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10/31/2018
Facilities
Location
1Prof.(Dr.) Anil Mishra
What is Plant location
 It refers to the choice of region and the selection of a
particular site for setting up a business or factory.
 But the choice is made only after considering cost and
benefits of different alternative sites.
 It is a strategic decision that cannot be changed once
taken.
10/31/2018 2Prof.(Dr.) Anil Mishra
Reasons for the
Facility Location Decision Arises
10/31/2018
•Changes in the market
•Expansion
•Contraction
•Geographic shift
•Changes in inputs
•Labor skills and/or costs
•Materials costs and/or availability
•Utility costs
•Changes in the environment
•Regulations and laws
•Attitude of the community
•Changes in technology
3Prof.(Dr.) Anil Mishra
Factors Influencing Plant
Location
10/31/2018 4
 General factors
 Specific factors
Prof.(Dr.) Anil Mishra
General factors
10/31/2018 5
1. Availability of land for present and future needs and cost of land and land development and
building etc.
2. Availability of inputs such as labor and raw material, etc.
3. Closeness to the market place
4. Stability of demand
5. Availability of communication facilities
6. Availability of necessary modes of transportation like road, rail, airport, and waterways.
7. Availability of infrastructural facilities such as power, water, financial institutions banks etc.
8. Disposal of waste and effluents and their impact on environment
9. Government support, grant, subsidy, tax structure
10. Availability of housing facilities and recreational facilities.
11. Demographic factors like population, trained man power, academic institutions, standard
of living, income level, etc.
12. Security culture of the society
13. Fuel cost
Prof.(Dr.) Anil Mishra
Specific factors
1. Economic stability of the country and the concern of the
country towards outside investments are to be considered
2. The success of operation of the factory depends upon the cultural
factors, language and cultural differences which can present
operating control and even policy problems. Units of
measurement are also very important in international business.
3. Analysis must be based on the factors like wage rate,
policy, duties, etc.,
4. The Company can set up joint ventures with any leading
local giants that will solve many local problems
10/31/2018 6Prof.(Dr.) Anil Mishra
Types Of Facilities
 Heavy manufacturing
 Auto plants, steel mills, chemical plants
 Light industry
 Small components mfg, assembly
 Warehouse & distribution centers
 Retail & service
10/31/2018 7Prof.(Dr.) Anil Mishra
Factors affecting in Heavy Manufacturing
Location
 Construction costs
 Land costs
 Raw material and finished goods shipment
modes
 Proximity to raw materials
 Utilities
 Labor availability
10/31/2018 8Prof.(Dr.) Anil Mishra
Factors affecting in Light Industry Location
 Construction costs
 Land costs
 Easily accessible geographic region
 Education & training capabilities
10/31/2018 9Prof.(Dr.) Anil Mishra
Factors affecting in Warehouse Location
 Transportation costs
 Proximity to markets
10/31/2018 10Prof.(Dr.) Anil Mishra
Factors affecting in Retail Location
 Proximity to customers
 Location is everything
10/31/2018 11Prof.(Dr.) Anil Mishra
Global Location Factors
 Government stability
 Government regulations
 Political and economic
systems
 Economic stability and
growth
 Exchange rates
 Culture
 Climate
 Export import
regulations, duties and
tariffs
 Raw material availability
 Number and proximity
of suppliers
 Transportation and
distribution system
 Labor cost and
education
 Available technology
 Commercial travel
 Technical expertise
 Cross-border trade
regulations
 Group trade agreements
10/31/2018 12Prof.(Dr.) Anil Mishra
Regional Location Factors
 Labor (availability,
education, cost and
unions)
 Proximity of
customers
 Number of
customers
 Construction/leasing
costs
 Land costs
 Modes and quality
of transportation
 Transportation costs
 Incentive packages
 Governmental
regulations
 Environmental
regulations
 Raw material
