ISE 536–Fall03: Linear Programming and Extensions
December 3, 2003
Lecture 25: LP in Research
Lecturer: Fernando Ord´
o˜nez
Robust Capacity Expansion of Transit Networks
1
Capacity expansion problem
We consider the problem of deciding investment decisions on a given transit network.
A
standard solution approach for this problem is to formulate this as a network flow prob
lem with decision variables for possible capacity expansions.
This leads to the following
formulation:
min
x,y
c
t
x
s
.
t
.
Nx
=
b
x
≤
u
+
y
d
t
y
≤
I
x
≥
0
, y
≥
0
,
(1)
where
•
y
are investment decisions,
d
t
y
is the total investment cost (bounded by a budget
I
).
•
Nx
=
b
are the conservation of flow equations.
•
c
t
x
is the total (average) travel time.
This is a classic network flow formulation for the network design problem. Some simple and
extensions to this model:
 Consider integer investment decision variables.
1
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 A more realistic representation of travel times.
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 Spring '05
 YY
 Trigraph, capacity expansion problem

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