ISE 536–Fall03: Linear Programming and Extensions
October 22, 2003
Lecture 14: Sensitivity Analysis
Lecturer: Fernando Ord´o˜nez
1
Reoptimizing a problem
In this section we will consider that we solve a problem
(
P
) min
c
t
x
s
.
t
.
Ax
=
b
x
≥
0
to optimality. We assume that we have access to the optimal basis
B
, which satisﬁes
1.
B

1
b
≥
0 (primal feasibility)
2.
c

c
B
B

1
A
≥
0 (dual feasibility)
1.1
Change in
b
Modify only the
i
th coordinate of
b
, from
b
i
to
b
i
+
ε
, with
ε
6
= 0.
Is
B
still optimal after the change?
How large can the change be for
B
to remain optimal?
How do we reoptimize?
1
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Change in
c
Modify only the
j
th coordinate of
c
, from
c
j
to
c
j
+
ε
, with
ε
6
= 0.
Is
B
still optimal after the change?
How large can the change be for
B
to remain optimal?
•
if
j
is nonbasic
•
if
j
is basic
How do we reoptimize?
1.3
A new variable
x
n
+1
is added
Add variable
x
n
+1
with column
A
n
+1
to matrix
A
and cost
c
n
+1
. The new problem becomes
(
P
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 Spring '05
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 Operations Research, Linear Programming, ax, Shadow price, Reduced cost, min cT

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