Business Location Decisions

1
Business Location Decisions

• Dr. Everette S. Gardner, Jr.

2
Complexity of the location problem

• If there are N potential facility sites, there
  are (2N) 1 different geographical
  configurations.
• Example 4 potential sites (A,B,C,D)
• (24) 1 15
• Number of Number of
• facilities used Alternatives Alternatives
• 1 A,B,C,D 4
• 2 AB, AC, AD, BC,
  6
• BC, CD
• 3 BC, ABD, ACD, 4
• BCD
• 4 ABCD 1
• 15

3
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 gt 105
• 100 gt 1030

4

• 
  100
• 
  Customer service level ()
• 
  
• Total distribution costs
• 
  
  
• Transportation costs
• 0
  0
• Number of warehouses ?
• Cost-service tradeoffs
• in logistics planning

Customer service axis of demand filled
within given time frame
Dollar cost axis
Inventory costs
Fixed facility costs
5
Analog model for facility location
Center.xls
6
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

7
Building a dimensional analysis model

• List the decision factors
• 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
• Weight each decision factor (scale of 1 to 5)
• Compute weighted ratios
• (Score for option A / Score for option B)Weight
• Compute preference number
• Product of weighted ratios

Dimensional.xls
8
Basic calculations in dimensional analysis U.S.
Air vs. Alaska airlines
9
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

10
Break-even analysis (cont.)

• 
  
  Sales revenue
• Profit
• 
  
• 
  
• 
  
• 
  
• 1000 2000 3000 4000
  5000
• Units of output

Total costs
Break- even point
Variable costs
Fixed costs
Losses
11
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

12
Determining market areas (cont.)

• Market boundaries are at points where lines of
  equal LDC intersect
• 
  
• 
  
• 
  
• 
  
  
• 
  
• 
  
  
• 
  
• 
  

x
C
2
4
6
N
A
8
y
2
4
6
B
8
2
z
4
6
13
LP models for location decisions

• Simple transportation model
• Sources ? Destinations

14
LP models for location decisions (cont.)

• Transshipment model
• Sources ? Transshipment ? Destinations
• points
• Both models can be used to plan shipments over
  multiple time periods

15
Preliminary steps in locating service outlets

• Group population into geographic areas (usually
  use census blocks)
• 2. Use demographic data to determine probable
  facility usage for each potential location
• 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

16

Y
20
7
6
11
21
2
10
3
1
8
5
10
City A
22
15
4
9
23
13
12
10
26
20
-10
18
X
14
17
25
30
19
29
32
31
20
16
24
27
26
City B
-10
City C
17
TABLE 12Location coordinates in miles for three
criteriaand 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 center
• 1 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.

18
TABLE 12Location coordinates in miles for three
criteriaand 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 -3.08
• 2 -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
  -3.19
• 4 -11.62
  3.24
• 5 11.04
  -2.00
• See figures 7 and 8 for locations of
  coordinates.

19

• City
  A
• 
  
• 
  Center
• 
  
  
• 
  
  Criterion governing
• center locations
• 
  
• 
  

3
15
10
5
2
-5
5
10
15
20
25
-15
-10
-5
1
-10
City B
City C