Transportation problems with some xij negative and transshipment problems

Abstract

AbstractThe general solution process of the Hitchcock transportation problem resulting from the application of the method of reduced matrices may give solutions with some negative xij values. This paper is devoted to a review of the reduced matrices method, an examination of suitable interpretation of sets of xij 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 cij 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.