Chapter 8 Sensitivity Analysis. Bottom line: How does the optimal solution change as some of the elements of the model change? For obvious reasons we shall focus on Linear Programming Models. Ingredients of LP Models. Linear objective function A system of linear constraints RHS values
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(1) xk is not in the old basis
(2) xk is in the old basis
rk >= , if opt=max
rk <= , if opt = min
Suppose that the reduced costs in the final simplex tableau are as follows:
r = (0,0,0,2 3 4)
with IB=(2,3,1), namely with x2,x3 and x1 comprising the basis.
What would happen if we change the value of c4 ?
First we observe that x4 is not in the basis (why?) and that the opt=max
If we add to the old c1, we would have instead
So we now have to restore the canonical form
of the x1 column.
3/4 ≥ ≥ -2/3