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Unformatted text preview: longest path with positive arc length. so the shortest path going from source or start to ﬁn or sink with negative arc length gives us the earliest time to complete the project. By inspection, the shortest path is start1235678ﬁnish . The earliest time to complete the project is 13. Problem 40 932.(a) 2 8 7 10 9 12 2 11 1 2 hours 3 hours 4 hours = $30 = $40 = $50 932.(b) Yes. There’s no arc going backward. The source node is node 7 , and the sink node is node 2 . The cost of each arc could be treated as the arc length, which means for each red arc the cost or length is 30, for the black arc the cost or length is 40, for the green arc the cost or length is 50. Therefore, ﬁnding out the minimum total cost is equivalent to ﬁnding out the shortest path going from node 7 to node 2. By inspection, the best schedule is 7112. 3...
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 Spring '11
 Smith
 Operations Research, Arc Length, Optimization, Shortest path problem, shortest path

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