting in state 0. Keilson has shown by analytical arguments that the time of first passage into state n has an increasing failure rate (IFR) distribution. We present a probabilistic proof for this. In addition, our proof shows that for a nonnegative diffusion process, the first passage time from state 0 to any state x is IFR.     

Parameter estimation for the EOQ lot-size model: Minimax and expected value choices

This article provides formulas for estimating the parameters to be used in the basic EOQ lot-size model. The analysis assumes that the true values of these parameters are unknown over known ranges and perhaps nonstationary over time. Two measures of estimator “goodness” are derived from EOQ sensitivity analysis. Formulas are given for computing the minimax choice and the minimum expected value choice for the parameter estimates using both measures of estimator “goodness”. A numerical example is included.