Optimal sequential replenishment of ships during combat

A carrier battle group is operating in an area where it is subject to attack by enemy aircraft. It is anticipated that air raids will occur in large waves. The uncertain time between raids is available for the replenishment of supplies. We consider the problem of how best to schedule ammunition replenishment during this period. The theory of Gittins indices provides the technical background to the development of a range of models which yield a hierarchy of index-based heuristics for replenishment. One such heuristic is assessed computationally in a more realistic scenario than is explicitly allowed for by the models.     

Lanchester attrition of interpenetrating forces

To approximate the solutions of detailed simulations of interpenetrating forces (or possibly to assist in curtailing Monte Carlo calculations), this article provides solutions to a simple problem assuming that the speed of advance is constant; the only interactions are local; Lanchester's linear or square law applies; force distributions are continuous if not initially uniform in depth. The resultant partial differential equations are solvable (1) in closed form if attrition is minimal or (2) with pain when attrition is sufficient to annihilate the leading edge of a force. This is exemplified only for the square law, where one must solve an integrodifferential equation for an ancillary function. A general solution is given for either law, and for the latter case a more complete one, assuming that initial force distributions are uniform. Useful properties of an unusual class of Bessel functions needed for this analysis are given in an appendix. Copies of computer programs are available.     

Diffusion approximation to the G/G/R machine repair problem with warm standby spares

The G/G/R machine repair problem with M operating machines, S warm standby spares, and R repairmen is studied as a diffusion process. The steady-state equations are formulated as diffusion equations subject to two reflecting barriers. The approximate diffusion parameters of the diffusion equations are obtained (1) under the assumption that the input characteristics of the problem are defined only by their first two moments rather than their probability distribution function, (2) under the assumption of heavy traffic approximation, that is, when queues of failed machines in the repair stage are almost always nonempty, and (3) using well-known asymptotic results from renewal theory. Expressions for the probability density functions of the number of failed machines in the system are obtained. A study of the derived approximate results, compared to some of the exact results, suggests that the diffusion approach provides a useful method for solving complex machine-repair problems.     

Modelling international conflict under conditions of state level economic and political uncertainty

Formal models of international conflict have tended to concentrate on change across the security dimension, assuming that the state level economic and political dimensions are constant. However, the conclusion of the Cold War suggests that over the long run these dimensions are not constant; indeed, the development of economic power, state level limits on defence expenditures, structural impediments to economic change, and several other ‘constants’ clearly do have an endogenous role in international conflict. This paper suggests one strategy for their inclusion as a causal factor in conflict modelling.     

Country Survey I–Military Spending in India 1

After a brief survey of the Indian economy, we survey the supply and demand of military expenditures in India over the last four decades. The causes of military expenditures appear to include regional rivalries and protracted conflicts, but it has proven difficult to delineate these with empirical models. The effects of military spending in India on economic growth appear to be benign, despite much speculation to the contrary. However, the opportunity costs of defence spending are shown to be considerable. We conclude with speculation about the role of debt and debt servicing in retarding future economic growth in India. We also speculate about the potential for the creation of a war economy in India.     

CONTRIBUTORS

Conventional wisdom states that the stability-instability paradox does not explain the effect of nuclear proliferation on the conflict propensity of South Asia, and that nuclear weapons have had a different and more dangerous impact in South Asia than Cold War Europe. I argue that the paradox explains nuclear South Asia; that the similarities between nuclear South Asia and Cold War Europe are strong; and that conventional instability does not cause revisionist challenges in the long run. I develop and probe a psychological causal mechanism that explains the impact of nuclear weapons on Cold War Europe and South Asia. Following the ten-month mobilized crisis in 2002, Pakistani President Pervez Musharraf may have adopted a more moderate foreign policy toward India after experiencing fear of imminent nuclear war, as Soviet Premier Nikita Khrushchev did forty years earlier. I argue that the stability-instability paradox explains Cold War Europe and nuclear South Asia and will, conditional on Iranian and North Korean revisionism, predict the impact of nuclear weapon development on these states' conflict propensities.     

Progress payments and cost overruns in defence contracts

In recent years military procurement agencies have used “progress payments” in contracting. Although, overall, the adoption of such a policy may well have contributed to a decrease in total costs of procurement, we identify a class of inefficiencies that are likely to have been generated by it.     

Estimated UK employment dependent on ministry of defence expenditure and defence exports

The Ministry of Defence (MOD) has published estimates of the number of average full‐time UK industry employees dependent on MOD expenditure and defence exports for a number of years. This paper provides the outcome of a recent review of the process used. The method of deriving MOD and defence export final demand vectors, and calculating from these estimates of direct employment (i.e. that in supplying companies) and indirect employment (i.e. that incurred through the supply chain) are described. Difficulties with the data are explored. Alternative approaches, methods used in other countries and challenges posed by changing MOD administrative systems are briefly discussed.     

Statistical equivalency and optimality of simple step‐stress accelerated test plans for the exponential distribution

Accelerated life testing (ALT) is commonly used to obtain reliability information about a product in a timely manner. Several stress loading designs have been proposed and recent research interests have emerged concerning the development of equivalent ALT plans. Step‐stress ALT (SSALT) is one of the most commonly used stress loadings because it usually shortens the test duration and reduces the number of required test units. This article considers two fundamental questions when designing a SSALT and provides formal proofs in answer to each. Namely: (1) can a simple SSALT be designed so that it is equivalent to other stress loading designs? (2) when optimizing a multilevel SSALT, does it degenerate to a simple SSALT plan? The answers to both queries, under certain reasonable model assumptions, are shown to be a qualified YES. In addition, we provide an argument to support the rationale of a common practice in designing a SSALT, that is, setting the higher stress level as high as possible in a SSALT plan. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013