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.     

Test for the extreme value and weibull distributions based on normalized spacings

Discussed in this article are tests for the extreme-value distribution, or, equivalently, for the two-parameter Weibull distribution when parameters are unknown and the sample may be censored. The three tests investigated are based on the median, the mean, and the Anderson-Darling A² statistic calculated from a set zⁱ of values derived from the spacings of the sample. The median and the mean have previously been discussed by Mann, Scheuer, and Fertig [10] and by Tiku and Singh [14]. Asymptotic distributions and points are given for the test statistics, based on recently developed theory, and power studies are conducted to compare them with each other and with two other statistics suitable for the test. Of the normalized spacings tests, A² is recommended overall; the mean also gives good power in many situations, but can be nonconsistent.     

Optimal replacement for fault-tolerant systems

We consider the optimal replacement problem for a fault tolerant system comprised of N components. The components are distingushable, and the state of the system is given by knowing exactly which components are operationl and which have failed. The individual component failure rates depend on the state of the entire system. We assume that the rate at which the system produces income decreases as the system deteriorates and the system replacement cost rises. Individual components cannot be replaced. We give a greedy-type algorithm that produces the replacement policy that maximizes the long-run net system income per unit time.     

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′.     

Book reviews

Die Faszination des Verrats: Eine Studie zur Dekadenz im Ost‐West Konflikt. By Thomas Noetzel. Hamburg, Junius (1989) DM48.

Les Nations Armées. By Maurice Faivre (Preface by Pierre Messmer), Paris FEDN/Economica (1988).

Insurgency and Terrorism: Inside Modern Revolutionary Warfare. By Bard E. O'Neill, Brassey's (US), Washington, DC (1990), $19.00.

LIC 2010: Special Operations and Unconventional Warfare in the Next Century. By Rod Paschall, Brassey's (US), Washington, DC, $24.00.

Air Power and Colonial Conflict: The Royal Air Force 1919–1939. By D. E. Omissi, Manchester University Press, Manchester and New York (1990), ISBN 0–7190–2960–0. £35.00.

Key to the Sinai: The Battles for Abu Ageila in the 1956 and 1967 Arab‐Israeli Wars. By George W. Gawrych. Combat Studies Institute Research Survey No. 7, US Army Command and General Staff College, Fort Leavenworth, Kansas, 1990. $8.00.

Arms Export Regulations. Edited by Ian Anthony. SIPRI/Oxford University Press, Oxford (1991), ISBN 0–19–829158–2, £25.00.     

Armed services recruiting research: Issues,findings, and needs

Manning the nation's armed services will continue to be a crucial issue for the remainder of the 1980s. With the projected growth of the services during this decade, the downturn in the 17–21-year-old male population, and the possible upturn in the economy, the ability of the services to meet their respective quality and quantity recruiting goals becomes of central concern. The accurate estimation of the supply for various types of recruits becomes especially important when one views the nearly $1 billion budgeted annually for recruiting and the impact that any military pay raises can have on the DOD's manpower costs of over $40 billion annually. In addition, perceived difficulties in recruiting can impact on weapon systems design decisions, authorized manning levels, and exacerbate the debate concerning the draft; hence, it is clear that few issues today warrant more attention than improving the efficiency and effectiveness of military recruiting. This article provides an introduction and review of some of the key issues involved in modeling and estimating the supply of military recruits. It summarizes and compares the findings of selected econometric models, all of which are based on enlistment experience since the introduction of the All-Volunteer Force in 1973. It also presents some new insights and directions for research dealing with simultaneity, validation, generation of rigorous confidence intervals, and data base selection. It concludes by listing some of the research needs to be addressed in the future.     

A method for reducing coefficients in integer linear inequalities

Approaches are considered for the reduction of coefficients in linear integer inequalities. It is shown that coefficients may be reduced easily in many practical examples. The (0-1) problem is also reconsidered and certain areas of exploration developed.     

An advanced dual algorithm with constraint relaxation for all-integer programming

In this article we present an all-integer cutting plane algorithm called the Reduced Advanced Start Algorithm (RASA). The technique incorporates an infeasible advanced start based on the optimal solution to the LP relaxation, and initially discards nonbinding constraints in this solution. We discuss the results of computational testing on a set of standard problems and illustrate the operation of the algorithm with three small examples.