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.     

Radar pulse interleaving for multi‐target tracking

In a multifunction radar, the maximum number of targets that can be managed or tracked is an important performance measure. Interleaving algorithms developed to operate radars exploit the dead‐times between the transmitted and the received pulses to allocate new tracking tasks that might involve transmitting or receiving pulses, thus increasing the capacity of the system. The problem of interleaving N targets involves a search among N! possibilities, and suboptimal solutions are usually employed to satisfy the real‐time constraints of the radar system. In this paper, we present new tight 0–1 integer programming models for the radar pulse interleaving problem and develop effective solution methods based on Lagrangian relaxation techniques. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

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     

Partial input to output impacts in DEA: Production considerations and resource sharing among business subunits

Data envelopment analysis (DEA) is a methodology for evaluating the relative efficiencies of peer decision‐making units (DMUs), in a multiple input/output setting. Although it is generally assumed that all outputs are impacted by all inputs, there are many situations where this may not be the case. This article extends the conventional DEA methodology to allow for the measurement of technical efficiency in situations where only partial input‐to‐output impacts exist. The new methodology involves viewing the DMU as a business unit, consisting of a set of mutually exclusive subunits, each of which can be treated in the conventional DEA sense. A further consideration involves the imposition of constraints in the form of assurance regions (AR) on pairs of multipliers. These AR constraints often arise at the level of the subunit, and as a result, there can be multiple and often inconsistent AR constraints on any given variable pair. We present a methodology for resolving such inconsistencies. To demonstrate the overall methodology, we apply it to the problem of evaluating the efficiencies of a set of steel fabrication plants. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

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.     

Outbound supply chain network design with mode selection and lead time considerations

We present a large‐scale network design model for the outbound supply chain of an automotive company that considers transportation mode selection (road vs. rail) and explicitly models the relationship between lead times and the volume of flow through the nodes of the network. We formulate the problem as a nonlinear zero‐one integer program, reformulate it to obtain a linear integer model, and develop a Lagrangian heuristic for its solution that gives near‐optimal results in reasonable time. We also present scenario analyses that examine the behavior of the supply chain under different parameter settings and the performance of the solution procedures under different experimental conditions. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007