The axial multi-index transportation problem is defined as follows. Given are k sets A r , each set having n r elements, r = 1, …, k. The cartesian product of the sets A r is denoted by A. To each element a ϵ A a certain cost, c a ϵ R , is associated. Further, a nonnegative demand e ri is associated to each set A ri = [ a ϵ A : a( r) = i]. The problem is to find nonnegative real numbers x a such that each demand is satisfied (that is ∑ aϵA ri x a = e ri for r = 1, …, k, i = 1, …, n r ) and such that total cost (that is ∑ aϵA c a · x a ) is minimized. In this paper we deal with a special case of this problem where the costs c a are decomposable, that is, given a real-valued function f and a distance d Ar × As ij between element i of A r and element j of A s , we assume that c a = f( d A 1 × A 2 a(1), a(2) , …, d A k − 1 × A k a( k−1), a( k) ) for all a ϵ A. We present two algorithms for this problem, and we analyze their worst-case behavior without requiring explicit knowledge of the cost-function f. Next, we use these results to derive explicit bounds in the case where f is the diameter cost-function (that is c a = max r, s d A r × A s a( r), a( s) ), and in the case where f is the Hamiltonian path cost-function (that is c a = min [∑ k − 1 i = 1 d A σ( i) × A σ( i + 1) a( σ( i)) , a(σ(i + σ is a cyclic permutation of [1, …, k]).