Matthew W Ford

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## Location & Layout Practice Problems (Updated 02/24/2007 06:43 PM)

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.

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