Estimating the common location parameter of exponential distributions with censored samples

Consider the problem of estimating the common location parameter of two exponential distributions when censored samples are taken. The unique minimum variance unbiased estimator (UMVUE) is found along with an expression for its variance. The asymptotic distribution is given for a special case and a generalized Bayes property is exhibited. Extensions include the case of k > 2 populations. Also the UMVUE is found for P(Y > X) and certain reliability functions.     

Optimal policies for a multi-product inventory system with negotiable lead times

The objective of this paper is to determine the optimum inventory policy for a multi-product periodic review dynamic inventory system. At the beginning of each period two decisions are made for each product. How much to “normal order” with a lead time of λ_n periods and how much to “emergency order” with a lead time of λ_e periods, where λe = λ_n - 1. It is assumed that the emergency ordering costs are higher than the normal ordering costs. The demands for each product in successive periods are assumed to form a sequence of independent identically distributed random variables with known densities. Demands for individual products within a period are assumed to be non-negative, but they need not be independent. Whenever demand exceeds inventory their difference is backlogged rather than lost. The ordering decisions are based on certain costs and two revenue functions. Namely, the procurement costs which are assumed to be linear for both methods of ordering, convex holding and penalty costs, concave salvage gain functions, and linear credit functions. There is a restriction on the total amount that can be emergency ordered for all products. The optimal ordering policy is determined for the one and N-period models.     

East versus West in the defeat of Nazi Germany

One of the most commonly expressed opinions about victory in the Second World War is that the Soviet Union was mostly responsible for beating Nazi Germany. Supposedly the great land war fought between these two powers in the East was the decisive front in Europe. The West's contribution to German defeat, on the other hand, is often seen as somewhat marginal. The Anglo‐American strategic bombing campaign in 1943 paid few dividends and it was not until after the Normandy landings in June 1944 that the West really began to divert a large amount of German resources.

The purpose of this article is to challenge some of these basic notions. Through analysing what Germany produced, where it was sent and how it was destroyed, the West's contribution to defeating Germany moves from an ancillary position to a dominant one. Taking German war production as a whole, from 1943 onwards the West was responsible for tying down and destroying a significantly larger share than the Soviet Union.     

Optimal defence structure for a small country

Small countries may not be able to afford all force elements (army, navy, air-force) operated by larger countries and certainly cannot afford all sub-elements (aircraft carriers, submarines, etc). This paper provides a framework for a small country to analyse its force structure, examining the influence of objectives, international co-operation, funding and technological constraints, and uncertainty. We analyse when a small country may choose to retain a balanced structure (with each force element) and when it may choose to drop one or more elements. The issues are illustrated with the decision by the New Zealand government over whether to retain a strike aircraft capacity.     

Lanchester for cyber: The mixed epidemic‐combat model

Future conflict between armed forces will occur both in the physical domain as well as the information domain. The linkage of these domains is not yet fully understood. We study the dynamics of a force subject to kinetic effects as well as a specific network effect–spreading malware. In the course of our study, we unify two well‐studied models: the Lanchester model of armed conflict and deterministic models of epidemiology. We develop basic results, including a rule for determining when explicit modeling of network propagation is required. We then generalize the model to a force subdivided by both physical and network topology, and demonstrate the specific case where the force is divided between front‐ and rear‐echelons. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Moving Beyond Population-Centric vs. Enemy-Centric Counterinsurgency

Historically, insurgency is one of the most prevalent forms of armed conflict and it is likely to remain common in the foreseeable future. Recent experiences with counterinsurgency in Iraq and Afghanistan offer many lessons for future counterinsurgents, but the discourse on the subject continues to be mired in a traditional dichotomy pitting population-centric approaches to counterinsurgency against enemy-centric approaches. Historical analysis suggests that this traditional dichotomy is not a sufficiently nuanced way to understand or plan for such operations. Instead, discussions of counterinsurgency should focus on two dimensions: actions (use of physical force vs. political or moral actions) and targets (active insurgents vs. insurgent support). This perspective divides the space of possible counterinsurgency efforts into four quadrants, suggesting that effective counterinsurgency campaigns find a balance of effort across the four quadrants that is well matched to the specific context.     

Transient solution of a finite-capacity M/Ga,b/1 queueing system

In this article we consider a single-server, bulk-service queueing system in which the waiting room is of finite capacity. Arrival process is Poisson and all the arrivals taking place when the waiting room is full are lost. The service times are generally distributed independent random variables and the distribution is depending on the batch size being served. Using renewal theory, we derive the time-dependent solution for the system-size probabilities at arbitrary time points. Also we give expressions for the distribution of virtual waiting time in the queue at any time t.     

Quadratic bottleneck problems

We study the quadratic bottleneck problem (QBP) which generalizes several well‐studied optimization problems. A weak duality theorem is introduced along with a general purpose algorithm to solve QBP. An example is given which illustrates duality gap in the weak duality theorem. It is shown that the special case of QBP where feasible solutions are subsets of a finite set having the same cardinality is NP‐hard. Likewise the quadratic bottleneck spanning tree problem (QBST) is shown to be NP‐hard on a bipartite graph even if the cost function takes 0–1 values only. Two lower bounds for QBST are derived and compared. Efficient heuristic algorithms are presented for QBST along with computational results. When the cost function is decomposable, we show that QBP is solvable in polynomial time whenever an associated linear bottleneck problem can be solved in polynomial time. As a consequence, QBP with feasible solutions form spanning trees, s‐t paths, matchings, etc., of a graph are solvable in polynomial time with a decomposable cost function. We also show that QBP can be formulated as a quadratic minsum problem and establish some asymptotic results. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Geopolitics over Proliferation: the Origins of US Grand Strategy and Their Implications for the Spread of Nuclear Weapons in South Asia

How much does the United States care about nonproliferation? Recent scholarship suggests that the fear of spreading nuclear weapons was central to the US grand strategy in the Cold War. In one important case, however, this argument does not hold. This article draws on theoretical debates and newly declassified archives to demonstrate the primacy of geopolitics over nonproliferation in Washington’s policy toward India and Pakistan. Despite their rhetoric, Democratic and Republican leaders consistently relegated nonproliferation to the backburner whenever it conflicted with other strategic goals. Moreover, they inadvertently encouraged proliferation in South Asia at three inter-connected levels: technology, security, and identity.     

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.