availability
 Commercial travel
 Climate
 Infrastructure
 Quality of life
10/31/2018 13Prof.(Dr.) Anil Mishra
Regional Location Factors
 Community
government
 Local business
regulations
 Government
services
 Business climate
 Community services
 Taxes
 Availability of sites
 Financial Services
 Community
inducements
 Proximity of
suppliers
 Education system
10/31/2018 14Prof.(Dr.) Anil Mishra
Site Location Factors
 Customer base
 Construction/
leasing cost
 Land cost
 Site size
 Transportation
 Utilities
 Zoning
restrictions
 Traffic
 Safety/security
 Competition
 Area business
climate
 Income level
10/31/2018 15Prof.(Dr.) Anil Mishra
10/31/2018
Relevant Factors for location in a
nutshell
Market related issues Cost related issues
Market for products and services Wage rates
Raw Material availability Transportation costs
Number and proximity of suppliers Taxes and other tariff issues
Availability of skilled labour
Quality of Infrastructure
Regulatory & Policy issues Other issues
Government & Economic stability Culture
Quality of legal and other institutions Climate
Trading blocks and trading agreementsQuality of Life
16Prof.(Dr.) Anil Mishra
10/31/2018
Location Planning Methods
 One facility – Multiple Candidates
 Location factor rating
 Centre of Gravity Method
 Load Distance Method
 Multiple Facility – Multiple Candidates
 Transportation Model
17Prof.(Dr.) Anil Mishra
10/31/2018
Location factor rating
Steps
 Identify and list down all the relevant factors for the
location decision
 Establish the relative importance of each factor in the
final decision
 Rate the performance of each candidate location using a
rating mechanism
 Compute a total score for each location based on its
performance against each factor and rank them in the
decreasing order of the score
18Prof.(Dr.) Anil Mishra
Example:1
Fuels in region 0 to 330
Power availability and reliability 0 to 200
Labor climate 0 to 100
Living conditions 0 to 100
Transportation 0 to 50
Water supply 0 to 10
Climate 0 to 50
Supplies 0 to 60
Tax policies and laws 0 to 20
Two refineries sites (A and B) are assigned the following range of
point values and respective points, where the more points the
better for the site location.
123
150
54
24
45
4
8
5
5
Major factors for site location
Pt.
Range
156
100
63
96
50
5
4
50
20
Sites
A B
Total pts. 418 544
Best
Site is B
10/31/2018 19Prof.(Dr.) Anil Mishra
Example:2
Labor pool and climate
Proximity to suppliers
Wage rates
Community environment
Proximity to customers
Shipping modes
Air service
LOCATION FACTOR
.30
.20
.15
.15
.10
.05
.05
WEIGHT
80
100
60
75
65
85
50
Site 1
65
91
95
80
90
92
65
Site 2
90
75
72
80
95
65
90
Site 3
SCORES (0 TO 100)
10/31/2018 20Prof.(Dr.) Anil Mishra
Sol.
Labor pool and climate
Proximity to suppliers
Wage rates
Community environment
Proximity to customers
Shipping modes
Air service
LOCATION FACTOR
.30
.20
.15
.15
.10
.05
.05
WEIGHT
80
100
60
75
65
85
50
Site 1
65
91
95
80
90
92
65
Site 2
90
75
72
80
95
65
90
Site 3
SCORES (0 TO 100)
24.00
20.00
9.00
11.25
6.50
4.25
2.50
77.50
Site 1
19.50
18.20
14.25
12.00
9.00
4.60
3.25
80.80
Site 2
27.00
15.00
10.80
12.00
9.50
3.25
4.50
82.05
Site 3
WEIGHTED SCORES
Weighted Score Site 1 = (0.30)(80) = 24
Best
Site is 310/31/2018 21Prof.(Dr.) Anil Mishra
10/31/2018
Example:3
 A manufacturer of garments is actively considering five alternative
locations for setting up its factory. The locations vary in terms of
the advantages that it provides to the firm. Hence the firm
requires a method of identifying the most appropriate location.
Based on a survey of its senior executives the firm has arrived at
six factors to be considered for final site selection. The ratings of
each factor on a scale of 1 to 100 provide this information.
Further, based some detailed analysis of both the qualitative and
quantitative data available for each of the location, the rating for
the locations against each factor has also been arrived at (on a
scale of 0 to 100). Using this information obtain a ranking of the
alternative locations.
