Monge sequences, antimatroids, and the transportation problem with forbidden arcs

Abstract

This paper considers the transportation problem, both in the standard form and in the case where flow is prohibited on some arcs. We review the celebrated Monge sequence result for the standard problem, give an antimatroid interpretation of an algorithm for constructing Monge sequences or determining that none exist, and extend this algorithm and the antimatroid interpretation to include the case of forbidden arcs. © 1990.