location strategic considerations in facility location access to markets, ie eu nissan, toyota...
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LocatioLocationn
Strategic Strategic Considerations in Considerations in Facility LocationFacility Location Access to markets, ie EUAccess to markets, ie EU
Nissan, Toyota & Honda invested $2.6 Nissan, Toyota & Honda invested $2.6 billion in UKbillion in UK
Responsiveness to CustomersResponsiveness to Customers
Access to technologyAccess to technology
GlobaGlobal Hot l Hot SpotsSpots
East Asia.East Asia. The Pacific Basin, The Pacific Basin, including Japan, South Korea, including Japan, South Korea, China, Taiwan, and Singapore China, Taiwan, and Singapore became the fastest-growing became the fastest-growing and foremost trading region in and foremost trading region in the world.the world.
JapanJapanSouth South KoreaKorea
TaiwanTaiwan
SingaporeSingapore
Hong KongHong Kong
Figure 9.1
GlobaGlobal Hot l Hot SpotsSpots
Mexico.Mexico. Thousands of plants Thousands of plants have been built by firms have been built by firms across the world in the across the world in the maquiladoras on Mexico's maquiladoras on Mexico's northern boarder.northern boarder. Figure 9.1
U.S. Sunbelt.U.S. Sunbelt. The sunbelt is The sunbelt is attracting many firms normally attracting many firms normally entrenched in the industrial entrenched in the industrial heartland of the United States heartland of the United States owing to lower labor costs, less owing to lower labor costs, less unionism, and a more-attractive unionism, and a more-attractive climate.climate.
NAFTA.NAFTA. The North American Free Trade Agreement The North American Free Trade Agreement makes trade easier between Canada, Mexico, and the makes trade easier between Canada, Mexico, and the United States. Other Latin American countries may United States. Other Latin American countries may follow suit.follow suit.
GlobaGlobal Hot l Hot SpotsSpots
Europe.Europe. The European The European Union (EU) encompasses Union (EU) encompasses 15 member nations and 15 member nations and special arrangements with special arrangements with most other European most other European states.states.
Figure 9.1
GlobaGlobal Hot l Hot SpotsSpots
Former Communist Countries.Former Communist Countries. The population of 410 million The population of 410 million promises huge market promises huge market opportunities and attractive opportunities and attractive possibilities for joint ventures.possibilities for joint ventures.
Figure 9.1
Russia
Managing Global Managing Global OperationsOperations
• Other LanguagesOther Languages• Different Norms and CustomsDifferent Norms and Customs• Workforce ManagementWorkforce Management• Unfamiliar Laws and Unfamiliar Laws and
RegulationsRegulations• Unexpected Cost MixUnexpected Cost Mix
Stages in Facility Stages in Facility Location DecisionsLocation Decisions
DeterminingDetermining the need for a new the need for a new
facilityfacility
Identifying the relevant factors Identifying the relevant factors in selecting a locationin selecting a location
Selecting a general locationSelecting a general location
Selecting a siteSelecting a site
Determining the Need Determining the Need for a New Factoryfor a New Factory
Change in demand, up or downChange in demand, up or down
New productNew product
Changes in the economics of the Changes in the economics of the business, e.g. labour costs, material business, e.g. labour costs, material costs, material sources, supporting costs, material sources, supporting industriesindustries
Government action, I.e. on Government action, I.e. on environmental groundsenvironmental grounds
Determining the Need Determining the Need for a New Factoryfor a New Factory
Plant Size
Cos
t
Production Costs
Transport Costs
Total Costs
Ideal Plant Size
Dominant Decision Factors - Manufacturing- Manufacturing
Favorable Labour ClimateFavorable Labour Climate Proximity to MarketsProximity to Markets Quality of LifeQuality of Life Proximity to SuppliersProximity to Suppliers Proximity to Parent CompanyProximity to Parent Company Utilities, Taxes, and Real Estate Utilities, Taxes, and Real Estate
CostsCosts
Dominant Decision Factors - Services- Services
Proximity to CustomersProximity to Customers Transportation Costs and Transportation Costs and
Proximity to MarketsProximity to Markets Location of CompetitorsLocation of Competitors Site-specific FactorsSite-specific Factors
Locating A Single Facility
* Assume no interdependence on facilities
• Expand onsite• Build another facility• Relocate to another site
Locating a Single Locating a Single FacilityFacility
On-site expansionOn-site expansion
++ Keeps management togetherKeeps management together
++ Reduces construction time & Reduces construction time & costscosts
++ Avoids splitting up operationsAvoids splitting up operations
-- Diseconomies of scaleDiseconomies of scale
-- Poor materials handlingPoor materials handling
-- Increasingly complex Increasingly complex production controlproduction control
-- Lack of spaceLack of space
Locating a Single Locating a Single FacilityFacility
Building a new plantBuilding a new plant
++ Reduced risk of complete loss Reduced risk of complete loss of of production due to production due to accidentaccident
++ Escape unproductive labourEscape unproductive labour++ Modernise with new Modernise with new
machinerymachinery
++ Reduce transport costsReduce transport costs
Locating a Facility – Comparing Sites
1. Determine dominant and secondary location factors
2. Develop alternative regions communities sites
3. Collect data lots of statistical data 4. Analyze quantitative factors down to a
single measurer and compare alternatives
5. Analyze qualitative factors to compare remaining alternatives
Comparison Tools
• Weighted scoring model using a preference matrix
• Load-Distance Model – Euclidean distance dab = √((xa-xb)2+(ya-yb)2)
– Rectilinear distance dab = |xa-xb| + |ya-yb|
– Load-Distance Score ld
– Center of gravity x*= ∑i (lixi) / ∑ li & y*= ∑i (liyi) / ∑ li
• Break-Even Analysis
LocatioLocationnHealth-WatchHealth-Watch
A new medical facility Health-Watch istargeted to serve seven census tracts inErie, Pennsylvania.
