Teaching Notes



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Solutions (continued)


9.




1

4

3







2

5

6




11.




1

2

3

4

5

6

7

8




# of A neighbours

II

I

IIII

II

IIII

II

II

IIII




4

3

1







5

8

6







7

2






















12.




1

2

3

4

5

6

7

8




# of A neighbours

2


3



3



3



1


1


4



3








3

2

4

8

5

1

7

6




13.




1

2

3

4

5

6

7

8

9




# of A neighbours

III



III



II


II



III



II


IIII I



II


III







(a)

(b)

(c)

(d)

(e)




Solutions (continued)


3

1

8

9

7

4

5

2

6





  1. One approach is to first combine the from-to number of trips into a single ‘between’ table. That is, add the trips from I to j to the number of trips from j to i.

Then rank the ‘between’ trips between departments:

1. 2, 4: 90
2. 1, 4: 80
3. 3, 4: 55
4. 2, 3: 40

Next, rank the locations from closest pair down:

A

2?
4?
A

4
B

2?
1?
C




D






, B: 40 metres
B, C: 40 metres
B, D: 50 metres
C, D: 60 metres
A, D: 70 metres
A, F: 80 metres

Finally, assign the pair with highest number of trips between them as close as possible on the floor plan. If there is a tie, use a question mark in front of the assignment, but mark alternate locations. In this case, 2,4 have the highest trip, and they can be in A,B or B,C.

T

1

4

2




3






he next high number of trips are for department 1,4. Given that 2 and 5 can only occupy either the pair of locations A,B or B,C, it follows that department 1 should occupy either A or C. Therefore, department 3 should be assigned to D. The 4th highest number of trips is between 2 and 3. The next closest locations are C and D. Therefore, 2 should be located in C:

Solutions (continued)

15. Pair of No. of Trips / day



departments (Two ways) Rank

1, 2 10


1, 3 5

1, 4 90


1, 5 370 1

1, 6 135 7

1, 7 125 8

1, 8 0


2, 3 360 2

2, 4 120 9

2, 5 40

2, 6 115 11

2, 7 45

2, 8 120 10

3, 4 350 3

3, 5 110 12

3, 6 40

3, 7 20


3, 8 200 4

4, 5 190 5

4, 6 70

4, 7 50


4, 8 190 6

5, 6 10


5, 7 40

5, 8 10


6, 7 50

6, 8 20


7, 8 20
Assign by rank:

1

5?







1

5?







1

5?







1

5?







1

5?







1

5?

6?








1

5?

6?








1

5




5?




3




5?




3




5?

2?

4?


3




5?


2?

4?


3




5?

4

3




5?

6?


4

3




5?

6?


4

3




6

4

3






























2?

4?







8

2?

4?







8

2






8

2




7

8

2




7

8

2
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