C is clearly better than either a or b. This problem illustrates the importance of having good scores on important factors. B has scores that are about as high as those of c, but in the wrong places.
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Weight
Location A
Location B
Location C
Labor Climate
10
35
45
20
Taxes
30
30
40
40
Utilities
20
25
20
45
Wages
40
10
25
25
Total
100
Weighted sum
2150
3050
3300
Weighted average
21.5
30.5
33.0
(Methods of evaluating location alternatives, moderate) {aacsb: Analytic Skills}
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Environmental Glass Products, Inc. wants to build a new centralized facility to receive household, commercial, and industrial glass for recycling. This center will be supplied by trucks coming from four "collection points," where recyclable glass is dropped off by individuals and businesses. The volume and the map coordinates for the four collection centers are shown below. Where should the collection center be located?
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Collection point
Load
(X,Y) Coordinates
A
9,000
(4,8)
B
4,000
(7,2)
C
2,000
(4,1)
D
5,000
(7,3)
The center should be built near coordinates (5.35, 4.85).
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Collection Point
Weight
X coord
Y coord
A
9,000
4
8
B
4,000
7
2
C
2,000
4
1
D
5,000
7
3
Sum
20,000
22
14
Average
5.5
3.5
Weighted Average
5.35
4.85
(Methods of evaluating location alternatives, moderate) {aacsb: Analytic Skills}
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A manufacturer of stamped metal auto parts has four parts factories in one city at the location coordinates shown below. Each coordinate unit represents a city block (roughly 100 meters). The yearly demand at each factory is also given.
-
Factories
Demand
X-Coord.
Y-Coord.
Rayburn Industrial Park
19,000
20
130
Port of Zavalla
3,000
60
40
Henderson Mfg. Center
5,000
70
100
Wax Mills Site
6,000
90
30
Management has decided to build a new sheet metal mill, to supply these factories, at a location central to these plants. What should be the map coordinates of the new plant? On the grid below, graph the locations of the four parts factories and the proposed sheet metal mill.
See solution on next page.
The mill should be located near (44, 99). The center-of-gravity model does not favor any single data point; it is the weighted average of them all. In this case, being central does not mean being close to any single factory, but it is closer to the collection of all four than any other mill location could be.
(Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills}
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A small producer of music boxes wants to move to a larger facility. Two alternative facilities have been found. Site 1 has a fixed cost of $500,000 per year, with a variable cost of $25 per unit. Site 2 has a fixed cost of $800,000 per year, but a variable cost of $22 per unit.
a. Write out the equation for total cost for each site.
b. At what volume of output would the two locations have the same total cost?
c. For what range of output would Site 1 be superior?
d. For what range of output would Site 2 be superior?
(a) The equation for the total cost at site 1 is TC = 500,000 + 25X, where X is volume. The equation for total cost at Site 2 is TC = 800,000 + 22X. (b) Set these two equations equal and solve for X. 500,000 + 25X = 800,000 + 22X leads to 300,000 = 3X, then to X = 100,000. Site 1 is preferred for volumes up to 100,000 units, and site 2 is preferred after 100,000 units.
(Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills}
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A small manufacturer is considering several locations for a new facility. They have identified four factors that they consider to be important for their location decision. They have decided to assign scores to the four factors, with a higher score indicating a more favorable location. Use the information in the following table to perform a factor rating to select the best location.
-
Weight
Location A
Location B
Location C
Wages
40
30
75
90
Labor Climate
30
40
70
40
Taxes
15
80
40
90
Utilities
15
75
60
10