Customers will travel from the sevencensus tract centers to the new facilitywhen they need health care.
LocatioLocationnHealth-WatchHealth-WatchNorth
Erie
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
State College
LocatioLocationnHealth-WatchHealth-WatchNorth
Erie
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
State College
Location Factor Weight Score
Total Patient miles per month 25 4Facility utilization 20 3Average time per emergency trip 20 3Expressway accessibility 15 4Land and construction costs 10 1Employee preference 10 5
LocatioLocationnHealth-WatchHealth-WatchNorth
Erie
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
State College
Location Factor Weight Score
Total Patient miles per month 25 4Facility utilization 20 3Average time per emergency trip 20 3Expressway accessibility 15 4Land and construction costs 10 1Employee preference 10 5
Weighted Score
LocatioLocationnHealth-WatchHealth-WatchNorth
Erie
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
State College
Location Factor Weight Score
Total Patient miles per month 25 4Facility utilization 20 3Average time per emergency trip 20 3Expressway accessibility 15 4Land and construction costs 10 1Employee preference 10 5
WS = (25 x 4)
Weighted Score
LocatioLocationnHealth-WatchHealth-WatchNorth
Erie
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
State College
Location Factor Weight Score
Total Patient miles per month 25 4Facility utilization 20 3Average time per emergency trip 20 3Expressway accessibility 15 4Land and construction costs 10 1Employee preference 10 5
WS = (25 x 4) + (20 x 3)
Weighted Score
LocatioLocationnHealth-WatchHealth-WatchNorth
Erie
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
State College
Location Factor Weight Score
Total Patient miles per month 25 4Facility utilization 20 3Average time per emergency trip 20 3Expressway accessibility 15 4Land and construction costs 10 1Employee preference 10 5
WS = (25 x 4) + (20 x 3) + (20 x 3)
Weighted Score
LocatioLocationnHealth-WatchHealth-WatchNorth
Erie
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
State College
Location Factor Weight Score
Total Patient miles per month 25 4Facility utilization 20 3Average time per emergency trip 20 3Expressway accessibility 15 4Land and construction costs 10 1Employee preference 10 5
WS = (25 x 4) + (20 x 3) + (20 x 3) + (15 x4) + (10 x 1) + (10 x 5)
Weighted Score
LocatioLocationnHealth-WatchHealth-WatchNorth
Erie
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
State College
Location Factor Weight Score
Total Patient miles per month 25 4Facility utilization 20 3Average time per emergency trip 20 3Expressway accessibility 15 4Land and construction costs 10 1Employee preference 10 5
WS = 340
Weighted Score
LocatioLocationnHealth-WatchHealth-Watch
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
Euclidean distanceEuclidean distance
dAB = ( xA - xB )2 + ( yA - yB )2
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
Euclidean distanceEuclidean distance
dAB = (50 - 175 )2 + (185 - 100 )2
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
Euclidean distanceEuclidean distance
dAB = (50 - 175 )2 + (185 - 100 )2
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
Euclidean distanceEuclidean distance
dAB = 151.2 miles
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
151.2 miles151.2 miles
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
151.2 miles151.2 miles
Rectilinear distanceRectilinear distance
dAB = | xA - xB | + | yA - yB |
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
151.2 miles151.2 miles
Rectilinear distanceRectilinear distance
dAB = | 50 - 175 | + | 185 - 100 |
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
151.2 miles151.2 miles
Rectilinear distanceRectilinear distance
dAB = | 50 - 175 | + | 185 - 100 |
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
151.2 miles151.2 miles
Rectilinear distanceRectilinear distance
dAB = 210 miles
LocatioLocationnHealth-WatchHealth-WatchErie
A(50, 185)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
North
0
50
100
150
200
y (
miles)
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
151.2 miles151.2 miles
210 miles210 miles
LocatioLocationn
Figure 9.3
Health-WatchHealth-WatchErie A (50, 185) North
0
50
100
150
200
y (m
iles)
PittsburghHarrisburg
Philadelphia
Scranton
Uniontown
x (miles)50 100 150 200 250 300
East
State CollegeB (175, 100)
151.2 miles151.2 miles
210 miles210 miles
Enter the x and y coordinates of the two towns.
x yErie (Point A) 50 185State College (Point B) 175 100
To find the Euclidian distance, subtract the second town’s x value from that of the first town, and square the result. Do the same with the two y values. Then add the two and compute the square root.