Factors Rating
Availability of infrastructure 90
Size of the market 60
Industrial relations climate 50
Tax benefits and concessions 30
Availability of cheap labour 30
Nearness to port 65
Factors Location 1 Location 2 Location 3 Location 4 Location 5
Availability of infrastructure 20 40 60 35 55
Size of the market 30 30 40 60 80
Industrial relations climate 80 30 50 60 50
Tax benefits and concessions 80 20 10 20 20
Availability of cheap labour 70 70 45 50 50
Nearness to port 20 40 90 50 60
Factor Ratings Rating of each locations against the factors
22Prof.(Dr.) Anil Mishra
10/31/2018
Solution
Factors Rating
Relative
weights
Availability of infrastructure 90 0.28
Size of the market 60 0.18
Industrial relations climate 50 0.15
Tax benefits and concessions 30 0.09
Availability of cheap labour 30 0.09
Nearness to port 65 0.20
Sum of all factor ratings 325 1.00
Factors
Relative
weights Location 1 Location 2 Location 3 Location 4 Location 5
Availability of infrastructure 0.28 20 40 60 35 55
Size of the market 0.18 30 30 40 60 80
Industrial relations climate 0.15 80 30 50 60 50
Tax benefits and concessions 0.09 80 20 10 20 20
Availability of cheap labour 0.09 70 70 45 50 50
Nearness to port 0.20 20 40 90 50 60
Overall score for the locations 41.23 37.54 54.77 46.46 56.15
Ranking of the locations 4 5 2 3 1
Overall rating for location 3 = 60*0.28 +
40*0.18 + 50*0.15 + 10*0.09 +
45*0.09 + 90*0.20 = 54.77
23Prof.(Dr.) Anil Mishra
10/31/2018
Centre of Gravity Method
 All the demand points (or the supply points, if raw material is
supplied from several locations) are represented in a Cartesian
coordinate system
 Each demand (or the supply point) will also have weight indicating
the quantum of shipment
 Therefore it is possible to identify the centre of gravity of the
various demand (or supply) points
 Notations:
 The number of demand (or supply) points in the grid map: n
 Co-ordinates of location i in the grid map: (xi,yi)
 Quantum of shipment between existing demand (or supply) point i
and proposed facility: Wi
 Co-ordinates of the center of gravity in the grid map: (XC,YC)




 n
i
i
n
i
ii
C
W
Wx
X
1
1
*)(




 n
i
i
n
i
ii
C
W
Wy
Y
1
1
*)(
24Prof.(Dr.) Anil Mishra
10/31/2018
Example 4.
 A manufacturer of certain industrial component is interested in
locating a new facility in a target market and would like to know
the most appropriate place in the target market to locate the
proposed facility. The manufacturer feels that there are no location
constraints in the target market (i.e. any point in the target
market is good enough).
 There are four supply points A(125,550), B(350,400), C(450,125)
and D(700,300) in the locality that will provide key inputs to the
new facility. A two-dimensional grid map of the target market in
which we would like to locate a new facility with distance
coordinates of the four supply points is available.
 The annual supply from these four points to the proposed facility is
200, 450, 175 and 150 tonnes respectively.
 The situation is graphically shown in the two-dimensional plot in
the figure. While the coordinates in the parentheses show the
distance from the origin of the target map of each of the supply
point, the number that follows is the annual shipment (in tonnes)
from these points to the proposed facility.
 Identify the most appropriate point in the grid map to locate the
new facility.
25Prof.(Dr.) Anil Mishra
10/31/2018
Solution to Example .
Grid Map
100 200 300 400 500 600 700
100
200
300
400
500
600
Distance in Kilometres
DistanceinKilometres
A (125,550), 200
B (350,400), 450
C (450,125), 175
D (700,300), 150
26Prof.(Dr.) Anil Mishra
Example:5
A B C D
x 200 100 250 500
y 200 500 600 300
Wt 75 105 135 60
y
700
500
600
400
300
200
100
0 x700500600400300200100
A
B
C
D
(135)
(105)
(75)
(60)
Miles
Miles
10/31/2018 27Prof.(Dr.) Anil Mishra
Sol.
y
700
500
600
400
300
20
0
100
0 x70050060040030020
0
100
A
B
C
D
(135)
(105)
(75)
(60)
Miles
Miles
A B C D
x 200 100 250 500
y 200 500 600 300
Wt 75 105 135 60x = =
= 238
n
 Wi
i = 1
 xiWi
i = 1
n

n
Wi
i = 1
 yiWi
i = 1
n
y = =
= 444
(200)(75) + (500)(105) + (600)(135) + (300)(60)
75 + 105 + 135 + 60
(200)(75) + (100)(105) + (250)(135) + (500)(60)
75 + 105 + 135 + 60
10/31/2018 28Prof.(Dr.) Anil Mishra
Sol.
A B C D
x 200 100 250 500
y 200 500 600 300
Wt 75 105 135 60
y
700
500
600
400
300
20
0
100
0 x70050060040030020
0
100
A
B
C
D
(135)
(105)
(75)
(60)
Miles
Miles
Center of gravity (238, 444)
10/31/2018 29Prof.(Dr.) Anil Mishra
Question: What is the best location for a new Z-Mobile
warehouse/temporary storage facility considering only
distances and quantities sold per month?
