In 1862, during the second year of the Civil War, General Thomas J. “Stonewall”
ID: 369209 • Letter: I
Question
In 1862, during the second year of the Civil War, General Thomas J. “Stonewall” Jackson fought a military campaign in the Shenandoah Valley in Virginia. One of his victories was at the Battle of McDowell. (a) Determine the shortest route from Winchester (node 1) to McDowell (node 14) by solving the problem by hand (show the work: the permanent set at all the iterations, and the list of available branches at the first two and last two iterations). (b) How many days will the army take to get to the destination, McDowell based on the solution in (a)? (c) Formulate an integer programming model for this problem. (d) Find the optimal path in (c) by using the computer, and compare it with the path in (a). (e) What is the new optimal path to McDowell if the path from Winchester to Moorefield were blocked due to a landslide? (f) What is the new optimal path to McDowell if his army couldn’t approach to Franklin because of epidemics in the village?
Romney Winchester Moorefield Strasburg Mount Jackson Front Royal Franklin Woodstock New Market 5 McDowell Luray 14 10 Harrisonburg 2 12 13 Port Republic StauntonExplanation / Answer
For shortest path we are required to list the branches, nodes and length of branches as follows:
Distance is in terms of days, therefore it will take 15 days to reach McDowell(14) from Winchester(1)
Start node End node Distance Branch 1 1 2 2 Branch 2 1 3 3 Branch 3 1 4 2 Branch 4 1 5 5 Branch 5 2 3 2 Branch 6 3 4 3 Branch 7 3 11 9 Branch8 4 5 3 Branch 9 4 6 2 Branch 10 5 8 5 Branch 11 6 7 1 Branch 12 7 9 2 Branch 13 8 9 3 Branch14 8 12 2 Branch15 9 10 3 Branch16 10 11 11 Branch17 10 13 4 Branch18 11 14 3 Branch19 12 13 3 Branch 20 0 0 0