The Flow and Distance Data in the Table Below Were

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?
$$\begin{array} { | c | c | c | c | c | c | } \hline \text { Flow Table } & \text { A } & \text { B } & \text { C } & \text { D } & \begin{array} { c } \text { Fixed } \\\text { room }\end{array} \\\hline \text { A } & 0 & 5 & 8 & 3 & \\\hline \text { B } & 0 & 0 & 7 & 6 & \\\hline \text { C } & 0 & 2 & 0 & 9 & \\\hline \text { D } & 5 & 12 & 4 & 0 & \\\hline & & & & & \\\hline \text { Distance Table } & \text { Room } 1 & \text { Room } 2 & \text { Room } 3 & \text { Room } 4 & \\\hline \text { Room } 1 & 0 & 30 & 60 & 80 & \\\hline \text { Room } 2 & 30 & 0 & 30 & 50 & \\\hline \text { Room } 3 & 60 & 30 & 0 & 20 & \\\hline \text { Room } 4 & 80 & 50 & 20 & 0 & \\\hline\end{array}$$