Numerical treatment of a class of semi-infinite programming problems

Many optimization problems occur in both theory and practice when one has to optimize an objective function while an infinite number of constraints must be satisfied. The aim of this paper in to describe methods of handling such problems numerically in an effective manner. We also indicate a number of applications.     

Economic lot scheduling of fully loaded processes with external setups

Without restricting the class of permissible schedules, we derive optimal schedules for economic lot scheduling problems that are fully loaded, have external setups, and have only two products. The fully loaded condition accurately represents certain types of bottlenecks. We show that the optimal schedule must have the Wagner-Whitin property. We also develop a measure of aggregate inventory, derive an optimal steady-state aggregate inventory policy, and provide conditions under which the aggregate inventory level of an optimal schedule must approach a steady state. By restricting the class of permissible schedules to rotation cycle schedules, we extend these results to more than two products.     

Estimating the probability that a simulated system will be the best

Consider a stochastic simulation experiment consisting of v independent vector replications consisting of an observation from each of k independent systems. Typical system comparisons are based on mean (long‐run) performance. However, the probability that a system will actually be the best is sometimes more relevant, and can provide a very different perspective than the systems' means. Empirically, we select one system as the best performer (i.e., it wins) on each replication. Each system has an unknown constant probability of winning on any replication and the numbers of wins for the individual systems follow a multinomial distribution. Procedures exist for selecting the system with the largest probability of being the best. This paper addresses the companion problem of estimating the probability that each system will be the best. The maximum likelihood estimators (MLEs) of the multinomial cell probabilities for a set of v vector replications across k systems are well known. We use these same v vector replications to form v^k unique vectors (termed pseudo‐replications) that contain one observation from each system and develop estimators based on AVC (All Vector Comparisons). In other words, we compare every observation from each system with every combination of observations from the remaining systems and note the best performer in each pseudo‐replication. AVC provides lower variance estimators of the probability that each system will be the best than the MLEs. We also derive confidence intervals for the AVC point estimators, present a portion of an extensive empirical evaluation and provide a realistic example. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 341–358, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10019     

Optimal service rates of a service facility with perishable inventory items

In this paper we optimally control service rates for an inventory system of service facilities with perishable products. We consider a finite capacity system where arrivals are Poisson‐distributed, lifetime of items have exponential distribution, and replenishment is instantaneous. We determine the service rates to be employed at each instant of time so that the long‐run expected cost rate is minimized for fixed maximum inventory level and capacity. The problem is modelled as a semi‐Markov decision problem. We establish the existence of a stationary optimal policy and we solve it by employing linear programming. Several numerical examples which provide insight to the behavior of the system are presented. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 464–482, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10021     

Bicriteria product design optimization: An efficient solution procedure using AND/OR trees

Competitive imperatives are causing manufacturing firms to consider multiple criteria when designing products. However, current methods to deal with multiple criteria in product design are ad hoc in nature. In this paper we present a systematic procedure to efficiently solve bicriteria product design optimization problems. We first present a modeling framework, the AND/OR tree, which permits a simplified representation of product design optimization problems. We then show how product design optimization problems on AND/OR trees can be framed as network design problems on a special graph—a directed series‐parallel graph. We develop an enumerative solution algorithm for the bicriteria problem that requires as a subroutine the solution of the parametric shortest path problem. Although this parametric problem is hard on general graphs, we show that it is polynomially solvable on the series‐parallel graph. As a result we develop an efficient solution algorithm for the product design optimization problem that does not require the use of complex and expensive linear/integer programming solvers. As a byproduct of the solution algorithm, sensitivity analysis for product design optimization is also efficiently performed under this framework. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 574–592, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10031     

Book Reviews

Iain McCallum, Blood Brothers Hiram and Hudson Maxim: Pioneers of Modern Warfare. London: Chatham, 1999. Pp. 224, 33 illus., 2 maps, biblio., index. £20. ISBN 1–86176–096–5.

Eric Ash, Sir Frederick Sykes and the Air Revolution, 1912–1918. London and Portland, OR: Frank Cass, 1999. Pp.xviii + 268, 20 illus., 3 maps, biblio., index. £42.50/$59.50 (cloth), £18.50/$27.50 (paper). ISBN 0–7146–4828–0 and ‐4382–3.

Azar Gat, Fascist and Liberal Visions of War: Fuller, Liddell Hart, Douhet, and other Modernists. Oxford: Clarendon Press, 1998. Ppviii + 334, biblio., index. £45. ISBN 0–19–820715–8.

David B. Woolner (ed.), The Second Quebec Conference Revisited: Waging War, Formulating Peace: Canada, Great Britain, and the United States in 1944–1945. Basingstoke; London: Macmillan Press, 1998. Pp.xiii + 210, index. £32.50. ISBN 0–333–75970–2.

Jeffrey Grey. Up Top: The Royal Australian Navy and Southeast Asian Conflicts 1955–1972. St Leonards NSW: Allen &; Unwin in association with the Australian War Memorial, 1998. Pp.xx + 380, 110 illus., 12 tables, 23 maps &; diagrams, appendices, notes, biblio., index. NP. ISBN 1–86448–290–7.

Susan L Carruthers, The Media at War. Basingstoke: Macmillan, 2000. Pp.321, biblio., index. £14.99 (paper). ISBN 0–333–69143–1, also available in hardback.

Edward J. Marolda and Robert J. Schneller Jr, Shield and Sword: The United States Navy and the Persian Gulf War. Washington DC: Naval Historical Center, 1998. Pp.xxi + 517, 120 illus., 14 maps, biblio., index. NP. ISBN 0–1604–9476–1.

Marvin Pokrant, Desert Shield at Sea: What the Navy Really Did and Desert Storm at Sea: What the Navy Really Did. Both Westport, CT: Greenwood Press, 1999. Pp.xxiii + 265,9 illus., biblio., index. £44.95. ISBN 0–313–31023–8. Pp.xxiv + 329,12 illus., biblio., index. NP. ISBN 0–313–31024–6.

David Kaularich and Ronald C. Kramer, Crimes of the American Nuclear State: At Home and Abroad. Boston: Northeastern University Press, 1999. Pp.xviii + 195, biblio., index. £42.75. ISBN 1–55553–371‐X.

Stanley Hoffmann, World Disorders: Troubled Peace in the Post‐Cold War Era. Lanham, MD: Rowman &; Littlefield, 1998. Pp.viii+279, notes, index. $29.95. ISBN 0–8476–8574–8.

Lawrence Freedman (ed.), Strategic Coercion: Concepts and Cases. Oxford: Oxford‐University Press, 1998. Pp.400, index. £48. ISBN 0–19–829–349–6.

Stephen J. Cimbala, Coercive Military Strategy. College Station, TX: Texas A&;M University Press, 1998. Pp.229, biblio, index; $39.95. ISBN 0–89096–836–5     

An Imperfect Jewel: Military Theory and the Military Profession

This article explores a perennial theme in the literature of strategic studies: the relationship between military theory and the military profession. It begins with a conceptual analysis of this relationship. It then investigates what military theorists themselves have had to say about the utility of their craft. It concludes by assessing the actual influence of military theory on selected individuals and institutions. The individuals are George S. Patton, Jr., and Ulysses S. Grant. The institutions are the United States Army and the United States Air Force in the late twentieth century. The fundamental finding is suggested in the title: military theory can indeed be quite useful in the maturation of military commanders and in the development of martial institutions, but it is not always necessary and by no means perfect. It should thus be studied assiduously but used with caution.