What is sensitivity analysis?

1
What is sensitivity analysis? Why do we perform
sensitivity analysis? How far do we like to
perform sensitivity analysis? In an LP
sensitivity analysis, what type of conditions or
information are considered? In an LP sensitivity
analysis, what type of conclusions are
considered?
IE 416, Chap 51, July 98
2
Shadow Price SP page 199 Shadow price for
the i th constraint of an LP is the amount by
which the optimal z-value is improved if the rhs
of the i th constraint is increased by
1. Reduced Cost RC page 205 For any
nonbasic variable Xk, the reduced cost is the
amount by which the objective function
coefficient of Xk must be improved before the LP
will have an optimal solution in which Xk is a
basic variable
IE 416, Chap 43, July 98
3
Terms Used in Different Books on Simplex
method Winston WinQSB System Binding Tight No
n-binding Loose Slack Slack Excess Surplus R
educed cost Opportunity cost Shadow price Dual
price
IE 416, Chap 44, July 98
4
Summary of LP Sensitivity Analysis,
Notations O.F. ZCBVXBV CNBVXNBV S.T.
ab1X1 ab2X2 lt bb an1X1
an2X2 . ltbn Where CBV coefficient of
basic variable in Z CNBV .. nonbasic
variable in Z XBV basic variable in optimal
solution XNBV nonbasic variable in optimal
solution bb right hand side of binding
constraint bn right hand side of nonbinding
constraint SPi shadow price of constraint i RCi
reduced cost of XNBV CBV new CBV , CNBV
new CNBV , bb new bb , bn new bn
IE 416, Chap 5, Feb. 98
5
Summary of LP Sensitivity Analysis Summary
information from output of the Quant software
Coefficient of OF .
RHS . Variable RC Min
Current Max Constraint si/ei SP Min
Current Max Summary sensitivity analysis .
IF . . THEN

.
Basis (var) bfs (value) Z
(value) . min CBV max
same same
Z( CBV)XBV CBv out of range
change change
change min CNBV max same
same
same CNBv out of range XNBV -gtXBV
change change min
bb max same
change ZSPb( bb) bb
out of range change
change change min
bn max same
same same bn out of
range change
change change Note
y y - y Note If output of the Lindo is being
used then Z SPb( bb) Use if O.F. is
max Use - if O.F. is min
IE 416, Chap 5, Dec. 98
6

• Managerial Use of Shadow Price
• What is the maximum amount that a manager would
  like to pay extra for an extra unit of a
  resource?
• Consider RMC problem and material 3 in the
  following table.

IE 416, Chap 5, Sept. 2009