Supply Chain
Management
Facility Location
Techniques
Facilities
Plants
 Warehouses
 Distribution centers
 Service centers
 Retail operations
 Public Service Facilities

Types Of Facilities

Heavy manufacturing
auto plants, steel mills, chemical plants

Light industry
small components manufacturing, assembly
Warehouse & distribution centers
 Retail & service
 Public sector

Factors In Heavy Manufacturing
Location
Construction costs
 Land costs
 Raw material & finished goods shipment
modes
 Proximity to raw materials
 Utilities
 Labor availability

Factors In Light Industry Location
Construction costs
 Land costs
 Easily accessible geographic region
 Education & training capabilities
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Factors In Warehouse Location

Transportation costs

Proximity to markets
Factors In Retail Location

Proximity to customers

Location is everything
Global Location Factors
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Government stability
Government regulations
Political & economic systems
Economic stability & growth
Exchange rates
Culture
Climate
Export import regulations
Duties & tariffs
Raw material availability
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Number and proximity of
suppliers
Transportation & distribution
system
Labor cost & education
Available technology
Commercial travel
Technical expertise
Cross-border trade regulations
Group trade agreements
Regional Location Factors 1
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Labor (availability,
education, cost & unions)
Proximity of customers
Number of customers
Construction/leasing costs
Land costs
Modes and quality of
transportation
Transportation costs
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Incentive packages
Governmental regulations
Environmental regulations
Raw material availability
Commercial travel
Climate
Infrastructure
Quality of life
Regional Location Factors 2
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Community government
Local business regulations
Government services
Business climate
Community services
Taxes
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Availability of sites
Financial Services
Community inducements
Proximity of suppliers
Education system
Site Location Factors
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Customer base
Construction/leasing
cost
Land cost
Site size
Transportation
Utilities
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Zoning restrictions
Traffic
Safety/security
Competition
Area business climate
Income level
Location Incentives
Tax credits
 Relaxed government regulation
 Job training
 Infrastructure improvement
 Money
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Location Analysis
Selected Techniques & Models
Location Rating Factor
 Median Location
 Center-of-Gravity
 Load-Distance
 Transportation Model
 p-Center Model

Location Rating Factor
Identify important factors
 Weight factors (0.00 - 1.00)
 Subjectively score each factor (0 - 100)
 Sum weighted scores

Location Factor Example
Scores (0 to 100)
Weight Site 1
Location Factor
Labor pool and climate .30
80
Proximity to suppliers
.20
100
Wage rates
.15
60
Community environment .15
75
Proximity to customers .10
65
Shipping modes
.05
85
Air service
.05
50
Site 2 Site 3
65
90
91
75
95
72
80
80
90
95
92
65
65
90
Location Factor Example
Location Factor
Labor pool and climate
Proximity to suppliers
Wage rates
Community environment
Proximity to customers
Shipping modes
Air service
Total Score
Weighted Scores
Site 1 Site 2 Site 3
24.00 19.50 27.00
20.00 18.20 15.00
9.00 14.25 10.80
11.25 12.00 12.00
6.50
9.00
9.50
4.25
4.60
3.25
2.50
3.25
4.50
77.50 80.80 *82.05
Single Facility Location (SFL)
Let wi = the interaction between the new
facility and customer i
 Let di(x,y) = the travel distance from
customer location i to any location (x,y)
 The SFL Model

Minimize
z 
n
 w d ( x, y )
i i
i 1
Distance Measures
Using the Rectilinear Distance measure

di(x,y) = |ai - x| + |bi - y|
 Using the Euclidean Distance measure

di(x,y) = [(ai - x)2 + (bi - y)2]1/2
 Using the Squared Euclidean Distance
measure (Used in Center of Gravity!)

di(x,y) = {[(ai - x)2 + (bi - y)2]1/2}2

SFL with Rectilinear Distance:
Median Problem

Place Existing Facilities in a Non-Decreasing Order of the
Coordinates (x and y, separately)

Find the Cumulative Sum of the Weights and obtain the
Median

The Coordinate which corresponds to the Cumulative Sum
of the Weights just Exceeding the Median point is the
Median Location for the New Facility
Example

Suppose four hospitals are located within a
city at A(10,6), B(8,5), C(4,3), and D(15,6).
Locate a centralized blood-bank facility at
(x, y) that will serve the hospitals. The
number of deliveries to be made per year
between the blood-bank and each hospital
is estimated to be 350, 900, 420, and 1350,
respectively.
Solution
For x*:
Hospital
ai
wi
C
4
420
B
8
900
A
10
350
D
15
1350
Median 3020/2 = 1510
wi
420
1320
1670
3020
x* = 10
Solution
For y*:
Hospital
C
B
A,D
bi
3
5
6
Then, y* = 6
wi
420
900
350+1350
wi
420
1320
3020
SFL with Squared Euclidean
Distance: Center-of-Gravity
Problem
Locate facility at center of geographic area
 Based on weight & distance traveled
 Establish grid-map of area
 Identify coordinates & weights shipped for
each location

Grid-Map And Coordinates
y
n
xW
i
2 (x2, y2), W2
x=
1 (x1, y1), W1
W
i=1
3 (x3, y3), W3 where,
x1
n
i
y3
x2
yW
i
i
i=1
y2
y1
n
x3
x
i
i=1
y=
n
W
i
i=1
x, y = coordinates of the new
facility at center of gravity
xi, yi = coordinates of existing
facility i
Wi = annual weight shipped
from facility i
Center-of-Gravity Example
y
X
Y
Wt
700
C
600
500
400
B
o
300
200
Center
D
A
100
0
100 200 300 400 500 600 700 x
A
200
200
75
B
100
500
105
C
250
600
135
D
500
300
60
Calculating Center-of-Gravity
n
xW
i
i
i=1
x=
=
n
W
(200)(75) + (100)(105) + (250)(135) + (500)(60)
75 + 105 + 135 + 60
= 238
i
i=1
n
yW
i
i
i=1
y=
n
W
i
i=1
=
(200)(75) + (500)(105) + (600)(135) + (300)(60)
75 + 105 + 135 + 60
= 444
Load-Distance Technique
Compute (Load x Distance) for each site
 Choose site with lowest (Load x Distance)
 Distance can be actual or straight-line

