Vector processing approach to constrained network problems

Modification of algorithms designed for scalar computing, to take advantage of vector processing, raises several challenges. This article presents the vectorization of the primal simplex based network algorithm and results in a 50% improvement in computational time. One of the major contributors to this improvement is the matching of the size of the pricing candidate list to the vector register size. The side constraints are relaxed into a single surrogate constraint. The single constraint network algorithm is vectorized and used as the basis for solving large-scale constrained network problems. Computational experiments are presented which illustrate the vectorization of the network code as well as the ability of the surrogate constraint approach to deal with large constrained network problems.     

Estimating a survival curve when new is better than used with respect to a distinguished set

Hollander, Park, and Proschan define a survival function S of a positive random variable X to be new better than used at age t₀ (NBU-{t₀}) if S satisfies $ \begin{array}{*{20}c} {\frac{{S(x + t_0)}}{{S\left({t_0} \right)}} \le S\left(x \right),} & {{\rm for}\,{\rm all}\,x\, \ge \,0,} \\ \end{array}$ where S(x) = P(X > x). The NBU-{t₀} class is a special case of the NBU-A family of survival distributions, where A is a subset of [0, ∞). These families introduce a variety of modeling possibilities for use in reliability studies. We treat problems of nonparametric estimation of survival functions from these classes by estimators which are themselves members of the classes of interest. For a number of such classes, a recursive estimation technique is shown to produce closed-form estimators which are strongly consistent and converge to the true survival distribution at optimal rates. For other classes, additional assumptions are required to guarantee the consistency of recursive estimators. As an example of the latter case, we demonstrate the consistency of a recursive estimator for S ∈ NBU-[t₀, ∞) based on lifetime data from items surviving a preliminary “burn-in” test. The relative precision of the empirical survival curve and several recursive estimators of S are investigated via simulation; the results provide support for the claim that recursive estimators are superior to the empirical survival curve in restricted nonparametric estimation problems of the type studied here.     

Allocating capacity in parallel queues to improve their resilience to deliberate attack

We develop models that lend insight into how to design systems that enjoy economies of scale in their operating costs, when those systems will subsequently face disruptions from accidents, acts of nature, or an intentional attack from a well‐informed attacker. The systems are modeled as parallel M/M/1 queues, and the key question is how to allocate service capacity among the queues to make the system resilient to worst‐case disruptions. We formulate this problem as a three‐level sequential game of perfect information between a defender and a hypothetical attacker. The optimal allocation of service capacity to queues depends on the type of attack one is facing. We distinguish between deterministic incremental attacks, where some, but not all, of the capacity of each attacked queue is knocked out, and zero‐one random‐outcome (ZORO) attacks, where the outcome is random and either all capacity at an attacked queue is knocked out or none is. There are differences in the way one should design systems in the face of incremental or ZORO attacks. For incremental attacks it is best to concentrate capacity. For ZORO attacks the optimal allocation is more complex, typically, but not always, involving spreading the service capacity out somewhat among the servers. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

A note on the optimality conditions for the bilevel programming problem

A counterexample is given to demonstrate that previously proposed necessary conditions for the bilevel programming problem are not correct. An interpretation of the difficulty is given by appealing to a “theorem of alternative” result presented in the original work.     

The optimal linear combination of control variates in the presence of asymptotically negligible bias

The optimal linear combination of control variates is well known when the controls are assumed to be unbiased. We derive here the optimal linear combination of controls in the situation where asymptotically negligible bias is present. The small-sample linear control which minimizes the mean square error (MSE) is derived. When the optimal asymptotic linear control is used rather than the optimal small-sample control, the degradation in MSE is c/n³, where n is the sample size and c is a known constant. This analysis is particulary relevant to the small-sample theory for control variates as applied to the steady-state estimation problem. Results for the method of multiple estimates are also given.     

A genetic algorithm methodology for complex scheduling problems

This paper considers the scheduling problem to minimize total tardiness given multiple machines, ready times, sequence dependent setups, machine downtime and scarce tools. We develop a genetic algorithm based on random keys representation, elitist reproduction, Bernoulli crossover and immigration type mutation. Convergence of the algorithm is proved. We present computational results on data sets from the auto industry. To demonstrate robustness of the approach, problems from the literature of different structure are solved by essentially the same algorithm. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 199–211, 1999     

Exploring the subsidiarity principle in policing and the operations of the Nigeria Police Force

The provisions of the 1999 Constitution, which recognises the existence of a single police force and forbids parallel police organisations, have oftentimes generated controversies among actors in the Nigerian federal polity. Rising insecurity precipitates lingering questions on the utility and adequacy of a single, highly centralised and centrally controlled police force given Nigeria’s geographic vastness and demographic diversity. Conversely, arguments have also dwelt on the dangers of fragmentation considering Nigeria’s psychosocial, economic and political nature. This article attempts to balance these arguments by analysing policing and the operations of the Nigeria Police Force (NPF) through the lens of the subsidiarity principle. Subsidiarity is a governance principle in federations, captured in the founding documents of the European Union (EU), which prescribes that governmental powers, authorities and duties should be held by the tier that can best perform them equitably, efficiently, effectively, suitably and based on interest and need. Drawing largely on interviews with purposively selected police scholars, political actors, civil society organisations and police personnel, the paper contends that this principle offers a pragmatic solution to the perennial problems of intergovernmental frictions on the use of the police within the context of governance in the Nigerian federation.     

Violence in context: Mapping the strategies and operational art of irregular warfare

The malaise that the United States, and the West, have experienced in recent campaigns stems in large part from unclear thinking about war, its political essence, and the strategies needed to join the two. Instead, analysis and response are predicated on entrenched theoretical concepts with limited practical utility. The inadequacy of understanding has spawned new, and not so new, terms to capture unanticipated trends, starting with the re-discovery of “insurgency” and “counterinsurgency” and leading to discussion of “hybrid threats” and “gray-zone” operations. New terminology can help, but the change must go deeper. Challenging analytical orthodoxy, this article sets out a unifying approach for the study of political violence, or more accurately: violent politics. It provides a conceptual foundation that helps to make sense of recent shifts in warfare. In effect, it offers sorely needed theoretical insights into the nature of strategy and guides the process of responding to nontraditional threats.