Transportation problems with some xij negative and transshipment problems

The general solution process of the Hitchcock transportation problem resulting from the application of the method of reduced matrices may give solutions with some negative x_ij values. This paper is devoted to a review of the reduced matrices method, an examination of suitable interpretation of sets of x_ij which include some negative values, and ways of interpreting these values in useful modifications of the Hitchcock problem. Such modifications include a) the reshipment problem, b) the overshipment problem, and c) the transshipment problem. Techniques are developed for determining and eliminating c_ij which are not optimal. These techniques and results are useful in solving the problems indicated above. The natural applicability of the simple and general method of reduced matrices is emphasized.     

Reflections on Transparency and Monitoring under the 1993 United States-Russian Federation Highly Enriched Uranium Purchase Agreement

ABSTRACT

The 1993 Highly Enriched Uranium (HEU) Purchase Agreement between the United States and Russian Federation is often described as one of the world's most successful nuclear nonproliferation programs. In 2013, the two states achieved the agreement's major goals of downblending 500 metric tons of Russian weapon-origin HEU to low enriched uranium (LEU) and delivering all resultant LEU to the United States. At one time, the LEU delivered under the agreement generated nearly 10 percent of all electricity in the United States. The agreement achieved its nonproliferation goals through a unique government/industry partnership. Commercial executive agents contracted for the annual sale and delivery of downblended LEU, while the US and Russian governments exercised reciprocal transparency monitoring measures to demonstrate that all LEU delivered under the agreement was derived from Russian weapons-origin HEU, and that the same LEU was used for exclusively peaceful purposes in the United States. The commercial development, negotiations, and implementation of the agreement have been well documented. This article describes the scope of US transparency monitoring activities in Russian HEU processing facilities, as well as Russian monitoring in the United States. In addition, it discusses the results of twenty years of reciprocal transparency monitoring and data analysis, and outlines lessons learned that are potentially applicable to future transparency monitoring and verification regimes and similar cooperative efforts.     

Use of completely reduced matrices in solving transportation problems with fixed charges

This paper shows how completely reduced matrices can be used in obtaining exact or approximate solutions to transportation problems with fixed charges. It does not treat methods for obtaining reduced matrices, which are available elsewhere, but it does discuss the problem of obtaining a completely reduced matrix, and then a general parametric solution to the primal problem, from any particular solution. Methods for obtaining particular solutions with determinacies of maximum order (solutions for the constant fixed charges problem) are then presented. The paper terminates with a discussion of methods which are useful in obtaining approximations to solutions of fixed charges problems with charges not constant.     

Fragmented forces: The development of the Gambian military

This article provides a detailed look at the history of the Gambia Armed Forces (GAF), a military that has received very little academic attention within the study of African state security forces. It identifies key turning points in the GAF’s history, and highlights the vastly different roles the military played in the state under President Jawara (1965–94) and President Jammeh (1994–2017). Yet, it also highlights important similarities regarding internal patterns within the armed forces and shows the ways in which these continuities may challenge attempts to restructure the security sector. The article draws on archival research and interviews conducted with retired and active duty Gambian military personnel, government officials, and Gambian scholars.     

A general treatment of upper unbounded and bounded hitchcock problems

This paper is designed to treat (a) the problem of the determination of the absolute minimum cost, with the associated assignments, when there is no limit, N, on the number of parcels available for shipment in a modified Hitchcock problem. This is accomplished with the use of a transformed cost matrix. C*, to which the so-called transportation paradox does not apply. The general Hitchcock solution using C* gives the cost T*, which is the absolute minimum cost of the original problem, as well as sets of assignments which are readily transformed to give the general assignments of the original problem. The sum of these latter assignments gives the value of N_u, the unbounded N for minimum cost. In addition, this paper is designed to show (b) how the method of reduced matrices may be used, (c) how a particular Hitchcock solution can be used to determine a general solution so that one solution using C* can provide the general answer, (d) how the results may be modified to apply to problems with fixed N, and hence (e) to determine the function of the decreasing T as N approaches N_u, and finally (f) to provide a treatment when the supplies at origin i and/or the demands at destination j, are bounded.     

Self-Interest versus the Common Cause: Austria,Prussia and Russia against Napoleon

This essay re-examines coalition warfare during the Napoleonic era by looking at the three eastern European powers – Austria, Prussia and Russia – how they interacted over time with France as well as each other, and how they managed French preponderance on the Continent. Before 1812, coalition warfare was dominated by eighteenth-century military and diplomatic attitudes: overall foreign political goals were ill-defined and were characterised by deep mistrust. The result was that the eastern powers pursued their own interests with little regard to coalition cohesion. If the coalition held together in 1813 and 1814, on the other hand, it was largely because individual powers' self-interest coincided with the overall objectives of the coalition – an increased determination to defeat Napoleon – along with a never before seen numerical superiority in allied troops. In this, Austria and especially Chancellor Metternich's role in juggling conflicting interests between the allies so that they could present, for the first time, a united front against France was fundamental.