Linear programming with variable matrix entries

We consider Linear Programming problems (either continuous or integer) where some matrix entries can be fixed by the decision maker to any value within an interval. In the assumption of non negativity of the variables the problem can be solved in two phases. First the variables are computed and then this solution is used to compute the matrix entries. In the paper it is also shown that introducing direct costs on the variable matrix entries makes the problem NP-hard. Finally a kind of strong duality result is provided for this problem.