Business Location Decisions
Dr. Everette S. Gardner, Jr.
Complexity of the location problem
• If there are N potential facility sites, there are (2^N) – 1
different geographical configurations.
• Example: 4 potential sites (A,B,C,D)
(2^4) – 1 = 15
Number of
facilities used
1
2
3
4
Alternatives
A,B,C,D
AB, AC, AD, BC,
BC, CD
BC, ABD, ACD,
BCD
ABCD
Business Location
Number of
Alternatives
4
6
4
1
15
2
Complexity of the location problem
(cont.)
● Number of
potential sites
5
10
20
50
100
Number of alternative
geographical configurations
31
1,023
1,048,575
> 10^5
> 10^30
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100%
Customer service axis:
% of demand filled within
given time frame
Customer service level (%)
Dollar cost axis
Total distribution costs
0
Transportation costs
Number of warehouses 
0
Cost-service tradeoffs
in logistics planning
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Analog model for facility location
Business Location
Center.xls
5
Dimensional analysis in location
decisions
• Location decisions are based on two types
of information:
Tangibles (objective or quantitative)
Intangibles (subjective)
• Dimensional analysis helps:
Measure and evaluate intangibles
Combine tangible and intangible
measurements into an overall value index for
each location
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Building a dimensional analysis model
1.
2.
List the decision factors
Score the decision factors:
•
•
3.
4.
Natural units for tangible factors (usually financial)
Subjective scores for intangibles, scale of 1 to 10
1 represents the ideal
10 represents a disaster
Weight each decision factor (scale of 1 to 5)
Compute weighted ratios
(Score for option A / Score for option B)^Weight
5.
Compute preference number
Product of weighted ratios
Business Location
Dimensional.xls
7
Basic calculations in dimensional
analysis: U.S. Air vs. Alaska airlines
US Airways
Alaska Airlines
Ratio (US Air/Alaska)
Weight
RatioWeight
On-Time
Arrival %
0.782
0.690
1.13
8.63
Denied
Boardings
0.34
1.36
0.25
-8.03
Mishandled
Baggage
3.86
3.00
1.29
-7.92
Customer
Complaints
1.87
1.27
1.47
-7.17
2.95
68,319.04
0.14
0.06
Preference number = 2.95 x 68,319.04 x 0.14 x 0.06 = 1,705.48
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Break-even analysis
• Break-even
point
in units
=
Total fixed costs
Unit
Variable cost
price
per unit
Example: FC = $25,000, P = $20, VC = $10
BE = $25,000 = 2,500 units
20 – 10
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Break-even analysis (cont.)
$ 100000
Sales revenue
80000
Profit
Breakeven
point
60000
Variable
costs
40000
20000
0
Total
costs
Fixed
costs
Losses
1000
2000
3000
4000
5000
Units of output
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Determining market areas
• “Laid down costs” are the delivered costs of a
product.
LDC = P + RX
Where
P = Production cost/unit
R = Transportation rate
X = Distance
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Determining market areas (cont.)
• Market boundaries are at points where lines of
equal LDC intersect:
x
C
$2
$4
$6
$8
N
A
$2
$4
$6
$8
y
B
z
$6
$4
$2
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LP models for location decisions
• Simple transportation model
Sources

Destinations
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LP models for location decisions
(cont.)
• Transshipment model
Sources

Transshipment
points

Destinations
• Both models can be used to plan shipments over multiple
time periods
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Preliminary steps in locating service
outlets
1.
Group population into geographic areas (usually use
census blocks)
2.
Use demographic data to determine probable facility
usage for each potential location
3.
Choose objective function:
A. Maximize utilization
B. Minimize distance per capita
C. Minimize distance per visit
D. Minimize average reduction in number of
visits made due to location decision
E. Weighted measures
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Y
20
7
6
11
2
City A
10
3
5 1
21
10
8
22
15
4
9
23
13
12
-10
10
18
14
20
17
25
19
16
20
24
City B
-10
26
X
30
29
32 31
27
26
City C
Figure 7. A hypothetical medical service area with 32 census blocks and
three cities. City populations are (approximately) A = 17,000, B = 9,000,
and C = 13,000. Distances on x-y axes are in miles.
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TABLE 12
Location coordinates in miles for three criteria
and different numbers of centers*
Criterion
Center number
(1) Maximize
utilization
x
I With 1 center
1
II With 2 centers
1
2
III With 3 centers
1
2
3
(2) Minimize distance
per capita
(4) Minimize distance
per encounter
y
x
y
x
y
21.00
-3.00
0.64
1.20
-8.70
10.10
21.4
-9.89
-3.7
10.4
17.6
9.89
-3.30
10.4
18.50
-9.90
-3.30
10.40
22.40
-10.16
3.63
-3.1
10.40
-2.75
21.52
-10.20
3.60
-2.78
10.40
-2.80
22.30
-10.20
3.60
-3.20
10.40
-2.80
* See figures 7 and 8 for locations of coordinates.
** Determined only for the first criterion.
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TABLE 12
Location coordinates in miles for three criteria
and different numbers of centers* (cont.)
Criterion
Center number
(1) Maximize
utilization
x
IV With 4 centers
1
22.40
2
-10.20
3
3.59
4
11.32
V With 5 centers**
1
22.40
2
-9.72
3
3.24
4
-11.62
5
11.04
(2) Minimize distance
per capita
(4) Minimize distance
per encounter
y
x
y
x
y
-3.14
10.40
-2.78
-2.25
22.00
-10.10
2.69
3.76
-3.50
10.30
-4.80
3.04
21.23
-9.80
3.61
-11.35
-3.08
10.40
- 2.70
3.00
-3.10
10.61
-3.19
3.24
-2.00
* See figures 7 and 8 for locations of coordinates.
** Determined only for the first criterion.
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City A
3
15
Center
10
Criterion governing
center locations
5
2
-15
-10
5
-5
10
15
20
25
-5
-10
City B
1
City C
Figure 8. Location of one center based on three different criteria.
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