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.