because only positive x,u in a solution indicates shipments and the rest zero- valued decision variables (i.e., empty cells in the transportation tableau) incur no shipments. Therefore, it is natural to focus on the positive variables in a transpor- tation solution. For this reason, the set of positive valued X,*s in a transportation solution is termed the basic solution, while the set of rest zero-valued X*s is termed the nonbasic solution.