Applying Order-of-Battle to Al Qaeda Operations

Since the global war on terror began, the pursuit of Al Qaeda is widely considered as warfare and not the pursuit of criminals. In light of counter-terrorism being redefined as war, the criteria applied for tracking militaries of conventional enemies may also be applicable to Al Qaeda. Intelligence analysts have long used the nine order-of-battle (OB) criteria as part of the estimative process for conventional, or nation-state, enemies. Applying OB criteria to Al Qaeda may assist intelligence analysts in knowing the enemy and identifying changes that will allow for predictive analysis. Many elements of Al Qaeda's OB prior to the events of 11 September were viewed as clutter and not significant changes that might have otherwise alerted intelligence analysts to the impending attack. This essay suggests how one might go about applying the nine OB criteria to analysis of Al Qaeda. Although more difficult and requiring modification, using an analytical procedure that has been tested successfully over many years is a logical step in the war on Al Qaeda. If all OB changes are tracked and analyzed using a systematic approach as outlined in this essay, Al Qaeda attacks may be predicted and/or curtailed in the future.     

Algorithmic and approximation analyses of the shorter queue model

A system of two parallel queues where the arrivals from a single stream of customers join the shorter queue is considered. Arrivals form a homogeneous Poisson stream and the service times in each of the two queues are independent exponential variates. By treating one of the queues as bounded, the steady-state probability vector for the system can be expressed in a modified matrix-geometric form and can be computed efficiently. Computational procedures for the sojourn time distribution and characteristics of the departure stream are developed. Some numerical results are presented, and based on these results an efficient approximation scheme for the model is developed which can be readily extended to systems with more than two parallel queues.     

A general age replacement model with minimal repair

A general age replacement is introduced which incorporates minimal repair, planned and unplanned replacements, and costs which depend on time. Finite and infinite horizon results are obtained. Various special cases are considered. Furthermore, a shock model with general cost structure is considered.     

An integer decomposition algorithm for solving a two‐stage facility location problem with second‐stage activation costs

We study a stochastic scenario‐based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first‐stage variables in our problem are the traditional binary facility‐location variables, whereas the second‐stage variables involve a mix of binary facility‐activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second‐stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two‐stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Neighborhood search heuristics for selecting hierarchically well‐formulated subsets in polynomial regression

The importance of subset selection in multiple regression has been recognized for more than 40 years and, not surprisingly, a variety of exact and heuristic procedures have been proposed for choosing subsets of variables. In the case of polynomial regression, the subset selection problem is complicated by two issues: (1) the substantial growth in the number of candidate predictors, and (2) the desire to obtain hierarchically well‐formulated subsets that facilitate proper interpretation of the regression parameter estimates. The first of these issues creates the need for heuristic methods that can provide solutions in reasonable computation time; whereas the second requires innovative neighborhood search approaches that accommodate the hierarchical constraints. We developed tabu search and variable neighborhood search heuristics for subset selection in polynomial regression. These heuristics are applied to a classic data set from the literature and, subsequently, evaluated in a simulation study using synthetic data sets. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

The Randomization of Terrorist Attacks

The purpose of this article is to explore the economic theoretical foundations of the idea that rational terrorist organizations deliberately randomize their attacks (by type, timing, location, and targets) to generate uncertainty and intimidation. A choice theoretic framework is applied to the analysis of the terrorist organization's behavior to determine whether welfare (utility) gains from the randomization of terrorist attacks are plausible and feasible. The randomization of attacks can appear to promise higher amounts of political influence for each resource input but it turns out that randomization cannot manufacture a situation where higher amounts of political influence are obtained for each resource input.The results imply that, rather than randomization and instability, the rational terrorist organization is more likely to prefer stability. The findings and implications provide a theoretical explanation for the non-randomness of terrorist attacks.Thismay be one small step towards explaining the patterns – non-randomness – in the time-series of terrorist incidents.     

Estimates of circular error probabilities

The general problem we are concerned with here is the estimation of P_θ(C) where C is some fixed event and P_θ is unknown in some class. The various available estimation procedures seem to involve the choice of some random probability measure. In particular we consider this problem when C is a disk in R² centered at o and P_θ is restricted to be bivariate normal. Details concerning the implementation of the estimation procedures and a Monte Carlo study are discussed for this case. This particular problem arises when we are concerned with assessing the accuracy of a targeting procedure.     

Robustness of preallocated preferential defense with assumed attack size and perfect attacking and defending weapons

The problem is to protect a set of t targets by n perfect interceptors against an attack by m perfect weapons. If the defender solves for an optimal preallocated preferential defense and associated game value assuming m₁ attackers, and the attacker knows the assumption of the defender and utilizes m₂ attackers, he may be able to achieve significantly more damage than had the defender assumed that there would be m₂ attackers. The article treats the robustness of preallocated preferential defense to assumptions about the size of the attack and presents results of an alternative approach.     

A dual criteria sequencing problem with earliness and tardiness penalties

We consider the problem of sequencing n jobs on a single machine, with each job having a processing time and a common due date. The common due date is assumed to be so large that all jobs can complete by the due date. It is known that there is an O(n log n)‐time algorithm for finding a schedule with minimum total earliness and tardiness. In this article, we consider finding a schedule with dual criteria. The primary goal is to minimize the total earliness and tardiness. The secondary goals are to minimize: (1) the maximum earliness and tardiness; (2) the sum of the maximum of the squares of earliness and tardiness; (3) the sum of the squares of earliness and tardiness. For the first two criteria, we show that the problems are NP‐hard and we give a fully polynomial time approximation scheme for both of them. For the last two criteria, we show that the ratio of the worst schedule versus the best schedule is no more than . © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 422–431, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10020