Asymptotic approach to solving the multi-index axial transportation problem (Q1571197)

The authors give a theoretical foundation to the fact that the plan for a \(p\)-index axial transportation problem (TP) of dimension \(n{_1}\times\ldots\times{n_p}\) constructed by the minimal element method (\(\psi\)-method) is closed to the optimal plan. Namely, it is proved that the objective function has asymptotically equal values on these plans as \(n_1,\ldots,n_p\) tend to infinity. In other words, it is proved that the relative number of \(p\)-index axial TPs among all problems for which the \(\psi\)-method yields an asymptotically optimal plan tends to unity.