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7/29/2019 2 Business Location
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Business Location Decisions
Dr. Everette S. Gardner, Jr.
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Business Location 2
Complexity of the location problem
If there are N potential facility sites, there are (2^N) 1different geographical configurations.
Example: 4 potential sites (A,B,C,D)
(2^4) 1 = 15
Number of Number of
facilities used Alternatives Alternatives1 A,B,C,D 4
2 AB, AC, AD, BC, 6
BC, CD
3 BC, ABD, ACD, 4
BCD
4 ABCD 1
15
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Complexity of the location problem(cont.)
Number of Number of alternative
potential sites geographical configurations
5 31
10 1,023
20 1,048,575
50 > 10^5
100 > 10^30
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Business Location 4
100%
Customer service level (%)
Total distribution costs
Transportation costs
0 0Number of warehouses
Cost-service tradeoffsin logistics planning
Customerserviceaxis:
%o
fdeman
dfilledwithin
giventimeframe
Dollarcostaxis
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Business Location 5
Analog model for facility location
Center.xls
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Dimensional analysis in locationdecisions
Location decisions are based on two typesof information:
Tangibles (objective or quantitative)
Intangibles (subjective) Dimensional analysis helps:
Measure and evaluate intangibles
Combine tangible and intangiblemeasurements into an overall value index foreach location
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Building a dimensional analysis model
1. List the decision factors2. Score the decision factors:
Natural units for tangible factors (usually financial)
Subjective scores for intangibles, scale of 1 to 10
1 represents the ideal
10 represents a disaster
3. Weight each decision factor (scale of 1 to 5)
4. Compute weighted ratios
(Score for option A / Score for option B)^Weight
5. Compute preference number
Product of weighted ratios
Dimensional.xls
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Basic calculations in dimensional
analysis: U.S. Air vs. Alaska airlines
On-Time Denied Mishandled Customer
Arrival % Boardings Baggage Complaints
US Airways 0.782 0.34 3.86 1.87
Alaska Airlines 0.690 1.36 3.00 1.27
Ratio (US Air/Alaska) 1.13 0.25 1.29 1.47
Weight 8.63 -8.03 -7.92 -7.17
RatioWeight 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 Total fixed costs
point = Unit Variable cost
in units 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.)
$
Sales revenue
Profit
1000 2000 3000 4000 5000
Units of output
0
20000
40000
60000
80000
100000
Totalcosts
Variablecosts
FixedcostsLosses
Break-evenpoint
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Determining market areas
Laid down costs are the delivered costs of a
product.
LDC = P + RX
WhereP = Production cost/unit
R = Transportation rate
X = Distance
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Determining market areas (cont.)
Market boundaries are at points where lines ofequal LDC intersect:
A
$2
$4$6
$8
x
y
z$4
$2
$6
B
C
$2$4
$6$8
N
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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 Destinationspoints
Both models can be used to plan shipments over multipletime periods
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Preliminary steps in locating serviceoutlets
1. Group population into geographic areas (usually usecensus blocks)
2. Use demographic data to determine probable facilityusage for each potential location
3. Choose objective function:
A. Maximize utilization
B. Minimize distance per capita
C. Minimize distance per visitD. Minimize average reduction in number of
visits made due to location decision
E. Weighted measures
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Figure 7. A hypothetical medical service area with 32 census blocks andthree cities. City populations are (approximately) A = 17,000, B = 9,000,and C = 13,000. Distances on x-y axes are in miles.
67
11
10
20
Y
X
-10
21
22
23
-10 10 2620
2
35 1
4
9
13
City A 108
15
12 18
14 2530
17
19
2029
32 3116 24
26 27
City C
City B
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TABLE 12Location coordinates in miles for three criteria
and different numbers of centers*
Criterion
Center number (1) Maximize (2) Minimize distance (4) Minimize distance
utilization per capita per encounter
x y x y x y
I With 1 center1 21.00 -3.00 0.64 1.20 -8.70 10.10
II With 2 centers
1 21.4 -3.7 17.6 -3.30 18.50 -3.30
2 -9.89 10.4 9.89 10.4 -9.90 10.40
III With 3 centers
1 22.40 -3.1 21.52 -2.78 22.30 -3.20
2 -10.16 10.40 -10.20 10.40 -10.20 10.40
3 3.63 -2.75 3.60 -2.80 3.60 -2.80
* See figures 7 and 8 for locations of coordinates.
** Determined only for the first criterion.
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TABLE 12Location coordinates in miles for three criteria
and different numbers of centers* (cont.)
Criterion
Center number (1) Maximize (2) Minimize distance (4) Minimize distance
utilization per capita per encounter
x y x y x y
IV With 4 centers
1 22.40 -3.14 22.00 -3.50 21.23 -3.082 -10.20 10.40 -10.10 10.30 -9.80 10.40
3 3.59 -2.78 2.69 -4.80 3.61 - 2.70
4 11.32 -2.25 3.76 3.04 -11.35 3.00
V With 5 centers**
1 22.40 -3.10
2 -9.72 10.61
3 3.24 -3.194 -11.62 3.24
5 11.04 -2.00
* See figures 7 and 8 for locations of coordinates.
** Determined only for the first criterion.
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CityA
Center
Criterion governingcenter locations
Figure 8. Location of one center based on three different criteria.
3
2
1
15
-5
-10 City B
City C
10
5
-15 -10 -5 5 10 15 20 25