Discrete equal‐capacity p‐median problem

This paper examines the discrete equal‐capacity p‐median problem that seeks to locate p new facilities (medians) on a network, each having a given uniform capacity, in order to minimize the sum of distribution costs while satisfying the demand on the network. Such problems arise, for example, in local access and transport area telecommunication network design problems where any number of a set of p facility units can be constructed at the specified candidate sites (hence, the net capacity is an integer multiple of a given unit capacity). We develop various valid inequalities, a separation routine for generating cutting planes that are specific members of such inequalities, as well as an enhanced reformulation that constructs a partial convex hull representation that subsumes an entire class of valid inequalities via its linear programming relaxation. We also propose suitable heuristic schemes for this problem, based on sequentially rounding the continuous relaxation solutions obtained for the various equivalent formulations of the problem. Extensive computational results are provided to demonstrate the effectiveness of the proposed valid inequalities, enhanced formulations, and heuristic schemes. The results indicate that the proposed schemes for tightening the underlying relaxations play a significant role in enhancing the performance of both exact and heuristic solution methods for this class of problems. © 2000 John & Sons, Inc. Naval Research Logistics 47: 166–183, 2000.     

Gittins-index heuristics for research planning

The classical work of Gittins, which resulted in the celebrated index result, had applications to research planning as an important part of its motivation. However, research planning problems often have features that are not accommodated within Gittins's original framework. These include precedence constraints on the task set, influence between tasks, stopping or investment options and routes to success in which some tasks do not feature. We consider three classes of Markovian decision models for research planning, each of which has all of these features. Gittins-index heuristics are proposed and are assessed both analytically and computationally. They perform impressively. © 1995 John Wiley & Sons, Inc.     

Evaluating the effects of machine breakdowns in stochastic scheduling problems

In most of the stochastic resource-allocation problems discussed in the literature it is supposed that the key resource, herein called the machine, is continuously available until all tasks are completed. Plainly, this will often be an unrealistic assumption. This paper supposes that intermittent availability of the machine is due to a breakdown proces, and describes various approaches to the evaluation of the effect of breakdowns. Firstly, for the case of geometric up times, conditions are given under which breakdowns have no effect on optimal allocation strategies. Secondly, two different procedures are given which yield an upper bound on the loss incurred when a processing strategy is adopted under the assumption of no breakdowns, when in fact breakdowns do occur. The first of these is based on Gittins's indices and is described for the case of geometric up times, and the second uses a bounding argument on the breakdown process.     

Some order relations in closed networks of queues with multiserver stations

Consider a closed network of queues of the “product-form” type, where each station has s servers (s ≥ 1 is identical for all stations). We show that the throughput function of the network is Schur concave with respect to the loading of the stations and arrangement increasing with respect to the assignment of server groups. Consequently, different loading/assignment policies can be compared under majorization/arrangement orderings and their relative merits decided according to the yields of throughput. The results can be used to support planning decisions in computer and production systems which are modeled as closed networks of queues.     

NUCLEAR MYTHOLOGY AND NUCLEAR USELESSNESS

Five Myths about Nuclear Weapons, by Ward Wilson. Houghton Mifflin Harcourt, 2013. 188 pages, $22.     

The road not taken: Conflict termination and guerrillaism in the American Civil War

Irrespective our views on the rationality of our opponent's continuing to conduct operations against us, unless utterly extirpated, he retains a vote on when and how conflict will end. This is because war is about power — compelling another actor to do something he would not otherwise do, or to cease doing something he would otherwise prefer to do. In planning for conflict termination we should account for the peculiarities of opponents who may decide not to quit when we have beat them fair and square. We do not desire that they cease conventional fighting, but that they cease fighting altogether.     

America's regions and US foreign policy

Peter Trubowitz, Defining the National Interest: Conflict and Change in American Foreign Policy. Chicago and London: University of Chicago Press, 1998. Pp.xvi + 353, biblio., figs, maps, index. $55 (cloth); $18.95 (paper). ISBN 0–226–81302–9.     

Political influence on civil war mortality rates: The electoral college as a battlefield

This paper employs public choice analysis to explain certain kinds of military decision‐making during the Civil War. Specifically, the political costs and benefits which may have influenced policy with respect to casualty rates in the Union army are considered. A primary empirical finding is that electoral votes per capita are a strong explainer of casualties across Union states, all else equal.