One-facility location with rectilinear tour distances

This article concerns the location of a facility among n points where the points are serviced by “tours” taken from the facility. Tours include m points at a time and each group of m points may become active (may need a tour) with some known probability. Distances are assumed to be rectilinear. For m ≤ 3, it is proved that the objective function is separable in each dimension and an exact solution method is given that involves finding the median of numbers appropriately generated from the problem data. It is shown that the objective function becomes multimodal when some tours pass through four or more points. A bounded heuristic procedure is suggested for this latter case. This heuristic involves solving an auxiliary three-point tour location problem.     

Weapon acquisition with target uncertainty

This article is concerned with choosing a mix of weapons, subject to constraints, when the targets to be attacked are known imprecisely. It is shown that the correct method for optimizing the mix of weapons involves a pair of nested optimization problems (two-stage optimization). Two methods for optimizing the expected utility of a mix are discussed. The first involves a simultaneous attack model, in which it is implicitly assumed that all weapons are used at once. The second involves a sequential attack model, in which targets appear in random order and are attacked one at a time. Particular attention is given to the question of the appropriate mix of general-purpose and special-purpose weapons.     

Comparative evaluation of prior versus progressive articulation of preference in bicriterion optimization

Procedures for solving multiple criteria problems are receiving increasing attention. Two major solution approaches are those involving prior articulation and progressive articulation of preference information. A progressive articulation (interactive) optimization approach, called the Paired Comparison Method (PCM) is compared to the prior articulation approach of a priori utility function measurement in a quality control decision environment from the perspective of the decision maker. The three major issues investigated included: (1) the ease of use of each method, (2) the preferences of solutions obtained, and (3) the insight provided by the methodology into the nature and structure of the problem. The problem setting involved management students who were rquired to determine an acceptance sampling plan using both methods. The PCM provided the most preferred solutions and was considered easier to use and understand. The prior articulation of preference method was found to give more insight into the problem structure. The results suggest that a hybrid approach, combining both prior preference assessment and an interactive procedure exploiting the advantages of each, should be employed to solve multiple criteria problems.     

The capital supply curve in capacity expansion models: Some economic and algorithmic aspects

Capacity expansion models typically minimize the discounted cost of acquisition and operation over a given planning horizon. In this article we generalize this idea to one in which a capital supply curve replaces the usual discount rate. A capital supply curve is a means to model financial outlook, investment limits, and risk. We show that when such a curve is included in a capacity expansion model, it will, under certain conditions, provide a less capital intensive solution than one which incorporates a discount rate. In this article, we also provide an algorithm that solves capacity expansion models that incorporate a capital supply curve. The attractive feature of this algorithm is that it provides a means to utilize the “discount rate” models efficiently. Throughout, we give applications in power generation planning and computational experience for this application is also presented.     

An optimum t-test for the scale parameter of an extreme-value distribution

A Student's t-test proposed by Ogawa is considered for the hypothesis Ho: σ=σo against the alternative hypothesis H₁: σ ≠ σo, where σ is the scale parameter of the Extremevalue distribution of smallest values with known location parameter μ. The test is based on a few sample quantiles chosen from a large sample so as to give asymptotically maximum power to the test when the number of sample quantiles is fixed. A table which facilitates the computation of the test statistic is given. Several schemes for determining the ranks of the sample quantiles by the optimal spacings are compared and the effect of the bias of the estimate of σ on the test is investigated through a Monte Carlo study.     

On the theory of semi-infinite programming and a generalization of the kuhn-tucker saddle point theorem for arbitrary convex functions

We first present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory. By the pairing of a finite dimensional vector space over an arbitrarily ordered field with a generalized finite sequence space, the major theorems of linear programming are generalized. When applied to Euclidean spaces, semi-infinite programming theory yields a dual theorem associating as dual problems minimization of an arbitrary convex function over an arbitrary convex set in n-space with maximization of a linear function in non-negative variables of a generalized finite sequence space subject to a finite system of linear equations. We then present a new generalization of the Kuhn-Tucker saddle-point equivalence theorem for arbitrary convex functions in n-space where differentiability is no longer assumed.     

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.     

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