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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