Multiindex transportation problems with $2$-embedded structure

We consider multiindex transportation problems of linear and integer linear programming. As a method of solving them, we propose an approach based on reductions of multiindex transportation problems to min-flow problems. We show that under the reduction scheme we consider, the $2$-embeddability condition for multiindex problems is a necessary and sufficient condition for the problem to be reducible to a min-cost flow problem.

Presented by the member of Editorial Board: A. A. Lazarev