An Insurance Claims Processing Center Has Six Work Centers, Any

Essay

An insurance claims processing center has six work centers, any of which can be placed into any of six physical departmental locations. Call the centers 1, 2, 3, 4, 5, and 6, and the departments A, B, C, D, E, and F. The current set of assignments is A-3, B-1, C-6, D-2, E-4, and F-5.
The (symmetric) matrix of departmental distances, in meters is
$$\begin{array} { | c | c | c | c | c | c | c | } \hline & \mathbf { 1 } & \mathbf { 2 } & \mathbf { 3 } & \mathbf { 4 } & \mathbf { 5 } & \mathbf { 6 } \\\hline \mathbf { 1 } & - - & 5 & 30 & 20 & 15 & 20 \\\hline \mathbf { 2 } & & - - & 40 & 15 & 10 & 10 \\\hline \mathbf { 3 } & & & - - & 50 & 20 & 5 \\\hline \mathbf { 4 } & & & & - - & 10 & 35 \\\hline \mathbf { 5 } & & & & & - - & 5 \\\hline \mathbf { 6 } & & & & & & - - \\\hline\end{array}$$
The matrix of work flow (estimated trips per day) is among centers
$\begin{array}{|c|c|c|c|c|c|c|} \hline& A & \mathrm{~B} & \mathrm{C} & \mathrm{D} & \mathrm{E} & \mathrm{F} \\\hline \mathrm{A} & -- & 15 & 20 & 0 & 30 & 0 \\\hline \mathrm{B} & 20 & -- & 50 & 0 & 160 & 10 \\\hline \mathrm{C} & 0 & 50 & -- & 30 & 0 & 30 \\\hline \mathrm{D} & 30 & 60 & 20 & -- & 70 & 0 \\\hline \mathrm{E} & 40 & 0 & 0 & 10 & -- & 60 \\\hline \mathrm{F} & 0 & 0 & 30 & 20 & 50 & -- \\\hline\end{array}$
The firm estimates that each trip costs approximately $4.
a. What is the cost of the current assignment?
b. Use trial-and-error to find one improved assignment.
c. What is that assignment, and what is its cost?