Let C be an n × m matrix. Then the sequence Sa: = ((il,jl),(i2,j2) ..... (inm,jnm)) of pairs of indices is called a Monge sequence with respect to the given matrix C if and only if, whenever (i,j) precedes both (i, s) and (r,j) in ~, then c[ i, j ] + c [ r, s] <~ c [ i, s] + c [ r, j ]. Monge sequences play an important role in greedily solvable transportation problems. Hoffman showed that the greedy algorithm which maximizes all variables along a sequence ~ in turn solves the classical Hitchcock transportation problem for all supply and demand vectors if and only if ~ is a Monge sequence with respect to the cost matrix C. In this paper we generalize Hoffman's approach to higher dimensions. We first introduce the concept of a d-dimensional Monge sequence. Then we show that the d-dimensional axial transportation problem is solved to optimality for arbitrary right-hand sides if and only if the sequence S a applied in the greedy algorithm is a d-dimensional Monge sequence. Finally we present an algorithm for obtaining a d-dimensional Monge sequence which runs in polynomial time for fixed d.