  This paper introduces a concept of a derivative of the optimal value function
in linear programming (LP). Basically, it is the the worst case optimal value
of an interval LP problem when the nominal data the data are inflated to
intervals according to given perturbation patterns. By definition, the
derivative expresses how the optimal value can worsen when the data are subject
to variation. In addition, it also gives a certain sensitivity measure or
condition number of an LP problem.
  If the LP problem is nondegenerate, the derivatives are easy to calculate
from the computed primal and dual optimal solutions. For degenerate problems,
the computation is more difficult. We propose an upper bound and some kind of
characterization, but there are many open problems remaining.
  We carried out numerical experiments with specific LP problems and with real
LP data from Netlib repository. They show that the derivatives give a suitable
sensitivity measure of LP problems. It remains an open problem how to
efficiently and rigorously handle degenerate problems.
