Question

To determine the shortest path from node A to node Z in a network flow problem with a total of n nodes and m arcs, node A should be assigned a supply/demand value of _____ and node Z should be assigned a supply/demand value of ______.

a) 0; 0
b) 1; -1
c) -1; 1
d) -1; -1

Answer 1

In a network flow problem to determine the shortest path from node A to node Z, node A should have a supply value of 1, and node Z should have a demand value of -1.

Step-by-step explanation:

To determine the shortest path from node A to node Z in a network flow problem with a total of n nodes and m arcs, node A should be assigned a supply/demand value of 1, and node Z should be assigned a supply/demand value of -1. This is because in network flow problems, a supply node outputs a quantity into the network, while a demand node receives a quantity from the network. By setting the supply value at node A to 1, we are indicating the start of a unit flow that must reach node Z, and by setting the demand value at node Z to -1, we indicate that this flow must be absorbed or satisfied at node Z. Hence, the correct answer is option b) 1; -1.