Approximation Algorithms for Multi-Index Transportation Problems With Decomposable Costs

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 2 A a certain cost, c a 2 IR, is associated. Further, a nonnegative demand e ri is associated to each set A ri = fa 2 A : a(r) = ig