Single‐machine scheduling with deadlines to minimize the total weighted late work

We consider scheduling a set of jobs with deadlines to minimize the total weighted late work on a single machine, where the late work of a job is the amount of processing of the job that is scheduled after its due date and before its deadline. This is the first study on scheduling with the late work criterion under the deadline restriction. In this paper, we show that (i) the problem is unary NP‐hard even if all the jobs have a unit weight, (ii) the problem is binary NP‐hard and admits a pseudo‐polynomial‐time algorithm and a fully polynomial‐time approximation scheme if all the jobs have a common due date, and (iii) some special cases of the problem are polynomially solvable.     

Index policies for the routing of background jobs

Arriving (generic) jobs may be processed at one of several service stations, but only when no other (dedicated) jobs are waiting there. We consider the problem of how to route these incoming background jobs to make best use of the spare service capacity available at the stations. We develop an approximative approach to Whittle's proposal for restless bandits to obtain an index policy for routing. The indices concerned are increasing and nonlinear in the station workload. A numerical study testifies to the strong performance of the index policies developed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

An algorithm for solving general fractional interval programming problems

A Linear Fractional Interval Programming problem (FIP) is the problem of extremizing a linear fractional function subject to two-sided linear inequality constraints. In this paper we develop an algorithm for solving (FIP) problems. We first apply the Charnes and Cooper transformation on (FIP) and then, by exploiting the special structure of the pair of (LP) problems derived, the algorithm produces an optimal solution to (FIP) in a finite number of iterations.     

Evaluation of force structures under uncertainty

A model, for assessing the effectiveness of alternative force structures in an uncertain future conflict, is presented and exemplified. The methodology is appropriate to forces (e.g., the attack submarine force) where alternative unit types may be employed, albeit at differing effectiveness, in the same set of missions. Procurement trade-offs, and in particular the desirability of special purpose units in place of some (presumably more expensive) general purpose units, can be addressed by this model. Example calculations indicate an increase in the effectiveness of a force composed of general purpose units, relative to various mixed forces, with increase in the uncertainty regarding future conflicts.     

An exact aggregation/disaggregation algorithm for large scale markov chains

Many Markov chain models have very large state spaces, making the computation of stationary probabilities very difficult. Often the structure and numerical properties of the Markov chain allows for more efficient computation through state aggregation and disaggregation. In this article we develop an efficient exact single pass aggregation/disaggregation algorithm which exploits structural properties of large finite irreducible mandatory set decomposable Markov chains. The required property of being of mandatory set decomposable structure is a generalization of several other Markov chain structures for which exact aggregation/disaggregation algorithms exist. © 1995 John Wiley & Sons, Inc.     

Book Reviews

Patrick Finney (ed.), The Origins of the Second World War. London: Arnold, 1997. Pp.xvi + 461, index. £15.99. ISBN 0–340–67640‐X.

Maria Emilia Paz, Strategy, Security, and Spies: Mexico and the US as Allies in World War II. University Park, PA: The Pennsylvania State University Press, 1997. Pp.xii + 264, 10 illus., biblio., index. $55 (cloth); $19.95 (paper). ISBN 0–271–01665–5 and 01666–3.

Norman J.W. Goda, Tomorrow the World: Hitler, Northwest Africa and the Path toward America. College Station, Texas A&;M University Press, 1998. Pp.xxvi + 307, 2 maps, biblio., index. $39.95. ISBN 0–89096–807–1.

Michael J. Hogan, A Cross of Iron: Harry S. Truman and the Origins of the National Security State, 1945–1954. Cambridge; New York: Cambridge University Press, 1998. Pp.xii + 525, biblio., index. £25; $34.95. ISBN 0–521–64044‐X.

Stephen Van Evera, Causes of War: Power and the Roots of Conflict. Ithaca, NY: Cornell University Press, 1999. Pp.viii + 270, index. $35. ISBN 0–801403201–4.

Eric Arnett (ed.), Nuclear Weapons and Arms Control in South Asia after the Test Ban, SIPRI Research Report No.14. Oxford: Oxford University Press/Stockholm Int Peace Research Institute, 1998. Pp.viii + 98, index. £12.99. ISBN 0–19–8294115.

T.V. Paul, Richard J. Harknett and James J. Wirtz (eds.), The Absolute Weapon Revisited: Nuclear Arms and Emerging International Order. Ann Arbor, Michigan: The University of Michigan Press, 1998. Pp.vi + 312, index. $47.50/£36. ISBN 0–472–10863–8.     

Warranty claims modeling

A company wishes to estimate or predict its financial exposure in a reporting period of length T (typically one quarter) because of warranty claims. We propose a fairly general random measure model which allows computation of the Laplace transform of the total claim made against the company in the reporting interval due to warranty claims. When specialized to a Poisson process of both sales and warranty claims, statistical estimation of relevant quantities is possible. The methodology is illustrated by analyzing automobile sales and warranty claims data from a large car manufacturer for a single car model and model year. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

ECONOMIC GROWTH AND VIOLENT INTERNATIONAL CONFLICT: 1875–1999

This paper extends the joint product model of military alliances to apply to the new strategic doctrine adopted by NATO in the 1990s. In particular, a choice must be made between protecting one's own territory and pooling forces for an alliancewide rapid reaction force. This new model accounts for a host of externalities and their implications for burden sharing, full financing, and allocative efficiency. The Pigouvian taxes that adjust for force thinning and attack deflection are shown to finance optimal border‐protecting forces under a variety of circumstances. Second‐best considerations arise owing to the pure publicness of rapid reaction forces. The ideal toll arrangement does not currently characterize NATO financing, nor is it likely to do so.     

Exploiting the Challenges to Bioweapons Development

ABSTRACT

Widespread and often exaggerated generalizations about the global spread weapons of mass destruction (WMDs) have proven to be not only misleading and technologically naïve, but also unhelpful in formulating effective policies to counter their threat. The new book by George Mason University's Sonia Ben Ouagrham-Gormley dispels the popular narrative that governments and terror groups can easily—and inevitably will—develop WMDs, particularly biological weapons, by exploring the complex external and internal conditions that such programs require, as demonstrated by the Cold War-era biological weapon programs of the superpowers. This empirically grounded and realistic assessment of how states try—and often fail—to develop such programs offers a more reliable basis to craft realistic counterproliferation policies that can elicit international support.