The Somali National Army: an assessment

To engage properly with the Somali National Army, to understand it in the hope of improving stability and the lives of over 12 million Somalis, good basic information on its composition and characteristics is necessary. Authoritative accounts on the subject have been scarce for over 25 years. This account seeks to detail the army’s dispositions across southern Somalia, and, more importantly, the brigades’ clan compositions and linkages. Clan ties supersede loyalties to the central government. The army as it stands is a collection of former militias which suffer from ill-discipline and commit crime along with greater atrocities. Estimates of numbers are unreliable, but there might be 13,000 or more fighters in six brigades in the Mogadishu area and five beyond.     

An assumption-free convergence analysis for a perturbation of the scaling algorithm for linear programs,with application to the L1 estimation problem

This article is concerned with the scaling variant of Karmarkar's algorithm for linear programming problems. Several researchers have presented convergence analyses for this algorithm under various nondegeneracy types of assumptions, or under assumptions regarding the nature of the sequence of iterates generated by the algorithm. By employing a slight perturbation of the algorithm, which is computationally imperceptible, we are able to prove without using any special assumptions that the algorithm converges finitely to an ε-optimal solution for any chosen ε > 0, from which it can be (polynomically) rounded to an optimum, for ε > 0 small enough. The logarithmic barrier function is used as a construct for this analysis. A rounding scheme which produces an optimal extreme point solution is also suggested. Besides the non-negatively constrained case, we also present a convergence analysis for the case of bounded variables. An application in statistics to the L₁ estimation problem and related computational results are presented.     

A flow-shop problem with sequence-dependent additive setup times

The flow-shop scheduling problem with sequence-dependent additive setup times is considered as a special case of the general problem, and a polynomially bounded approximate method is developed to find a minimum makespan permutation schedule. The approximate algorithm is shown to yield optimal results for the two-machine case. A version of Sule's model is defined that produces the first approximation of the optimal solution for this problem. Computational experience along with numerical examples are provided to test the effectiveness of the method.     

Extension of Bolzano search to rectangles which preserves rectangles as iterates

Multivariable elimination algorithms, which may be regarded as generalizations of various one-dimensional search procedures, have not found wide application. A probable reason may be the generally very irregularly shaped regions of uncertainty that evolve iteratively in the procedures. Hence hope for practical salvage of this class of algorithms seems to lie in controlling the shape of the successively smaller regions of uncertainty. In this article an extension of Bolzano search to rectangles which preserves rectangular iterates is given. Since the result is essentially geometrical in nature, a geometric proof of this procedure is given. Hopefully the proof procedure will be of independent interest. A numerical illustration of the procedure is given for a game problem, such problems lending themselves to this method.     

Suppression of enemy air defenses (SEAD) as an information duel

Blue strike aircraft enter region ? to attack Red targets. In Case 1, Blue conducts (preplanned) SEAD to establish air superiority. In the (reactive) SEAD scenario, which is Case 2, such superiority is already in place, but is jeopardized by prohibitive interference from Red, which threatens Blue's ability to conduct missions. We utilize both deterministic and stochastic models to explore optimal tactics for Red in such engagements. Policies are developed which will guide both Red's determination of the modes of operation of his engagement radar, and his choice of Blue opponent to target next. An index in the form of a simple transaction kill ratio plays a major role throughout. Published 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 723–742, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10046     

A model for step‐stress accelerated life testing

Modern technology is producing high reliability products. Life testing for such products under normal use condition takes a lot of time to obtain a reasonable number of failures. In this situation a step‐stress procedure is preferred for accelerated life testing. In this paper we assume a Weibull and Lognormal model whose scale parameter depends upon the present level as well as the age at the entry in the present stress level. On the basis of that we propose a parametric model to the life distribution for step‐stress testing and suggest a suitable design to estimate the parameters involved in the model. A simulation study has been done by the proposed model based on maximum likelihood estimation. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Bounding methods for facilities location algorithms

Single- and multi-facility location problems are often solved with iterative computational procedures. Although these procedures have proven to converage, in practice it is desirable to be able to compute a lower bound on the objective function at each iteration. This enables the user to stop the iterative process when the objective function is within a prespecified tolerance of the optimum value. In this article we generalize a new bounding method to include multi-facility problems with l_p distances. A proof is given that for Euclidean distance problems the new bounding procedure is superior to two other known methods. Numerical results are given for the three methods.     

Estimating the accuracy of the coverages of outer β-content tolerance intervals,which control both tails of the normal distribution

Tolerance limits which control both tails of the normal distribution so that there is no more than a proportion β₁ in one tail and no more than β₂ in the other tail with probability γ may be computed for any size sample. They are computed from X? - k₁S and X? - k₂S, where X? and S are the usual sample mean and standard deviation and k₁ and k₂ are constants previously tabulated in Odeh and Owen [3]. The question addressed is, “Just how accurate are the coverages of these intervals (– Infin;, X? – k₁S) and (X? + k₂S, ∞) for various size samples?” The question is answered in terms of how widely the coverage of each tail interval differs from the corresponding required content with a given confidence γ′.