2. Given the location information and volume of material movements from a distribution center to several retail outlets (Table 2), find the best location using the center-of-gravity method.

Table 2: Location and Demand Data for Retail Sites

Solution:

For center-of-gravity,

Best location in a direction is TVZ / TV

Where

T=transportation cost per unit

V=volume of material moved

Z=coordinate in the direction being evaluated

Note that in this case, there is no difference in transportation costs, so assume T=1 for all.

Remember, secret is to evaluate one direction at a time.

In x direction:

[1*1200*20+1*2500*18+1*1600*3+1*1100*3+1*2000*10]/[1*1200+1*2500+1*1600+1*1100+1*2000]

=11.6

Similarly, in y direction=13.5

Locate at (11.6,13.5)

3.  Refer to Table 3 and Figures 1 and 2.  Given the layout of departments, the frequency of movements among them, and the distance between them, determine if less materials handling is achieved by switching departments D and F.  Assume diagonal distances to be two unitis and horizontal/vertical distances between adjacent departments to be one unit.

Table 3: Frequency of Movements Among Departments

Use CVD method, and assume costs are the same throughout (C=1)

From A to other departments in current layout, CVD=10 trips*1 unit/trip + 0 + 2*5 + 5*2 + 10*3 = 60

Similar calculations for other departments yield:

B=50

C=34

D=37

E=40

F=35

Total distance traveled=60+50+34+37+40+35=256 units

Using same method and distance relationships of proposed layout:

A=55

B=50

C=38

D=49

E=45

F=25

Total distance traveled=55+50+38+49+45+25=262 units

Since more distance is required in the proposed layout, keep current layout.

NOTE:  These problems are adapted from Evans, J.R. (1997). Production/Operations Management, 5th ed. Minneapolis/St. Paul: West.