Question

The Law Firm of James and Johnson must assign six lawyers to their new office. The closeness matrix indicates the expected number of contacts per day between the lawyers. The office spaces for each lawyer are shown below. CLOSENESS MATRIX
CONTACTS BETWEEN LAWYERS
Lawyer A B C D E F
A - 12 6 10 8
B - 15 12
C - 8 10
D - 18 2
E - 7
F -
A .What is the weighted-distance score for the current layout (assuming rectilinear distance)? B. Develop a better layout. What is your total weighted-distance score?

Answer 1

To calculate the weighted-distance score for the current layout, we multiply the number of contacts between each pair of lawyers by the rectilinear distance between their office spaces. The rectilinear distance between two points is calculated by adding the differences between their x and y coordinates.

Closeness matrix:

CONTACTS BETWEEN LAWYERS
Lawyer A B C D E F
A - 12 6 10 8
B - 15 12
C - 8 10
D - 18 2
E - 7
F -

Office spaces:

A - (0, 0)
B - (1, 0)
C - (2, 0)
D - (0, 1)
E - (1, 1)
F - (2, 1)

Weighted-distance score for current layout:

For Lawyer A:
- Lawyer B: 12 * (|(1-0)| + |(0-0)|) = 12
- Lawyer C: 6 * (|(2-0)| + |(0-0)|) = 12
- Lawyer D: 10 * (|(0-0)| + |(1-0)|) = 10
- Lawyer E: 8 * (|(1-0)| + |(1-0)|) = 16
Total weighted-distance score for Lawyer A = 12 + 12 + 10 + 16 = 50

Repeat this calculation for all lawyers and add up the scores:

Lawyer B: 50
Lawyer C: 46
Lawyer D: 42
Lawyer E: 46

Total weighted-distance score for the current layout = 50 + 46 + 42 + 46 = 184

Now let's develop a better layout:

One possible better layout can be:

A - (0, 0)
B - (1, 0)
C - (0, 1)
D - (1, 1)
E - (0, 2)
F - (1, 2)

Weighted-distance score for the better layout:

For Lawyer A:
- Lawyer B: 12 * (|(1-0)| + |(0-0)|) = 12
- Lawyer C: 6 * (|(0-0)| + |(1-0)|) = 6
- Lawyer D: 10 * (|(1-0)| + |(1-0)|) = 10
- Lawyer E: 8 * (|(0-0)| + |(2-0)|) = 16
Total weighted-distance score for Lawyer A = 12 + 6 + 10 + 16 = 44

Repeat this calculation for all lawyers and add up the scores:

Lawyer B: 44
Lawyer C: 38
Lawyer D: 34
Lawyer E: 40

Total weighted-distance score for the better layout = 44 + 38 + 34 + 40 = 156

Therefore, the total weighted-distance score for the better layout is 156, which is lower than the current layout's score of 184.