1. Facility Location Decisions
Chapter 13
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2. Facility Location in Location Strategy
PLANNING
ORGANIZING
CONTROLLING
Transport Strategy •
Transport fundamentals
Transport decisions
Customer
service goals
The product
Logistics service
Ord
. proc. & info. sys.
Inventory Strategy
Forecasting
Inventory decisions
Purchasing and supply
scheduling decisions
Storage fundamentals
Storage decisions
Location Strategy
Location decisions
The network planning process
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3. Location Overview What's located? Sourcing points Plants Vendors Ports
Intermediate points
Warehouses
Terminals
Public facilities (fire, police, and ambulance stations)
Service centers
Sink points
Retail outlets
Customers/Users
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4. Location Overview (Cont’d)
Key Questions
How many facilities should there be?
Where should they be located?
What size should they be?
Why Location is Important
Gives structure to the network
Significantly affects inventory and transportation costs
Impacts on the level of customer service to be achieved
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5. When to Analyze Location
Changing service requirements
Partnerships
Shifting locations (customer/supplier)
Changing corporate ownership
Cost pressure
Global markets
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6. Nature of Location Analysis
Manufacturing (plants & warehouses)
Decisions are driven by economics. Relevant costs such as transportation, inventory carrying, labor, and taxes are traded off against each other to find good locations.
Retail
Decisions are driven by revenue. Traffic flow and resulting revenue are primary location factors, cost is considered after revenue.
Service
Decisions are driven by service factors. Response time, accessibility, and availability are key dimensions for locating in the service industry.
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7. Location Overview (Cont’d)
Methods of Solution
Single warehouse location
Graphic
Grid, or center-of-gravity, approach
Multiple warehouse location
Simulation
Optimization
Heuristics
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8. Optimization Method Finding solution can be challenging
But with the advent of fast PCs, it is more widely used these days
Model formulation
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9. COG Method Method appraisal A continuous location method
Locates on the basis of transportation costs alone
The COG method involves
Determining the volumes by source and destination point
Determining the transportation costs based on $/unit/mi.
Overlaying a grid to determine the coordinates of source and/or destination points
Finding the weighted center of gravity for the graph
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10. COG Method (Cont’d) where Vi = volume flowing from (to) point I
Ri = transportation rate to ship Vi from (to) point i
Xi,Yi = coordinate points for point i
= coordinate points for facility to be located
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11. COG Method (Cont’d)
Example Suppose a regional medical warehouse is to be established to serve several Veterans Administration hospitals throughout the country. The supplies originate at S1 and S2 and are destined for hospitals at H1 through H4. The relative locations are shown on the map grid. Other data are:
Note rate is a
per mile cost
Point i
Prod-
ucts
Location
Annual
volume,
cwt.
Rate, $/
cwt/
mi. X Y
1 S 1 A
Seattle
8,000
0.02
0.6
7.3
2 S 2 B
Atlanta
10,000
8.6
3.0
3 H
A & B
Los
Angeles
5,000
0.05
2.0
4 H
Dallas
3,000
5.5
2.4
5 H 3
Chicago
4,000
7.9
6 H 4
New York
6,000
10.6
5.2
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12. COG Method (Cont’d) Map scaling factor, K
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13. COG Method (Cont’d) Solve the COG equations in table form i X Y V R 1
0.6
7.3
8,000
0.02
160 96
1,168 2
8.6
3.0
10,000
200
1,720
600 3
2.0
5,000
0.05
250
500
750 4
5.5
2.4
3,000
150
825
360 5
7.9
4,000
1,580
1,100 6
10.6
5.2
6,000
300
3,180
1,560
1,260
7,901
5,538
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14. COG Method (Cont’d) Now, = 7,901/1,260 = 6.27 = 5,538/1,260 = 4.40X
= 7,901/1,260 = 6.27 Y
= 5,538/1,260 = 4.40
This is approximately Columbia, MO.
The total cost for this location is found by:
where K
is the map scaling factor to convert
coordinates into miles.
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15. COG Method (Cont’d)
COG
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16. COG Method (Cont’d) Calculate total cost at COG 660,492 0.05 6,000 5.2
10.6 6
196,644
4,000
5.5
7.9 5
160,733
3,000
2.4 4
561,706
5,000
3.0
2.0 3
271,825
0.02
10,000
8.6 2
509,482
8,000
7.3
0.6 1 TC Ri Vi Yi Xi i
Calculate total cost at COG
Total
2,360,882
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17. COG Method (Cont’d) å and is the iteration number. Note
The center-of-gravity method does not necessarily
give optimal answers, but will give good answers if there are
a large numbers of points in the problem (>30) and the
volume for any one point is not a high proportion of the total
volume. However, optimal locations can be found by the
exact center of gravity
method. å = i n /d R V Y , X
where 2 ) (Y (X d - +
and
is the iteration number.
