Which Integer Linear Programs are easy?
It is a special case of the transportation problem (or the minimum-cost flow problem), and so can be solved in polynomial time.  The coefficient matrix is totally unimodular since it is the incidence matrix of a bipartite graph.

The following Wikipedia articles could be useful.


http://en.wikipedia.org/wiki/Minimum_cost_flow_problem
http://en.wikipedia.org/wiki/Unimodular_matrix