  In this paper we consider the problem of analyzing the effect a change in the
load vector can have on the optimal power generation in a DC power flow model.
The methodology is based upon the recently introduced concept of the
$\mathcal{OPF}$ operator. It is shown that for general network topologies
computing the worst-case sensitivities is computationally intractable. However,
we show that certain problems involving the $\mathcal{OPF}$ operator can be
equivalently converted to a graphical discrete optimization problem. Using the
discrete formulation, we provide a decomposition algorithm that reduces the
computational cost of computing the worst-case sensitivity. A 27-bus numerical
example is used to illustrate our results.
