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For the network below, the objective is to find the length of the shortest path from node P to node G. Let d_ij be the length of directed arc from node i to node j. Let s_j be the length of the shortest path from P to node j. Which of the following equations can be used to find s_G?

1. s_G = Min{s_O, s_R}
2. s_G = Min{s_O - d_OG, s_R - d_RG}
3. s_G = Min{s_O + d_OG, s_R + d_RG}
4. s_G = Min{d_OG, d_RG}

Correct answer: s_G = Min{s_O + d_OG, s_R + d_RG}

Solution

This option correctly represents the shortest path to node G by considering the shortest paths to its predecessors (O and R) and adding the respective arc lengths from those nodes to G, ensuring that all possible routes are evaluated.

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