The solution of tall distribution problems

Abstract

The problem is to allocate the shipments (i.eo, to find the numbers xij) so as to minimize T. More formally, the problem is to P q find integers xij such that (1) xij > O, (2) Z xij = a (3) Z x i = bi, i=l J ' j=l and such that T is minimized. In many situations, particularly in industrial and governmental operations, it happens that p is much greater than q (in which case the matrix (cij) is said to be "tall"). This would occur, for instance, in csse there were just a few mannfacturing plants which were supplying many warehouses and for ret~il customer~ with their products. On the other hsnd, it might also happen that q is much greater than p (in ~hich csse the cost matrix is said to be "flat"). Such a situation would arise in