The fixed charge problem

The fixed charge problem is a nonlinear programming problem of practical interest in business and industry. Yet, until now no computationally feasible exact method of solution for large problems had been developed. In this paper an exact algorithm is presented which is computationally feasible for large problems. The algorithm is based upon a branch and bound approach, with the additional feature that the amount of computer storage required remains constant throughout (for a problem of any given size). Also presented are three suboptimal heuristic algorithms which are of interest because, although they do not guarantee that the true optimal solution will be found, they usually yield very good solutions and are extremely rapid techniques. Computational results are described for several of the heuristic methods and for the branch and bound algorithm.     

On computing the expected discounted return in a markov chain

The discounted return associated with a finite state Markov chain X₁, X₂… is given by g(X₁)+ αg(X₂) + α²g(X₃) + …, where g(x) represents the immediate return from state x. Knowing the transition matrix of the chain, it is desired to compute the expected discounted return (present worth) given the initial state. This type of problem arises in inventory theory, dynamic programming, and elsewhere. Usually the solution is approximated by solving the system of linear equations characterizing the expected return. These equations can be solved by a variety of well-known methods. This paper describes yet another method, which is a slight modification of the classical iterative scheme. The method gives sequences of upper and lower bounds which converge mono-tonely to the solution. Hence, the method is relatively free of error control problems. Computational experiments were conducted which suggest that for problems with a large number of states, the method is quite efficient. The amount of computation required to obtain the solution increases much slower with an increase in the number of states, N, than with the conventional methods. In fact, computational time is more nearly proportional to N², than to N³.     

Landmarks in defense literature

Winston S. Churchill, The World Crisis 1911-1918, 4 Vols, The Unknown War, The Aftermath. Charles Scribner's Sons, New York (1923-1931) and Marlborough, His Life and Times, 6 Vols. Charles Scribner's Sons, New York (1933-1938).     

Book Reviews

National Security Concepts of States: New Zealand. By Kennedy Graham. Taylor & Francis, London (1989), ISBN 0-8448-1614-0, £27.00

Power and Prestige in the British Army. By R.G. L. von Zugbach. Gower, Aldershot (1988), ISBN 0-566-05561-9, £22.50

The American Civil War and the Origins of Modern Warfare—Ideas, Organization, and Field Command. By Edward Hagerman. Indiana University Press, Bloomington, IN (1988), ISBN 0-253-30546-2, $37.50 (£23.29)

British Seapower and Procurement between the Wars: a Reappraisal of Rearmament. By G. A. H. Gordon. Macmillan, London (1988), ISBN 0-333-42332-1. £29.50

Armies in Low-intensity Conflict: a Comparative Analysis. Edited by David A. Charters and Maurice Tugwell. Brassey's Defence Publishers, London (1989), ISBN 0-08-036253-2, £25.00 ($45.00); Deadly Paradigms: the Failure of U.S. Counterinsurgency Policy. By Michael Shafer, Leicester University Press, Leicester (1988), ISBN 0-7185-1311-8, £28.00

British Defence Policy Striking the Right Balance. By J. Baylis. Macmillan, London (1989), ISBN 0-333-49133-5, £29.50 or £9.99     

Book reviews

America's Secret Power: the CIA in a Democratic Society. By Loch K. Johnson. Oxford University Press, New York (1989), ISBN 0–19–505490–3, $24.95

The Bundeswehr and Western Security. Edited by Stephen F. Szabo. Houndmills, Basingstoke, and Macmillan, London (1990), ISBN 0–333–49880–1, £45.00

Symbolic Defense: the Cultural Significance of the Strategic Defense Initiative. By Edward Tabor Linenthal. University of Illinois Press, Chicago, IL (1989), ISBN 0–252–01619‐X, $19.95

Rethinking European Security. Edited by Furio Cerutti and Rodolfo Ragionieri. Crane Russak, New York (1990), £29.00

Alternative Conventional Defense Postures in the European Theater, Vol. 1: The Military Balance and Domestic Constraints. Edited by Hans Günter Brauch and Robert Kennedy, Crane Russak, New York (1990), £32.00

The Gulf War. Edited by Hanns Maull and Otto Pick. Pinter, London (1989), ISBN 0–86187–763–2, £36.00     

Ricochet quantification using a multiple sensor approach

This study investigates the ricochet behaviour of three different small-arms projectile types using a novel ricochet measuring device.The results can be used to estimate the danger potential of ricochets on shooting ranges.A ricochet is the change of direction and velocity of a projectile after impacting an oblique surface.This impact produces strong vibrations on a rigid plate.During this impact,flexural waves travel radially outwards from the point of impact.These waves are used to determine the properties of the impactor with accelerometers situated on the target surface.With the use of two measurement plates,one can produce a ricochet and detect the velocity at the same time.Accelerometers are suitable for accurate momentum measurements of single impacts.However,depending upon strike velocity and the impact angle,a ricochet can separate in multiple fragments after being deflected.From the operational safety perspective,these fragments need to be detected,as well.The approach of a coupled sensor concept was chosen to solve this problem.Thermographic sensors were additionally used to visualise the heat which is produced after pene-trating a rubber layer pasted in front of the steel target plate.With this approach one was able to detect the position of impact.The investigations showed that the measurement system performance is better with a multiple sensor design,which includes accelerometers for the velocity,impact strength and partly the position measurement,while the thermographic sensor was used for the position measurement and partly the momentum measurement.The investigated ammunition showed plausible fragmentation behaviour,and the results can already be used to estimate the danger potential of different ammunition types.Frangible projectiles fragment to small particles already after being deflected under a small angle.However,Full Metal Jacket projectiles with or without a steel core do not fragment under angles which are less than 5°.The objective of the paper is to demonstrate the possibility of measuring the complex ricochet me-chanics of small projectiles using standard accelerometers with the adequate signal processing approach.This measuring system is supported by an off the shelf thermographic camera.     

A decomposition algorithm applied to planning the interdiction of stochastic networks

We describe the application of a decomposition based solution method to a class of network interdiction problems. The problem of maximizing the probability of sufficient disruption of the flow of information or goods in a network whose characteristics are not certain is shown to be solved effectively by applying a scenario decomposition method developed by Riis and Schultz [Comput Optim Appl 24 (2003), 267–287]. Computational results demonstrate the effectiveness of the algorithm and design decisions that result in speed improvements. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

On the asymptotic optimality of algorithms for the flow shop problem with release dates

We consider the nonpermutation flow shop problem with release dates, with the objective of minimizing the sum of the weighted completion times on the final machine. Since the problem is NP‐hard, we focus on the analysis of the performance of several approximation algorithms, all of which are related to the classical Weighted Shortest Processing Time Among Available Jobs heuristic. In particular, we perform a probabilistic analysis and prove that two online heuristics and one offline heuristic are asymptotically optimal. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.