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PRELIM 3
ORIE 3310/5310
April 14, 2009
Closed book exam. Justify all work.
1. A
supplydemand network
is a digraph
G
= (
V, E
) , for which
V
=
S
∪
D
∪
I
, with the disjoint subsets
S, D, I
denoting, respectively,
supply
,
demand
, and
intermediate
nodes. For each
i
∈
S
we are given
a
i
>
0
units of supply of some commodity and to each
i
∈
D
there is an associated demand,
b
i
>
0
units of the commodity. We assume that
∑
i
∈
S
a
i
=
∑
i
∈
D
b
i
. For this model the lower ±ow limit along
any arc is 0 and there are arc capacities
c
ij
≥
0
∀
(
i, j
)
∈
E
which limit the ±ow of the commodity
along individual arcs
a. (5) Give a mathematical programming formulation whose constraints (±ow conservation restric
tions and arc±ow limitations) must be satis²ed by any feasible ±ow in
G
which meets the speci²ed
demand from the existing supply.
b. (10) Give a max±ow model which can be used to determine whether there is a feasible ±ow in
G
which satis²es the speci²ed demand from the existing supply.
c. (20) Show that if your model is feasible, then for any cut
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 Spring '08
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