 Example:6
Several automobile showrooms are located according to
the following grid which represents coordinate
locations for each showroom
Showroom No ofZ-Mobile s
s old pe r month
A 1250
D 1900
Q 2300X
Y
A
(100,200)
D
(250,580)
Q
(790,900)
(0,0)
10/31/2018 30Prof.(Dr.) Anil Mishra
10/31/2018
Load Distance Method
 Enables a location planner to evaluate two or more potential
candidates for locating a proposed facility vis-à-vis the demand (or
supply) points
 Provides an objective measure of total load-distance for each candidate
 Notations
 Number of demand (or supply) points in the grid map: n
 Index used for demand (or supply) points: i
 Co-ordinates of demand (or supply) point i in the grid map: (xi,yi)
 Quantum of shipment between demand (or supply) point i and
proposed facility: Wi
 Number of candidates for the proposed facility: m
 Index used for the candidates for the proposed facility: j
 Co-ordinates of candidate j in the grid map: (Xj,Yj)
 Distance measure for Cartesian coordinates between demand (or
supply) point i and a candidate j for the proposed facility: Dij
 The load – distance for candidate j for the proposed facility: LDj
22
)()( jijiij YyXxD 


n
i
iijj WDLD
1
*
31Prof.(Dr.) Anil Mishra
10/31/2018
Example:7
 Consider example .2.
 Suppose the manufacturer came to know that there are constraints in
locating the new facility.
 Based on an initial survey of possible sites for the proposed facility, the
manufacturer identified four candidates.
 The figure has the location coordinates of the four candidates
(numbered 1 to 4).
 What is the best location for the proposed new facility?
Existing Supply Points Candidates for proposed facility
xi yi Wi Xj Yj
A 125 550 200 1 300 500
B 350 400 450 2 200 500
C 450 125 175 3 500 350
D 700 300 150 4 400 200
32Prof.(Dr.) Anil Mishra
10/31/2018
Solution
00.182)50(175()500550()300125()()( 22222
1
2
11  YyXxD AAA
Dij values
1 2 3 4
A 182.00 90.14 425.00 445.11
B 111.80 180.28 158.11 206.16
C 403.89 450.69 230.49 90.14
D 447.21 538.52 206.16 316.23
LDj values
1 2 3 4
224474.41 258801.57 227410.05 245000.8
33Prof.(Dr.) Anil Mishra
10/31/2018
Solution Grid Map
100 200 300 400 500 600 700
100
200
300
400
500
600
Distance in Kilometres
DistanceinKilometres
A (125,550), 200
B (350,400), 450
C (450,125), 175
D (700,300), 150
1 (300,500)
2 (200,500) 3 (500,350)
4 (400,200)
Candidate for proposed facility
Existing Demand (or supply) point
34Prof.(Dr.) Anil Mishra
Example:8
Potential Sites
Site X Y
1 360 180
2 420 450
3 250 400
Suppliers
A B C D
X 200 100 250 500
Y 200 500 600 300
Wt 75 105 135 60
Compute distance from each site to each supplier
= (200-360)2 + (200-180)2dA = (xA - x1)2 + (yA - y1)2Site 1 = 161.2
= (100-360)2 + (500-180)2dB = (xB - x1)2 + (yB - y1)2 = 412.3
dC = 434.2 dD = 184.4
10/31/2018 35Prof.(Dr.) Anil Mishra
sol
Site 2 dA = 333 dC = 226.7dB = 323.9 dD = 170
Site 3 dA = 206.2 dC = 200dB = 180.4 dD = 269.3
Compute load-distance
i = 1
n
 li di
LD =
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
10/31/2018 36Prof.(Dr.) Anil Mishra
10/31/2018
Multi-facility location problem
Transportation Model
 Locating distribution centers for nation-wide
distribution of products is one typical example
belonging to this category
 Decisions variables in a multiple location – multiple
candidate problem
 Identifying k out of n candidates for locating facilities
 Which of the demand points will be served by each of
these locations and to what extent
 the problem is one of managing network flows of
satisfying a set demand points using a combination of
supply points
 The transportation model is ideally suited for solving
this combinatorial optimisation problem
37Prof.(Dr.) Anil Mishra
10/31/2018
Multiple facilities location problem
Transportation table (Example:9)
Market 1 Market 2 Market 3 Market 4 Market 5 Supply
70 40 10 0 0
Warehouse A
2800 100
2900
0 65 0 95 10
Warehouse B
2000 300
2300
55 0 35 20 0
Warehouse C
400 900 2400
3700
0 20 65 65 50
Warehouse D
1100
1100
Demand 2000 1500 1200 2800 2500 10000
Market 1 Market 2 Market 3 Market 4 Market 5 Supply
100 70 50 30 40
Warehouse A 2900
30 95 40 125 50
Warehouse B 2300
75 20 65 40 30
Warehouse C 3700
20 40 95 85 80
Warehouse D 1100
Demand 2000 1500 1200 2800 2500 10000
Problem
Solution using
Vogal’s Approximation
Method (VAM)
38Prof.(Dr.) Anil Mishra
10/31/2018
