Rectilinear m-Center problem

In this article we consider the unweighted m-center problem with rectilinear distance. We preent an O(n^m–2 log n) algorithm for the m-center problem where m ≥ 4.     

Book reviews

Encyclopaedia of Modern Air Force Squadrons. By Chris Ashworth. Patrick Stephens, London (1989), ISBN 1-8526-013-6, £19.95

The Future of Sea Power. By Eric Grove. Routledge, London (1990), ISBN 0-415-00482-9, £35.00

Soviet Strategic Interests in the North. By Kirsten Amundsen. Pinter, London (1990), ISBN 0-86187-018-2, £30.00

Soviet Seapower in Northern Waters. Edited by John Skogan and Arne Brundtland. Pinter, London (1990), ISBN 0-86187-038-7, £35.00

Glasnost, Perestroika, and U.S. Defense Spending. By William W. Kaufmann, Brookings Institution, Washington, DC (1990), ISBN 0-8157-4881-7, $8.95

The Educating of Armies. Edited by Michael D. Stephens. Macmillan, London (1989), ISBN 0-333-43447-1, £35.00     

Book Reviews

Strategic Geography. By Hugh Faringdon. Routledge, London (1989), ISBN 0-415-00980-4, £40.00

Field Artillery and Firepower. By J. B. A. Bailey. The Military Press, Oxford (1989), ISBN 0-85066-810-7, £25.00 (hardback), ISBN 0-85066-811-5, £14.50 (paperback)

U.S.-Soviet Security Cooperation. Edited by Alexander L. George, Philip J. Farley and Alexander Dallin. Oxford University Press, New York (1988), ISBN 0-19-505397-4, £30.00 (hardback), $19.95 (paperback)

Non-production by Industry of Chemical-warfare Agents: Technical Verification under a Chemical Weapons Convention. Edited by S. J. Lundin. SIPRI/Oxford University Press, Oxford (1988), ISBN 0-19-829129-9, £19.50

Ireland's Terrorist Trauma: Interdisciplinary Perspectives. Edited by Alan O'Day and Yonah Alexander. Harvester Wheatsheaf, Hemel Hempstead (1989), ISBN 7450-049003, £27.50 ($48.65)

Pilots and Rebels: the Use of Aircraft in Unconventional Warfare 1918-1988. By P. A. Towle. Brassey's (UK), London (1989), ISBN 0-08-036712-7, £29.95 ($53.95)     

A primal-dual cutting-plane algorithm for all-integer programming

The integer programming literature contains many algorithms for solving all-integer programming problems but, in general, existing algorithms are less than satisfactory even in solving problems of modest size. In this paper we present a new technique for solving the all-integer, integer programming problem. This algorithm is a hybrid (i.e., primal-dual) cutting-plane method which alternates between a primal-feasible stage related to Young's simplified primal algorithm, and a dual-infeasible stage related to Gomory's dual all-integer algorithm. We present the results of computational testing.     

A heterogeneous arrival and service queueing loss model

Consider a single-server exponential queueing loss system in which the arrival and service rates alternate between the paris (γ₁, γ₁), and (γ₂, μ₂), spending an exponential amount of time with rate cμ_i in (γ_i, μ_i), i = 1.2. It is shown that if all arrivals finding the server busy are lost, then the percentage of arrivals lost is a decreasing function of c. This is in line with a general conjecture of Ross to the effect that the “more nonstationary” a Poisson arrival process is, the greater the average customer delay (in infinite capacity models) or the greater the precentage of lost customers (in finite capacity models). We also study the limiting cases when c approaches 0 or infinity.     

Determining confidence bounds for highly reliable coherent systems based on a paucity of component failures

A computationally simple method for obtaining confidence bounds for highly reliable coherent systems, based on component tests which experience few or no failures, is given. Binomial and Type I censored exponential failure data are considered. Here unknown component unreliabilities are ordered by weighting factors, which are firstly presumed known then sensitivity of the confidence bounds to these assumed weights is examined and shown to be low.     

AN ALGORITHM FOR THE SEGREGATED STORAGE PROBLEM

The segregated storage problem involves the optimal distribution of products among compartments with the restriction that only one product may be stored in each compartment. The storage capacity of each compartment, the storage demand for each product, and the linear cost of storing one unit of a product in a given compartment are specified. The problem is reformulated as a large set-packing problem, and a column generation scheme is devised to solve the associated linear programming problem. In case of fractional solutions, a branch and bound procedure is utilized. Computational results are presented.     

Optimal replacement under additive damage and other failure models

A machine or production system is subject to random failure. Upon failure the system is replaced by a new one, and the process repeats. A cost is associated with each replacement, and an additional cost is incurred at each failure in service. Thus, there is an incentive for a controller to attempt to replace before failure occurs. The problem is to find an optimal control strategy that balances the cost of replacement with the cost of failure and results in a minimum total long-run average cost per unit time. We attack this problem under the cumulative damage model for system failure. In this failure model, shocks occur to the system in accordance with a Poisson process. Each shock causes a random amount of damage or wear and these damages accumulate additively. At any given shock, the system fails with a known probability that depends on the total damage accumulated to date. We assume that the cumulative damage is observable by the controller and that his decisions may be based on its current value. Supposing that the shock failure probability is an increasing function of the cumulative damage, we show that an optimal policy is to replace either upon failure or when this damage first exceeds a critical control level, and we give an equation which implicitly defines the optimal control level in terms of the cost and other system parameters. Also treated are some more general models that allow for income lost during repair time and other extensions.     

A model in which component failure rates depend on the working set

We consider a multicomponent system in which the failure rate of a given component at any time depends on the set of working components at that time. Sufficient conditions are presented under which such a system has a life distribution of specified type. The Laplace transform of the time until all components are down is derived. When repair is allowed, conditions under which the resulting process is time reversible are presented.