The two-on-one stochastic duel

The one-on-one stochastic duel is extended to the general two-on-one duel for the first time. The state equations, win probabilities, mean value, and variance functions are derived. The case where one side has Erlang (2) firing times and the other is negative exponential is compared with the corresponding “Stochastic Lanchester” and Lanchester models to demonstrate their nonequivalence.     

A note on the constrained shortest-path problem

The subject of this note is the validity of the algorithm described by Aneja and Nair to solve the constrained shortest-path problem.     

Measures of component importance for markov chain imbeddable reliability structures

In this article we study the reliability importance of the components for the wide class of Markov chain imbeddable systems (MIS). Methods for the evaluation of Birnbaum importance are developed for a general MIS, and some generating function techniques are demonstrated for the special case of homogeneous MISs. As an application, the reliability ordering for the components of a k‐out‐of‐n and consecutive‐k‐out‐of‐n structure is examined in some detail. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 613–639, 1999     

Minimization of expected variance of completion times on single machine for stochastic jobs

This article deals with the problem of scheduling jobs with random processing times on single machine in order to minimize the expected variance of job completion times. Sufficient conditions for the existence of V-shaped optimal sequences are derived separately for general and ordered job processing times. It is shown that when coefficient of variation of random processing times are bounded by a certain value, an optimal sequence is V-shaped. © 1997 John Wiley & Sons, Inc.     

Estimating negative binomial demand for retail inventory management with unobservable lost sales

The importance of effective inventory management has greatly increased for many major retailers because of more intense competition. Retail inventory management methods often use assumptions and demand distributions that were developed for application areas other than retailing. For example, it is often assumed that unmet demand is backordered and that demand is Poisson or normally distributed. In retailing, unmet demand is often lost and unobserved. Using sales data from a major retailing chain, our analysis found that the negative binomial fit significantly better than the Poisson or the normal distribution. A parameter estimation methodology that compensates for unobserved lost sales is developed for the negative binomial distribution. The method's effectiveness is demonstrated by comparing parameter estimates from the complete data set to estimates obtained by artificially truncating the data to simulate lost sales. © 1996 John Wiley & Sons, Inc.     

A fast infiltration game on n arcs

Starting from a safe base, an Infiltrator tries to reach a sensitive zone within a given time limit without being detected by a Guard. The Infiltrator can move with speed at most u, while the Guard can only perform a restricted number of searches. A discrete variant of this zero-sum game played on a graph consisting of two vertices joined by n nonintersecting arcs is investigated. Optimal strategies and an explicit expression for its value are obtained. © 1996 John Wiley & Sons, Inc.     

Killing Your Own: Confronting Desertion and Cowardice in the British Army During the Two World Wars

Military units can become to some extent self-governing in war-time battle. At times, they may take the discipline of their soldiers into their own hands and such discipline may be severe. This paper examines incidents in the British military, in both World Wars, where British soldiers were killed by their comrades because they would not fight in the heat of battle. The judicial execution by the military authorities of deserters in the First World War led to much controversy in Britain. It may be much less well-known that in both World Wars there was, on occasion, an extra-judicial practice within the British military of executing soldiers who would not fight in the heat of battle. In such situations ethical dilemmas become very difficult indeed and some of the relevant issues are examined here.     

Leaderless Global Jihadism: The Paradox of Discriminate Violence

Jihadist violence is typically associated with being particularly indiscriminate. Often, as in variations of the ‘new terrorism’ thesis, this characteristic is proposed to correspond in some way to its other attributes such as its globalised, decentralised and ‘postmodern’ religious nature. Recent work appears to give more substance to such claims, by claiming to show a relationship between indiscriminate violence and decentralised group organisation. However, in this paper we show, based on an analysis of jihadist targeting in Western Europe and America from 2001 to 2013, that targeting choices by jihadists unconnected to organised militant groups have in fact been consistently more, rather than less discriminate in their targeting choices than their better-integrated peers. Drawing on this finding, as well as a broader reading of jihadist targeting discourses, we argue for a more complex understanding of the relationship between radicalisation, extremist ideology, decentralisation, and targeting choice.