Thank you
39Prof.(Dr.) Anil Mishra

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Facilty location.2nd

  • 2. What is Plant location  It refers to the choice of region and the selection of a particular site for setting up a business or factory.  But the choice is made only after considering cost and benefits of different alternative sites.  It is a strategic decision that cannot be changed once taken. 10/31/2018 2Prof.(Dr.) Anil Mishra
  • 3. Reasons for the Facility Location Decision Arises 10/31/2018 •Changes in the market •Expansion •Contraction •Geographic shift •Changes in inputs •Labor skills and/or costs •Materials costs and/or availability •Utility costs •Changes in the environment •Regulations and laws •Attitude of the community •Changes in technology 3Prof.(Dr.) Anil Mishra
  • 4. Factors Influencing Plant Location 10/31/2018 4  General factors  Specific factors Prof.(Dr.) Anil Mishra
  • 5. General factors 10/31/2018 5 1. Availability of land for present and future needs and cost of land and land development and building etc. 2. Availability of inputs such as labor and raw material, etc. 3. Closeness to the market place 4. Stability of demand 5. Availability of communication facilities 6. Availability of necessary modes of transportation like road, rail, airport, and waterways. 7. Availability of infrastructural facilities such as power, water, financial institutions banks etc. 8. Disposal of waste and effluents and their impact on environment 9. Government support, grant, subsidy, tax structure 10. Availability of housing facilities and recreational facilities. 11. Demographic factors like population, trained man power, academic institutions, standard of living, income level, etc. 12. Security culture of the society 13. Fuel cost Prof.(Dr.) Anil Mishra
  • 6. Specific factors 1. Economic stability of the country and the concern of the country towards outside investments are to be considered 2. The success of operation of the factory depends upon the cultural factors, language and cultural differences which can present operating control and even policy problems. Units of measurement are also very important in international business. 3. Analysis must be based on the factors like wage rate, policy, duties, etc., 4. The Company can set up joint ventures with any leading local giants that will solve many local problems 10/31/2018 6Prof.(Dr.) Anil Mishra
  • 7. Types Of Facilities  Heavy manufacturing  Auto plants, steel mills, chemical plants  Light industry  Small components mfg, assembly  Warehouse & distribution centers  Retail & service 10/31/2018 7Prof.(Dr.) Anil Mishra
  • 8. Factors affecting in Heavy Manufacturing Location  Construction costs  Land costs  Raw material and finished goods shipment modes  Proximity to raw materials  Utilities  Labor availability 10/31/2018 8Prof.(Dr.) Anil Mishra
  • 9. Factors affecting in Light Industry Location  Construction costs  Land costs  Easily accessible geographic region  Education & training capabilities 10/31/2018 9Prof.(Dr.) Anil Mishra
  • 10. Factors affecting in Warehouse Location  Transportation costs  Proximity to markets 10/31/2018 10Prof.(Dr.) Anil Mishra
  • 11. Factors affecting in Retail Location  Proximity to customers  Location is everything 10/31/2018 11Prof.(Dr.) Anil Mishra
  • 12. Global Location Factors  Government stability  Government regulations  Political and economic systems  Economic stability and growth  Exchange rates  Culture  Climate  Export import regulations, duties and tariffs  Raw material availability  Number and proximity of suppliers  Transportation and distribution system  Labor cost and education  Available technology  Commercial travel  Technical expertise  Cross-border trade regulations  Group trade agreements 10/31/2018 12Prof.(Dr.) Anil Mishra
  • 13. Regional Location Factors  Labor (availability, education, cost and unions)  Proximity of customers  Number of customers  Construction/leasing costs  Land costs  Modes and quality of transportation  Transportation costs  Incentive packages  Governmental regulations  Environmental regulations  Raw material availability  Commercial travel  Climate  Infrastructure  Quality of life 10/31/2018 13Prof.(Dr.) Anil Mishra
