The Transportation Method

Although the transportation problem can be solved as an ordinary linear programming problem, its special structure can be exploited, resulting in a special-purpose algorithm, the so-called transportation method. The method was actually developed in 1941 by F.L. Hitchcock and therefore preceded the simplex method by half a dozen years. Still, it can be viewed as a streamlined version of the simplex method. The problem under consideration can be described as follows. At location, called origins, O1, O2, ..., Om are supplies of a certain commodity, in quantities si at origin Oi, i=1, ..., m. All of this commodity is to be transported to locations, called destinations D1, D2, ..., Dn in quantities dj to Dj, j=1, ..., n. Shipments of the commodity from an origin to a destination can only be done directly between the two. The cost of sending one unit of the commodity from origin Oi to destination Dj is given as cij. We assume that the