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hw2orie321

# hw2orie321 - ORIE 321/521 Optimization II Summer 2006...

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ORIE 321/521 Optimization II Summer 2006 Homework # 2 Due: Tuesday, July 26, 4 p.m. in the OR homework drop box for OR321. Please print your name clearly on the first page of your homework. These first few problems are “practice” problems, not to be handed in. Problems 1 and 5 are from the Bradley, Hax, and Magnanti text, while problems 2,3,4 are based on the class lecture notes on shortest paths. 1. Problem #6, BHM Chapter 11. 2. Consider the example on page 5 of the shortest path notes. For j = 1 , . . . , 6 , compute the values v j (5) = min 1 i 6 { v i (4) + c ij } . Do the values v j (5) differ from v j (4) ? Why? Now let c 34 = - 3 , instead of 9 (the remaining data are unchanged). This change creates a negative cycle in the graph ( 3 4 5 3 ). Re-do the computation for the modified graph (from scratch!). Are the
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