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 5:1, July 98

2. Shadow Price: SP page 230 Reduced Cost: RC page 236
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 236
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 4:3, July 98

3. Terms Used in Different Books on Simplex method
Winston WinQSB System
Binding Tight
Non-binding Loose
Slack Slack
Excess Surplus
Reduced cost Opportunity cost
Shadow price Dual price
IE 416, Chap 4:4, July 98

4. Summary of LP Sensitivity Analysis, Notations
O.F. Z=CBV*XBV + CNBV*XNBV
S.T. ab1*X1 + ab2*X2 + … =< bb
an1*X1 + an2*X2 + …. =<bn
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
C’BV = new CBV , C’NBV = new CNBV , b’b= new bb , b’n= 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 C’BV max same same Z+( CBV)XBV
C’Bv out of range change change change
min C’NBV max same same same
C’NBv out of range XNBV ->X’BV change change
min b’b max same change Z+SPb( bb)
b’b out of range change change change
min b’n max same same same
b’n 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