A finiteness proof for modified dantzig cuts in integer programming

Let be a basic solution to the linear programming problem subject to: where R is the index set associated with the nonbasic variables. If all of the variables are constrained to be nonnegative integers and x_u is not an integer in the basic solution, the linear constraint is implied. We prove that including these “cuts” in a specified way yields a finite dual simplex algorithm for the pure integer programming problem. The relation of these modified Dantzig cuts to Gomory cuts is discussed.     

Spike swapping in basis reinversion

During basis reinversion of either a product form or elimination form linear programming system, it may become necessary to swap spike columns to effect the reinversion and maintain the desired sparsity characteristics. This note shows that the only spikes which need be examined when an interchange is required are those not yet processed in the current external bump.     

Evaluation of commonly used rules for detecting “steady state” in computer simulation

A definition of the problem of the initial transient with respect to the steady-state mean value has been formulated. A set of criteria has been set forth by which the efficaacy of any proposed rule may be assessed. Within this framework, five heuristic rules for predicting the approximate end of transiency, four of which have been quoted extensively in the simulation literature, have been evaluated in the M/M/1 situation. All performed poorly and are not suitable for their intended use.     

Estimation in single server queues

Moment and maximum likelihood estimates (m.l.e.'s) arc investigated for nonparametric and parametric models for a single server queue observed over a random time horizon, namely, up to the nth departure epoch. Also. m.l.e's of the mean interarrival time and mean service time in anM/M/1 queue observed over a fixed time-interval are studied Limit distributions of these estimates are obtained Without imposing steady state assumptions on the queue-size or waiting time processes.     

A new storage reduction technique for the solution of the group problem

This paper shows that by making use of an unusual property of the decision table associated with the dynamic programming solution to the goup problem, it is possible to dispense with table storage as such, and instead overlay values for both the objective and history functions. Furthermore, this storage reduction is accomplished with no loss in computational efficiency. An algorithm is presented which makes use of this technique and incorporates various additional efficiencies. The reduction in storage achieved for problems from the literature is shown.     

Optimal state-dependent pricing policies for a class of stochastic multiunit service systems

This paper models a k-unit service system (e.g., a repair, maintenance, or rental facility) with Poisson arrivals, exponential service times, and no queue. If we denote the number of units that are busy as the state of the system, the state-dependent pricing model formalizes the intuitive notion that when most units are idle, the price (i.e., the service charge per unit time) should be low, and when most units are busy, the price should be higher than the average. A computationally efficient algorithm based on a nonlinear programming formulation of the problem is provided for determination of the optimal state-dependent prices. The procedure ultimately reduces to the search on a single variable in an interval to determine the unique intersection point of a concave increasing function and a linear decreasing function. The algorithm takes, on the average, only about 1/2 second per problem on the IBM 360/65 (FORTRAN G Compiler). A discrete optimal-control approach to the problem is shown to result in essentially the same procedure as the nonlinear-programming formulation. Several properties of the optimal state-dependent prices are given. Comparisons of the optimal values of the objective function for the state-dependent and state-independent pricing policies show that the former is on the average, only about 0.7% better than the latter, which may explain partly why state-dependent pricing is not prevalent in many service systems. Potential generalizations of the model are discussed.     

Landmarks in defense literature

The Power of Personality in War. By Major General Baron Hugo von Freytag-Lorighoven, Military Service Publishing Company, Harrisburg, PA (1955)     

Polynomial‐time approximation schemes for two‐machine open shop scheduling with nonavailability constraints

This paper addresses a two‐machine open shop scheduling problem, in which the machines are not continuously available for processing. The processing of an operation affected by a non‐availability interval can be interrupted and resumed later. The objective is to minimize the makespan. We present two polynomial‐time approximation schemes, one of which handles the problem with one non‐availability interval on each machine and the other for the problem with several non‐availability intervals on one of the machines. Problems with a more general structure of the non‐availability intervals are not approximable in polynomial time within a constant factor, unless . © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

The demand for defense in East Asia: Modeling security alternatives∗

An interactive economic model of military spending is proposed. It is quantified on the basis of cross section data for East Asia. Projections of military spending to the end of the decade suggest that the growth of military spending in the region will decline slightly in the current decade. East Asian military spending can, however, be greatly influenced by the path of Chinese and US military efforts. An expansion of military spending by China could cause neighboring countries to greatly increase their military expenditures.     

THE GEOGRAPHY OF NUCLEAR PROLIFERATION NETWORKS

This article uses a geographic approach to examine one aspect of the nuclear black market: the coordinators who bring buyers and sellers together, and transport goods between them. The most important factor in determining the geographical structure of a proliferation network is the network coordinator's access (or lack thereof) to unique state resources. Coordinators with access to state resources and prerogatives can avoid embedding themselves in hostile countries or relying on commercial infrastructure, often leading to territorially diffuse logistical networks. Coordinators without such access are forced to rely on commercial infrastructure and favorable local political, economic, and social conditions, often resulting in territorially centralized logistical networks. This is illustrated through case studies of Abdul Qadeer Khan's supply networks to Pakistan, Libya, and Iran. The article concludes with some observations about the implications of a geographical approach for understanding nuclear proliferation networks.