Question

3. You are asked to determine a location for a recycling depot serving three urban centres. They 1. Smallville, population 2,200, at grid location (5.8, 2.8); 2. Bigburg, population 3,400, at grid location (8.5, 2.1); and 3. Middleton, population 1,900, at grid location (1.8, 7.2). a) Determine the centre of gravity of the three locations. b) It is determined that planners would prefer to have the depot in either Bigburg or Middleton (although it will serve all three centres). Using metropolitan distances, determine the load distance scores for both Bigburg and Middleton and make a recommendation as to which town should have the depot. c) You are asked to provide input on a layout for a new office. The old layout is thought of as being inefficient. You are asked to redesign the layout and evaluate your redesign using load distance scores. The current layout is shown below. The overall shape cannot change; you can merely move the individual departments around. (8 marks) Trips between the different departments are as follows: A-B 6 trips per day, A--C 7, A-D 9,A-E 11 C A 6, C- B 75, C-»D 3, C-*E 10 D-A 6,D-B2, D-C3, D-»E5 E A 6, E-B 5, E-C 3, E D2

Answer 1

(a)

Location (j)	Population (Lj)	Xj	Yj	Lj.Xj	Lj.Yj
Smallvile	2,200	5.8	2.8	12,760	6,160
Bigburg	3,400	8.5	2.1	28,900	7,140
Middleton	1,900	1.8	7.2	3,420	13,680
Total	7,500			45,080	26,980
Cx =	Sum (Lj.Xj) / Sum (Lj) =		6.01
Cy =	Sum (Lj.Yj) / Sum (Lj) =		3.60

As computed, the Center of Gravity is located at (6.01, 3.60)

(b)

From Bignurg
To	Bigburg	Middleton	Smallville	Total
Load	2,200	1,900	3,400
Distance	0	|8.5 - 1.8|+|2.1 - 7.2| = 11.8	|5.8 - 8.5| + |2.8 - 2.1| = 3.4
Load*Distance	0	22,420	11,560	33,980
From Middleton
To	Bigburg	Middleton	Smallville	Total
Load	2,200	1,900	3,400
Distance	|8.5 - 1.8|+|2.1 - 7.2| = 11.8	0	|5.8 - 1.8| + |2.8 - 7.2| = 8.4
Load*Distance	25960	0	28,560	54,520

Total load.distance is minimum for Bigburg (33,980). So, the facility should be located at Bigburg.

(c)

Find the number of trips between each pair of departments (i.e. pair A-B represents the number of trips from A to B and from B to A = 6+7=13) and sort them in descending order.

Between		# trips
B	C	79
A	E	17
A	D	15
A	B	13
A	C	13
C	E	13
B	E	9
B	D	8
D	E	7
C	D	6

Design a layout such that the top pairs (maximum number possible) are adjacent. Such a layout will be:

Assume that the adjacent locations are having 10' distant and only metropolitan movements are possible.

Load-stance score for the given layout

Between		# trips (load)	Distance	Load*Distance
B	C	79	20	1580
A	E	17	30	510
A	D	15	20	300
A	B	13	10	130
A	C	13	10	130
C	E	13	20	260
B	E	9	20	180
B	D	8	10	80
D	E	7	10	70
C	D	6	10	60
			TOTAL	3300

Load-stance score for the improved layout

Between		# trips (load)	Distance	Load*Distance
B	C	79	10	790
A	E	17	10	170
A	D	15	10	150
A	B	13	10	130
A	C	13	20	260
C	E	13	10	130
B	E	9	20	180
B	D	8	20	160
D	E	7	20	140
C	D	6	30	180
			TOTAL	2290

Note that the improvement is from 3300 to 2290.