I have a linear programming problem such that its set of constraints can be divided into two parts. The first part are general linear constraints and the second part are uncertain constraints. It means that some of coefficients are uncertain but given in an interval. A small example of the problem is as follows:
Min $f_{12} + f_{23} + f_{24} + f_{45} + f_{35}$
s.t: $f_{12}=1$
$f_{23} + f_{24} - f_{12} = 0$
$f_{35} - f_{23} = 0$
$f_{45} - f_{24} = 0$
$ f_{45} + f_{35} = -1$
$ f_{24} - p_{24} f_{12} = 0$
$f_{23} - p_{23} f_{12} =0$
$p_{23} + p_{24} =1$
$ p_{23} \in [0, 1/6]$
$ p_{24} \in [1/6, 1]$
$ f_{ij} \geq 0 $ for all ij
Can this problem be solved in polynomial time?