THE FRAGILE TRADITION OF NUCLEAR RESTRAINT

The Tradition of Non-Use of Nuclear Weapons by T.V. Paul. Stanford University Press, 2009. 319 pages, $29.95.     

End effects in capacity expansion models with finite horizons

Capacity expansion models are typically formulated in the context of some finite horizon. Because the firm lasts longer than the horizon, a bias can enter into the optimal solution from the model horizon chosen. Recently, Grinold [8] has proposed a “dual-equilibrium method” for ameliorating possible distortions. Although the dual-equilibrium method has superior analytical properties to other methods, it is conceptually more complex. In this paper it is shown that there are situations where the “primal-equilibrium” approach of Manne [15] provides equivalent results and that the use of annualized capital costs in the objective function, although somewhat less efficient, results in a similar model.     

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.     

On convexity proofs in location theory

It is often assumed in the facility location literature that functions of the type ø_i(x_i, y) = β_i[(x_i-x)²+(y_i-y)²]^K/2 are twice differentiable. Here we point out that this is true only for certain values of K. Convexity proofs that are independent of the value of K are given.     

Optimality conditions for the bilevel programming problem

The bilevel programming problem (BLPP) is a sequence of two optimization problems where the constraint region of the first is determined implicitly by the solution to the second. In this article it is first shown that the linear BLPP is equivalent to maximizing a linear function over a feasible region comprised of connected faces and edges of the original polyhedral constraint set. The solution is shown to occur at a vertex of that set. Next, under assumptions of differentiability, first-order necessary optimality conditions are developed for the more general BLPP, and a potentially equivalent mathematical program is formulated. Finally, the relationship between the solution to this problem and Pareto optimality is discussed and a number of examples given.     

Two-characteristic markov-type manpower flow models

A two-dimensional state space Markov Model of a Manpower System with special structure is analyzed. Examples are given from the military services. The probabilistic properties are discussed in detail with emphasis on computation. The basic equations of manpower stocks and flows are analyzed.     

The interface of computer science and statistics

Current scientific, technical, and management progress is characterized by the generation of a tremendous amount of data for analysis. This, in turn, poses a significant challenge: to effectively and efficiently extract meaningful information from the large volume of data. Two relatively young professions, computer science and statistics, are intimately linked in any response to the challenge. They have consequently become indispensable to scientific, technical, and management progress, occupying a position at its very heart Computer science and statistics have each been separately documented by many books as well as numerous papers. However, the interface of computer science and statistics, the area of their interaction, has been documented only in part. This paper begins characterization of the entire interface by providing a structure and an historical background for it A structure for the interface is introduced initially, followed by an historical background for the interface presented in two parts. First to be summarized is the evolution of the interface from an interweaving of the mechanical prerequisites to the computer and mathematical prerequisities to computer science and of the foundations for probability and statistics. Development of statistics prior to 1900 then is reviewed.