  • 14. Regional Location Factors  Community government  Local business regulations  Government services  Business climate  Community services  Taxes  Availability of sites  Financial Services  Community inducements  Proximity of suppliers  Education system 10/31/2018 14Prof.(Dr.) Anil Mishra
  • 15. Site Location Factors  Customer base  Construction/ leasing cost  Land cost  Site size  Transportation  Utilities  Zoning restrictions  Traffic  Safety/security  Competition  Area business climate  Income level 10/31/2018 15Prof.(Dr.) Anil Mishra
  • 16. 10/31/2018 Relevant Factors for location in a nutshell Market related issues Cost related issues Market for products and services Wage rates Raw Material availability Transportation costs Number and proximity of suppliers Taxes and other tariff issues Availability of skilled labour Quality of Infrastructure Regulatory & Policy issues Other issues Government & Economic stability Culture Quality of legal and other institutions Climate Trading blocks and trading agreementsQuality of Life 16Prof.(Dr.) Anil Mishra
  • 17. 10/31/2018 Location Planning Methods  One facility – Multiple Candidates  Location factor rating  Centre of Gravity Method  Load Distance Method  Multiple Facility – Multiple Candidates  Transportation Model 17Prof.(Dr.) Anil Mishra
  • 18. 10/31/2018 Location factor rating Steps  Identify and list down all the relevant factors for the location decision  Establish the relative importance of each factor in the final decision  Rate the performance of each candidate location using a rating mechanism  Compute a total score for each location based on its performance against each factor and rank them in the decreasing order of the score 18Prof.(Dr.) Anil Mishra
  • 19. Example:1 Fuels in region 0 to 330 Power availability and reliability 0 to 200 Labor climate 0 to 100 Living conditions 0 to 100 Transportation 0 to 50 Water supply 0 to 10 Climate 0 to 50 Supplies 0 to 60 Tax policies and laws 0 to 20 Two refineries sites (A and B) are assigned the following range of point values and respective points, where the more points the better for the site location. 123 150 54 24 45 4 8 5 5 Major factors for site location Pt. Range 156 100 63 96 50 5 4 50 20 Sites A B Total pts. 418 544 Best Site is B 10/31/2018 19Prof.(Dr.) Anil Mishra
  • 20. Example:2 Labor pool and climate Proximity to suppliers Wage rates Community environment Proximity to customers Shipping modes Air service LOCATION FACTOR .30 .20 .15 .15 .10 .05 .05 WEIGHT 80 100 60 75 65 85 50 Site 1 65 91 95 80 90 92 65 Site 2 90 75 72 80 95 65 90 Site 3 SCORES (0 TO 100) 10/31/2018 20Prof.(Dr.) Anil Mishra
  • 21. Sol. Labor pool and climate Proximity to suppliers Wage rates Community environment Proximity to customers Shipping modes Air service LOCATION FACTOR .30 .20 .15 .15 .10 .05 .05 WEIGHT 80 100 60 75 65 85 50 Site 1 65 91 95 80 90 92 65 Site 2 90 75 72 80 95 65 90 Site 3 SCORES (0 TO 100) 24.00 20.00 9.00 11.25 6.50 4.25 2.50 77.50 Site 1 19.50 18.20 14.25 12.00 9.00 4.60 3.25 80.80 Site 2 27.00 15.00 10.80 12.00 9.50 3.25 4.50 82.05 Site 3 WEIGHTED SCORES Weighted Score Site 1 = (0.30)(80) = 24 Best Site is 310/31/2018 21Prof.(Dr.) Anil Mishra
  • 22. 10/31/2018 Example:3  A manufacturer of garments is actively considering five alternative locations for setting up its factory. The locations vary in terms of the advantages that it provides to the firm. Hence the firm requires a method of identifying the most appropriate location. Based on a survey of its senior executives the firm has arrived at six factors to be considered for final site selection. The ratings of each factor on a scale of 1 to 100 provide this information. Further, based some detailed analysis of both the qualitative and quantitative data available for each of the location, the rating for the locations against each factor has also been arrived at (on a scale of 0 to 100). Using this information obtain a ranking of the alternative locations. Factors Rating Availability of infrastructure 90 Size of the market 60 Industrial relations climate 50 Tax benefits and concessions 30 Availability of cheap labour 30 Nearness to port 65 Factors Location 1 Location 2 Location 3 Location 4 Location 5 Availability of infrastructure 20 40 60 35 55 Size of the market 30 30 40 60 80 Industrial relations climate 80 30 50 60 50 Tax benefits and concessions 80 20 10 20 20 Availability of cheap labour 70 70 45 50 50 Nearness to port 20 40 90 50 60 Factor Ratings Rating of each locations against the factors 22Prof.(Dr.) Anil Mishra
