You are required to determine the shortest route from station O to S on a networ

Question

You are required to determine the shortest route from station O to S on a network. There are five other stations (call them A, B, C, D, E) that you might pass through on the way. The following table summarizes the distance travelled in kilometers along each arc that directly connects two stations without any intervening stations where a dash indicates that there is no are directly connecting these two stations without going through any other stations. a) Formulate this problem as a shortest-path problem by drawing a network where nodes represent stations, links represent paths, and numbers indicate the length of each link in Km. b) Use the algorithm described the lecture notes to solve this shortest path problem. c) Formulate and solve this problem using Solver.

Explanation / Answer

This is a travelling sales problem under prohinbited assignement problem. From some origins to some destination, there are no root no kilometers is below. For the sake of doing this question, we put the cost is $10000 in order to calculate prohibited assignment problem. If we kept this as zero that values will become least costly,Hence i am choosing a larger number say $10000. The new assignment table will be

This 10000 is large quantity, given in the area where there are no cost

The solution to the assignement, and travelling routes are given below.

Station A B C D E S O 40 60 50 10000 10000 10000 A 10000 10 10000 70 10000 10000 B 10000 10000 20 55 40 10000 C 10000 10000 10000 10000 50 10000 D 10000 10000 10000 10000 10 60 E 10000 10000 10000 10000 10000 80

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