The Flow and Distance Data in the Table Below Were

question 104

Essay

The flow and distance data in the table below were input into a layout software program, and solved by "pairwise comparison." That solution called for assignments A-4, B-1, C-3, and D-2, with a total movement of 2430. Verify that result. Is that solution optimal?
Can you offer an improved solution?
What is the total movement of your alternate solution?
$\begin{array}{|l|r|r|r|r|r|}\hline&&&&& \text { Fixed } \\\text { Flow Table } & \text { A } & \text { B } & \text { C } & \text { D } &\text{room}\\\hline\mathrm{A} & 0 & 5 & 8 & 3 \\\hline \mathrm{B} & 0 & 0 & 7 & 6 \\\hline \mathrm{C} & 0 & 2 & 0 & 9 \\\hline \mathrm{D} & 5 & 12 & 4 & 0 \\\hline & & & & \\\hline \text { Distance } & & & & \\\text { Table } & \text { Room 1 } & \text { Room 2 } & \text { Room 3 } & \text { Room 4 } \\\hline \text { Room 1 } & 0 & 30 & 60 & 80 \\\hline \text { Room 2 } & 30 & 0 & 30 & 50 \\\hline \text { Room 3 } & 60 & 30 & 0 & 20 \\\hline \text { Room 4 } & 80 & 50 & 20 &0\\\hline\end{array}$

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