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.     

On labeling the vertices of products of complete graphs with distance constraints

Variations of Hale's channel assignment problem, the L(j, k)‐labeling problem and the radio labeling problem require the assignment of integers to the vertices of a graph G subject to various distance constraints. The λ_j,k‐number of G and the radio number of G are respectively the minimum span among all L(j, k)‐labelings, and the minimum span plus 1 of all radio labelings of G (defined in the Introduction). In this paper, we establish the λ_j,k‐number of ∏ K for pairwise relatively prime integers t₁ < t₂ < … < t_q, t₁ ≥ 2. We also show the existence of an infinite class of graphs G with radio number |V(G)| for any diameter d(G). © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Terrorist choice: a stochastic dominance and prospect theory analysis

The paper explores terrorist choice by applying two well-known theoretical frameworks: stochastic dominance and prospect theory (PT). We analyse each pair of attack methods that can be formed from the RAND-MIPT database and the Global Terrorism Database. Instances of stochastic dominance are identified. PT orderings are computed. Attention is accorded to the identification of ‘trigger points’ and the circumstances that may lead to an increased likelihood that a terrorist will select an attack method associated with a higher expected number of fatalities, i.e. a potentially more damaging attack method.     

Military Expenditure,Economic Growth and Heterogeneity

This paper examines the impact of military expenditure on economic growth on a large balanced panel, using an exogenous growth model and dynamic panel data methods for 106 countries over the period 1988–2010. A major focus of the paper is to consider the possibility group heterogeneity and non-linearity. Having estimated the model for all of the countries in the panel and finding that military burden has a negative effect on growth in the short and long run, the panel is broken down into various groupings based upon a range of potentially relevant factors, and the robustness of the results is evaluated. The factors considered are different levels of income, conflict experience, natural resources abundance, openness and aid. The estimates for the different groups are remarkably consistent with those for the whole panel, providing strong support for the argument that military spending has adverse effects on growth. There are, however, some intriguing results that suggest that for certain types of countries military spending has no significant effect on growth.