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18. COG Method (Cont’d) Solution procedure for exact COG Solve for COG
Using find di
Re-solve for using exact formulation
Use revised to find revised di
Repeat steps 3 through 5 until there is no change in
Calculate total costs using final coordinates
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19. Multiple Location Methods
A more complex problem that most firms have.
It involves trading off the following
costs: -
Transportation inbound to and outbound from the facilities -
Storage and handling costs -
Inventory carrying costs -
Production/purchase costs -
Facility fixed costs
Subject to: -
Customer service constraints -
Facility capacity restrictions
Mathematical methods are popular for this type of problem
that: -
Search for the best combination of facilities to minimize
costs -
Do so within a reasonable computational time -
Do not require enormous amounts of data for the analysis
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20. Multiple COG Formulated as basic COG model
Can search for the best locations for a selected number of sites.
Fixed costs and inventory consolidation effects are handled outside of the model.
A multiple COG procedure
Rank demand points from highest to lowest volume
Use the M largest as initial facility locations and assign remaining demand centers to these locations
Compute the COG of the M locations
Reassign all demand centers to the M COGs on the basis of proximity
Recompute the COGs and repeat the demand center assignments, stopping this iterative process when there is no further change in the assignments or COGs
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21. Examples of Practical COG Model Use
Location of truck maintenance terminals
Location of public facilities such as offices, and police and fire stations
Location of medical facilities
Location of most any facility where transportation cost (rather than inventory carrying cost and facility fixed cost) is the driving factor in location
As a suggestor of sites for further evaluation
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22. Mixed Integer Programming
A method used commercially -
Has good problem scope
Can be implemented on a PC
- Running times may be long and memory
requirements substantial
Handles fixed costs well
Nonlinear inventory costs are not well
handled
A linear programming-like solution procedure can be used (MIPROG in LOGWARE)
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23. Location by Simulation
Can include more variables than typical algorithmic methods
Cost representations can be precise so problem can be more accurately described than with most algorithmic methods
Mathematical optimization usually is not guaranteed, although heuristics can be included to guide solution process toward satisfactory solutions
Data requirements can be extensive
Has limited use in practice
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24. Commercial Models for Location
Features
Includes most relevant location costs
Constrains to specified capacity and customer service levels
Replicates the cost of specified designs
Handles multiple locations over multiple echelons
Handles multiple product categories
Searches for the best network design
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25. Commercial Models (Cont’d)
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13-46

26. Retail Location Methods Contrasts with plant and warehouse location. -
Contrasts with plant and warehouse location. -
Revenue rather than cost driven
Factors other than costs such as parking, nearness to competitive
outlets, and nearness to customers are dominant
Weighted checklist
Good where many subjective factors are involved
Quantifies the comparison among alternate locations
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27. A Hypothetical Weighted Factor Checklist for a Retail Location Example
(1)
(2)
(3)=(1)
(2)
Factor
Weight
Factor Score
Weighted
(1 to 10) a
Location Factors
(1 to 10) b
Score 8
Proximity to competing stores 5 40 5
Space rent/lease
considerations 3 15 8
Parking space 10 80 7
Proximity to complementary 56
stores 8 6
Modernity of store space 9 54 9
Customer accessibility 8 72 3
Local taxes 2 6 3
Community service 4 12 8
Proximity to major
transportation arteries 7 56
Total index
391
13-48
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28. å Retail Location (Cont’d) E P C S T = / · Huff's gravity model -
A take
off on Newton's law of gravity.
"Mass" or retail "variety" attracts customers, and the distance from
customers repels them.
The basic model is: E P C S T ij i j a = å /
where
expected demand from population cen
ter
that will be attracted to
retail location
probability of customers from point
traveling to retail location
customer demand at point
size of retail location
travel time between customer location
and retail locati on n
number of competing locations
an empirically estimated parameter
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29. Retail Location (Cont’d)
Solution matrix
Time from S / T 2 2 P = j ij S / T E P C ij i =
Custo -
Customer T 2 i ij å S / T 2 j ij ij j ij
mer i
to Location j j A B A B A B A B A B C
30.0
56.6
900
320
555
313
0.64
0.36
$6.4
$3.6 1 C
44.7
30.0
2000
900
250
1111
0.18
0.82
0.9
4.1 2 C
36.0
28.3
1300
800
385
1250
0.24
0.76
1.7
5.3 3
Total shopping center sales ($ million)
$9.0
$13.0
13-50
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30. Retail Location (Cont’d)Y 80 70 C R 2 B 60 50 C 3
Time (minutes) 40 30 C R 1 A 20 10 X
Time (minutes)
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31. Retail Location (Cont’d)
Location-Allocation Model
Mixed-Integer Programming Example – p.592
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