Load-Distance Calculations
n
LD =
 ld
i
i
i=1
where,
LD =
the load-distance value
li
the load expressed as a weight, number of trips or units
being shipped from the proposed site and location i
the distance between the proposed site and location i
=
di
=
di
=
(xi - x)2 + (yi - y)2
where,
(x,y) =
coordinates of proposed site
(xi , yi) = coordinates of existing facility
Load-Distance Example
Potential Sites
Site X
Y
1
360 180
2
420 450
3
250 400
X
Y
Wt
A
200
200
75
Suppliers
B
C
100 250
500 600
105 135
D
500
300
60
Compute distance from each site to each supplier
Site 1 dA =
(xA - x1)2 + (yA - y1)2
=
(200-360)2 + (200-180)2 = 161.2
dB =
(xB - x1)2 + (yB - y1)2
=
(100-360)2 + (500-180)2 = 412.3
dC = 434.2
dD = 184.4
Site 2 dA = 333
dB = 323.9 dC = 226.7 dD = 170
Site 3 dA = 206.2 dB = 180.4 dC = 200
dD = 269.3
Compute load-distance
n
LD =
 ld
i
i
i=1
Site 1 = (75)(161.2) + (105)(412.3) + (135)(434.2) + (60)(434.4) = 125,063
Site 2 = (75)(333) + (105)(323.9) + (135)(226.7) + (60)(170) = 99,789
Site 3 = (75)(206.2) + (105)(180.3) + (135)(200) + (60)(269.3) = 77,555*
* Choose site 3
Transportation Model
M different sources
 N different customers
 Si represents the capacity at source i
 Dj represents the demand of customer j
 cij is the cost per unit to produce the product
at source i and send it to customer j

Transportation Model
xij = number of units to be shipped from
source i to customer j
 The objective is to determine the minimum
cost production and distribution plan for a
given set of facilities

Mathematical Formulation of the
Transportation model
Minimize 
M
N
cx
ij ij
i 1
j 1
N
Subject to
x
ij
 Si , for each factory i
ij
 Dj , for every customer j
j 1
M
x
i 1
The Transportation Model

Ship items at lowest cost

Sources have fixed supplies

Destinations have fixed demand
1
Transportation Problem
Grain Elevator
Supply
1. Kansas City
2. Omaha
3. Des Moines
150
175
275
600 tons
Mill
Demand
A. Chicago
B. St. Louis
C. Cincinnati
200
100
300
600 tons
2
Shipping Cost Table
Grain
Elevator
Kansas City
Omaha
Des Moines
Chicago
A
$6
7
4
Mill
St. Louis
B
$8
11
5
Cincinnati
C
$10
11
12
3
The Transportation Tableau
To
From
Chicago
St. Louis Cincinnati
6
8
10
7
11
11
4
5
12
Kansas City
Omaha
Supply
150
175
275
Des Moines
Demand
200
100
300
600
4
Network Of Routes
4
Des Moines (275)
12
5
7
Chicago (200)
11
Omaha (175)
Cincinnati (300)
11
6
10
Kansas City (150)
8
St. Louis (100)
5
Solving Transportation Problems

Manual methods
Stepping-stone
Modified distribution (MODI)

Computer solution
Excel
POM for Windows
6
Solution For Grain Shipment
Elevator
Kansas City
Omaha
Des Moines
Demand
Shipped
Cost
Chicago
25
0
175
200
200
Mill
St. Louis Cincinnati Supply Shipped
0
125
150
150
0
175
175
175
100
0
275
275
100
300
600
100
300
4525
7
A Solution
Example S9.1: The Transportation Method
Mills
Grain
Grain Elevators Chicago St. Louis Cincinnati Supply Shipped
Kansas City
Omaha
Des Moines
Demand
Grain Shipped
Cost
0
25
175
200
200
4525
0
0
100
100
100
150
150
0
300
300
150
175
275
600
150
175
275
8
Unbalanced Problems
Location
A. Charlotte
B. Raleigh
C. Lexington
D. Danville
Capacity(tons)
90
50
80
60
280
Location
Demand (tons)
1. Richmond
120
2. Winston-Salem
100
3. Durham
110
330
9
Shipping Costs
From
A
B
C
D
1
$70
120
70
90
To
2
$100
90
30
50
3
$50
40
110
70
10
Transportation Solution Tableau
To
From
WinstonRichmond Salem
500
100
120
90
30
40
50
50
110
80
Lexington
90
80
50
Danville
40
20
Demand
120
100
Cost
90
20
70
Supply
50
90
Charlotte
Raleigh
Durham
70
60
110
15900
11
Public Service Facility Location
Model: p-Center Model
Let :
yi = 1, if a facility is opened at site j;
0, otherwise
xij = 1, if people at location j are assigned to the facility at site i;
0, otherwise
w = the maximum distance between any customer and the
serving (closest) facility
p-Center Model
Minimize
z  w
St
M

yi  p
i 1
M
x
ij
 1

for every customer j = 1, … , N
ij
 Nyi

for every site i = 1, … , M
 w

for every customer j = 1, … , N
i 1
N
x
j 1
M
dx
ij ij
i 1