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Looking at the diagram, we see that node 1 is the origin and the nodes 2 and 3 are neighbours to the origin. Among the two nodes, we see that node 2 is at a distance of 40 units from node 1 whereas node 3 is at a distance of 100 units from node 1. The minimum of {40, 100} is 40.

Looking at the diagram, we see that node 1 is the origin and the nodes 2 and 3 are neighbours to the origin. Among the two nodes, we see that node 2 is at a distance of 40 units from node 1 whereas node 3 is at a distance of 100 units from node 1. The minimum of {40, 100} is 40. Thus, the node nearest to the origin is node 2, with a distance of 40 units. So, out of the two nodes 2 and 3, we select node 2. We form a set of nodes {1, 2} and construct a path connecting the node 2 with node 1 by a thick line and mark the distance of 40 in a box by the side of node 2. This first iteration is shown in the following diagram.

Now we search for the next node nearest to the set of nodes {1, 2}. For this purpose, consider those nodes which are neighbours of either node 1 or node 2. The nodes 3, 4 and 5 fulfill this condition. We calculate the following distances.

The distance between nodes 1 and 3 = 100.

The distance between nodes 2 and 3 = 35.

The distance between nodes 2 and 4 = 95.

The distance between nodes 2 and 5 = 65.

Minimum of {100, 35, 95, 65} = 35.

Therefore, node 3 is the nearest one to the set {1, 2}. In view of this observation, the set of nodes is enlarged from {1, 2} to {1, 2, 3}. For the set {1, 2, 3}, there are two possible paths, viz. Path 1 → 2 → 3 and Path 1 → 3 →2. The Path 1 → 2 → 3 has a distance of 40 + 35 = 75 units while the Path 1 → 3 → 2 has a distance of 100 + 35 = 135 units.

Minimum of {75, 135} = 75. Hence we select the path 1 → 2 → 3 and display this path by thick edges. The distance 75 is marked in a box by the side of node 3. We obtain the following diagram at the end of Iteration No. 2.

We repeat the process. The next node nearest to the set {1, 2, 3} is either node 4 or node 5.

Node 4 is at a distance of 95 units from node 2 while node 2 is at a distance of 40 units from node 1. Thus, node 4 is at a distance of 95 + 40 = 135 units from the origin.

As regards node 5, there are two paths viz. 2 → 5 and 3 → 5, providing a link to the origin. We already know the shortest routes from nodes 2 and 3 to the origin. The minimum distances have been indicated in boxes near these nodes. The path 3 → 5 involves the shortest distance. Thus, the distance between nodes 1 and 5 is 95 units (20 units between nodes 5 and 3 + 75 units between node 3 and the origin). Therefore, we select node 5 and enlarge the set from {1, 2, 3} to {1, 2, 3, 5}. The distance 95 is marked in a box by the side of node 5. The following diagram is obtained at the end of Iteration No. 3.

Now 2 nodes remain, viz., nodes 4 and 6. Among them, node 4 is at a distance of 135 units from the origin (95 units from node 4 to node 2 + 40 units from node 2 to the origin). Node 6 is at a distance of 135 units from the origin (40 + 95 units). Therefore, nodes 4 and 6 are at equal distances from the origin. If we choose node 4, then travelling from node 4

Tags : Operations Management - Network Problems

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