
168 Introduction to Linear Optimization and Extensions with MATLAB
R
c
T
N
− c
T
B
B
−1
N = (c
N
+ 4c
N
)
T
− c
T
B
B
−1
N
= c
T
N
− c
T
B
B
−1
N + 4c
N
T
= r
N
+ 4c
N
T
≥ 0,
or equivalently
r
N
≥ −4c
N
T
.
Thus, if a perturbation of non-basic variables 4c
N
violates the above
condition, then the reduced costs of the perturbed problem are not all non-
negative and the revised simplex method can be used to generate the optimal
solution for the perturbed problem.
4.8.3 Changes in the Constraint Matrix
Sensitivity analysis concerning perturbations in the constraint matrix is not
easy. A small change in a single coefficient in a current basis can render the
basis infeasible or singular. We consider