Location & Layout Problems

1. The data in Table 1 provide the operating costs of 3 possible locations for a new electronic component assembly plant. Which location would minimize total costs given annual production of 50,000 units?

Table 1: Assembly Plant Site Location Info

	Location 1	Location2	Location3
Fixed costs	$110,000	$125,000	$150,000
Direct material cost/unit	8.5	8.4	8.6
Direct labor cost/unit	4.2	3.9	3.7
Overhead/unit	1.2	1.1	1.0
Transport cost/1000 units	800	1,100	950

Solution:

This is like our Sam’s Club example. For 50,000 units:

Cost Component	Site 1	Site 2	Site 3
Fixed costs	$110,000	$125,000	$150,000
Direct material	425,000	420,000	430,000
Direct labor	210,000	195,000	185,000
Overhead	60,000	55,000	50,000
Transport	40,000	55,000	47,500
Total cost	845,000	850,000	862,500

Site 1 looks nice ("locate where it’s cheapest").

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

Retail Outlet	Location East	Location North	Demand (loads)
1	20	5	1,200
2	18	15	2,500
3	3	16	1,600
4	3	4	1,100
5	10	20	2,000

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

	Frequency of Movements to:
From	A	B	C	D	E	F
A	0	10	0	5	5	10
B	5	0	0	5	10	5
C	2	10	0	5	5	1
D	5	10	2	0	5	5
E	10	5	0	0	0	5
F	0	10	5	0	5	0

Figure 1: Current Layout

B	D	F
A	C	E

Figure 2: Proposed Layout

B	F	D
A	C	E

Solution:

Key upfront question: Is this a job or flow layout that we’re dealing with??

The current layout:

B	D	F
A	C	E

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

Proposed layout:

B	F	D
A	C	E

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.