PRELIM 2
ORIE 3310/5310
March 12, 2009
Closed book exam. Justify all work.
1.
a. (10) Explain Bellman’s basic procedure for determining a shortest path in a directed acyclic graph;
i.e., give (and explain) the optimal value function and recursive equations for the model along
with an indication of the order of computation to be used in solving the recursive equations.
b. (8) Now suppose we wish to Fnd a shortest
(1
, n
) path
which contains a specifc edge
, say edge
(
i, j
) . How would you use the basic procedure to achieve this?
c. (8) .
..as in part (b), but we wish to
avoid
edge
(
i, j
) .
d. (12) .
..as in part (b), but we wish to determine a shortest
(1
, n
) path
which contains a specifc
node
, say node
k
.
e. (12) .
..as in part (b), but we wish to
avoid
node
k
.
2. ±or trade among banks, mortgages are packaged in $20 million
instruments
. In such a package, individ
ual mortgages cannot be subdivided, but the packaging need not be exact. E.g., a group of mortgages
of total value $19,970,000 could be used to create one instrument with $30,000
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 Spring '08
 TODD
 Graph Theory, Recursion, Optimization, Bellman equation, optimal value function

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