Sensitivity Analyses of LP's
After an LP is solved and the optimal solution is obtained, it is
useful to test the sensitivity of the solution and the OV to
possible changes in the problem data, in particular, to objective
function coefficients (OFC) and the right hand sides (RHS) of the
constraints. For instance, if one knows that the OFC of a
variable was entered wrong, or that after the solution is
obtained, the OFC (whose value is probably determined in the
market place) has changed, can we still use the solution, or do
we need to solve the problem again? In most cases, there is
enough information on the solution report that we do not need to
solve the problem over. If the change is within allowable range,
in most cases we can say precisely, what the solution and the OV
would have been, had we solved the problem over. Even if the
change in the OFC is outside the allowable range, one can still
state (1)an interval of values within which the OV would be found
(these intervals are marked as blue areas in the graphs that
follow); and (2) at least qualitatively, in which direction the
solution values will change.
The purpose of this note is not to give you a set of
relationships that you must remember but it is
to help you to learn to reason and make economic
sense out of the solution of a linear programming
problem. Ideally you should be able to recreate these
relationships by applying several simple intuitive results.
The two documents below first summarize a set of basic principles
and then apply those principles to a set of scenarios: These
scenarios are listed in a table of content in each document that
you can click to link. While you are studying one of these
scenarios you can go back and view the principle behind a
particular statement related to that scenario.
[Objective Function Coefficients] [Right Hand Sides]