  • 23. 10/31/2018 Solution Factors Rating Relative weights Availability of infrastructure 90 0.28 Size of the market 60 0.18 Industrial relations climate 50 0.15 Tax benefits and concessions 30 0.09 Availability of cheap labour 30 0.09 Nearness to port 65 0.20 Sum of all factor ratings 325 1.00 Factors Relative weights Location 1 Location 2 Location 3 Location 4 Location 5 Availability of infrastructure 0.28 20 40 60 35 55 Size of the market 0.18 30 30 40 60 80 Industrial relations climate 0.15 80 30 50 60 50 Tax benefits and concessions 0.09 80 20 10 20 20 Availability of cheap labour 0.09 70 70 45 50 50 Nearness to port 0.20 20 40 90 50 60 Overall score for the locations 41.23 37.54 54.77 46.46 56.15 Ranking of the locations 4 5 2 3 1 Overall rating for location 3 = 60*0.28 + 40*0.18 + 50*0.15 + 10*0.09 + 45*0.09 + 90*0.20 = 54.77 23Prof.(Dr.) Anil Mishra
  • 24. 10/31/2018 Centre of Gravity Method  All the demand points (or the supply points, if raw material is supplied from several locations) are represented in a Cartesian coordinate system  Each demand (or the supply point) will also have weight indicating the quantum of shipment  Therefore it is possible to identify the centre of gravity of the various demand (or supply) points  Notations:  The number of demand (or supply) points in the grid map: n  Co-ordinates of location i in the grid map: (xi,yi)  Quantum of shipment between existing demand (or supply) point i and proposed facility: Wi  Co-ordinates of the center of gravity in the grid map: (XC,YC)      n i i n i ii C W Wx X 1 1 *)(      n i i n i ii C W Wy Y 1 1 *)( 24Prof.(Dr.) Anil Mishra
  • 25. 10/31/2018 Example 4.  A manufacturer of certain industrial component is interested in locating a new facility in a target market and would like to know the most appropriate place in the target market to locate the proposed facility. The manufacturer feels that there are no location constraints in the target market (i.e. any point in the target market is good enough).  There are four supply points A(125,550), B(350,400), C(450,125) and D(700,300) in the locality that will provide key inputs to the new facility. A two-dimensional grid map of the target market in which we would like to locate a new facility with distance coordinates of the four supply points is available.  The annual supply from these four points to the proposed facility is 200, 450, 175 and 150 tonnes respectively.  The situation is graphically shown in the two-dimensional plot in the figure. While the coordinates in the parentheses show the distance from the origin of the target map of each of the supply point, the number that follows is the annual shipment (in tonnes) from these points to the proposed facility.  Identify the most appropriate point in the grid map to locate the new facility. 25Prof.(Dr.) Anil Mishra
  • 26. 10/31/2018 Solution to Example . Grid Map 100 200 300 400 500 600 700 100 200 300 400 500 600 Distance in Kilometres DistanceinKilometres A (125,550), 200 B (350,400), 450 C (450,125), 175 D (700,300), 150 26Prof.(Dr.) Anil Mishra
  • 27. Example:5 A B C D x 200 100 250 500 y 200 500 600 300 Wt 75 105 135 60 y 700 500 600 400 300 200 100 0 x700500600400300200100 A B C D (135) (105) (75) (60) Miles Miles 10/31/2018 27Prof.(Dr.) Anil Mishra
  • 28. Sol. y 700 500 600 400 300 20 0 100 0 x70050060040030020 0 100 A B C D (135) (105) (75) (60) Miles Miles A B C D x 200 100 250 500 y 200 500 600 300 Wt 75 105 135 60x = = = 238 n  Wi i = 1  xiWi i = 1 n  n Wi i = 1  yiWi i = 1 n y = = = 444 (200)(75) + (500)(105) + (600)(135) + (300)(60) 75 + 105 + 135 + 60 (200)(75) + (100)(105) + (250)(135) + (500)(60) 75 + 105 + 135 + 60 10/31/2018 28Prof.(Dr.) Anil Mishra
  • 29. Sol. A B C D x 200 100 250 500 y 200 500 600 300 Wt 75 105 135 60 y 700 500 600 400 300 20 0 100 0 x70050060040030020 0 100 A B C D (135) (105) (75) (60) Miles Miles Center of gravity (238, 444) 10/31/2018 29Prof.(Dr.) Anil Mishra
  • 30. Question: What is the best location for a new Z-Mobile warehouse/temporary storage facility considering only distances and quantities sold per month?  Example:6 Several automobile showrooms are located according to the following grid which represents coordinate locations for each showroom Showroom No ofZ-Mobile s s old pe r month A 1250 D 1900 Q 2300X Y A (100,200) D (250,580) Q (790,900) (0,0) 10/31/2018 30Prof.(Dr.) Anil Mishra
  • 31. 10/31/2018 Load Distance Method  Enables a location planner to evaluate two or more potential candidates for locating a proposed facility vis-à-vis the demand (or supply) points  Provides an objective measure of total load-distance for each candidate  Notations  Number of demand (or supply) points in the grid map: n  Index used for demand (or supply) points: i  Co-ordinates of demand (or supply) point i in the grid map: (xi,yi)  Quantum of shipment between demand (or supply) point i and proposed facility: Wi  Number of candidates for the proposed facility: m  Index used for the candidates for the proposed facility: j  Co-ordinates of candidate j in the grid map: (Xj,Yj)  Distance measure for Cartesian coordinates between demand (or supply) point i and a candidate j for the proposed facility: Dij  The load – distance for candidate j for the proposed facility: LDj 22 )()( jijiij YyXxD    n i iijj WDLD 1 * 31Prof.(Dr.) Anil Mishra
  • 32. 10/31/2018 Example:7  Consider example .2.  Suppose the manufacturer came to know that there are constraints in locating the new facility.  Based on an initial survey of possible sites for the proposed facility, the manufacturer identified four candidates.  The figure has the location coordinates of the four candidates (numbered 1 to 4).  What is the best location for the proposed new facility? Existing Supply Points Candidates for proposed facility xi yi Wi Xj Yj A 125 550 200 1 300 500 B 350 400 450 2 200 500 C 450 125 175 3 500 350 D 700 300 150 4 400 200 32Prof.(Dr.) Anil Mishra
  • 33. 10/31/2018 Solution 00.182)50(175()500550()300125()()( 22222 1 2 11  YyXxD AAA Dij values 1 2 3 4 A 182.00 90.14 425.00 445.11 B 111.80 180.28 158.11 206.16 C 403.89 450.69 230.49 90.14 D 447.21 538.52 206.16 316.23 LDj values 1 2 3 4 224474.41 258801.57 227410.05 245000.8 33Prof.(Dr.) Anil Mishra
  • 34. 10/31/2018 Solution Grid Map 100 200 300 400 500 600 700 100 200 300 400 500 600 Distance in Kilometres DistanceinKilometres A (125,550), 200 B (350,400), 450 C (450,125), 175 D (700,300), 150 1 (300,500) 2 (200,500) 3 (500,350) 4 (400,200) Candidate for proposed facility Existing Demand (or supply) point 34Prof.(Dr.) Anil Mishra
  • 35. Example:8 Potential Sites Site X Y 1 360 180 2 420 450 3 250 400 Suppliers A B C D X 200 100 250 500 Y 200 500 600 300 Wt 75 105 135 60 Compute distance from each site to each supplier = (200-360)2 + (200-180)2dA = (xA - x1)2 + (yA - y1)2Site 1 = 161.2 = (100-360)2 + (500-180)2dB = (xB - x1)2 + (yB - y1)2 = 412.3 dC = 434.2 dD = 184.4 10/31/2018 35Prof.(Dr.) Anil Mishra
  • 36. sol Site 2 dA = 333 dC = 226.7dB = 323.9 dD = 170 Site 3 dA = 206.2 dC = 200dB = 180.4 dD = 269.3 Compute load-distance i = 1 n  li di LD = 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 10/31/2018 36Prof.(Dr.) Anil Mishra
  • 37. 10/31/2018 Multi-facility location problem Transportation Model  Locating distribution centers for nation-wide distribution of products is one typical example belonging to this category  Decisions variables in a multiple location – multiple candidate problem  Identifying k out of n candidates for locating facilities  Which of the demand points will be served by each of these locations and to what extent  the problem is one of managing network flows of satisfying a set demand points using a combination of supply points  The transportation model is ideally suited for solving this combinatorial optimisation problem 37Prof.(Dr.) Anil Mishra
  • 38. 10/31/2018 Multiple facilities location problem Transportation table (Example:9) Market 1 Market 2 Market 3 Market 4 Market 5 Supply 70 40 10 0 0 Warehouse A 2800 100 2900 0 65 0 95 10 Warehouse B 2000 300 2300 55 0 35 20 0 Warehouse C 400 900 2400 3700 0 20 65 65 50 Warehouse D 1100 1100 Demand 2000 1500 1200 2800 2500 10000 Market 1 Market 2 Market 3 Market 4 Market 5 Supply 100 70 50 30 40 Warehouse A 2900 30 95 40 125 50 Warehouse B 2300 75 20 65 40 30 Warehouse C 3700 20 40 95 85 80 Warehouse D 1100 Demand 2000 1500 1200 2800 2500 10000 Problem Solution using Vogal’s Approximation Method (VAM) 38Prof.(Dr.) Anil Mishra

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