(Erie x – State College x)2 15.625 Euclidian distance 151.16(Erie y – State College y)2 7,225
To find the rectilinear distance, get the absolute value of the result of subtracting the second town’s x from the first town’s. Do the same with y. Then add the absolute distances together.
(Erie x – State College x) 125 Rectilinear distance 210(Erie y – State College y) 85
Tutor 9.2 - Distance Measures
LocatioLocationnHealth-WatchHealth-Watch
LocatioLocationnHealth-WatchHealth-Watch
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22
5.5 - 2.5 = 35.5 - 2.5 = 3
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22
5.5 - 2.5 = 35.5 - 2.5 = 34.5 - 4.5 = 04.5 - 4.5 = 0
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22 3 + 0 = 33 + 0 = 3
5.5 - 2.5 = 35.5 - 2.5 = 34.5 - 4.5 = 04.5 - 4.5 = 0
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22 3 + 0 = 33 + 0 = 3 66
2 * 3 = 62 * 3 = 6
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22 3 + 0 = 33 + 0 = 3 66
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22 3 + 0 = 33 + 0 = 3 66EE (8, 5)(8, 5) 1010
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22 3 + 0 = 33 + 0 = 3 66EE (8, 5)(8, 5) 1010 2.5 + 0.5 = 3 2.5 + 0.5 = 3
8 - 5.5 = 2.58 - 5.5 = 2.55 - 4.5 = 0.55 - 4.5 = 0.5
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22 3 + 0 = 33 + 0 = 3 66EE (8, 5)(8, 5) 1010 2.5 + 0.5 = 32.5 + 0.5 = 3 3030
10 * 3 = 3010 * 3 = 30
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
CensusCensus Population Population DistanceDistanceTractTract ((xx,,yy)) ((ll)) ((dd)) ldld
AA (2.5, 4.5)(2.5, 4.5) 22 3 + 0 = 33 + 0 = 3 66EE (8, 5)(8, 5) 1010 2.5 + 0.5 = 32.5 + 0.5 = 3 3030
LocatioLocationnHealth-WatchHealth-Watch
(a) Locate at C (5.5, 4.5)(a) Locate at C (5.5, 4.5)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
TractTract ldldAA 66BB 2525CC 00DD 2121EE 3030FF 8080GG 7777
TotalTotal239239
LocatioLocationnHealth-WatchHealth-Watch
(b) Locate at F (7, 2)(b) Locate at F (7, 2)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
LocatioLocationnHealth-WatchHealth-Watch
(b) Locate at F (7, 2)(b) Locate at F (7, 2)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
LocatioLocationnHealth-WatchHealth-Watch
(b) Locate at F (7, 2)(b) Locate at F (7, 2)
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
TractTract ldldAA 1414BB 2525CC 4040DD 1414EE 4040FF 00GG 3535
TotalTotal168168
LocatioLocationnHealth-WatchHealth-Watch
Alternative LocationsAlternative Locations
North
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
LocatioLocationnHealth-WatchHealth-Watch
Alternative LocationsAlternative Locations
North
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
391
355
331
326
283
247
223
233
197
173
253
233
228168218
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles)
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) CensusCensus Population PopulationTractTract ((xx,,yy)) ((ll)) lxlx lyly
AA (2.5, 4.5)(2.5, 4.5) 22BB (2.5, 2.5)(2.5, 2.5) 55CC (5.5, 4.5)(5.5, 4.5) 1010DD (5, 2)(5, 2) 77EE (8, 5)(8, 5) 1010FF (7, 2)(7, 2) 2020GG (9, 2.5)(9, 2.5) 1414
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) CensusCensus Population PopulationTractTract ((xx,,yy)) ((ll)) lxlx lyly
AA (2.5, 4.5)(2.5, 4.5) 22 55BB (2.5, 2.5)(2.5, 2.5)CC (5.5, 4.5)(5.5, 4.5)DD (5, 2)(5, 2)EE (8, 5)(8, 5)FF (7, 2)(7, 2)GG (9, 2.5)(9, 2.5)
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) CensusCensus Population PopulationTractTract ((xx,,yy)) ((ll)) lxlx lyly
AA (2.5, 4.5)(2.5, 4.5) 22 55 99BB (2.5, 2.5)(2.5, 2.5)CC (5.5, 4.5)(5.5, 4.5)DD (5, 2)(5, 2)EE (8, 5)(8, 5)FF (7, 2)(7, 2)GG (9, 2.5)(9, 2.5)
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) CensusCensus Population PopulationTractTract ((xx,,yy)) ((ll)) lxlx lyly
AA (2.5, 4.5)(2.5, 4.5) 22 55 99BB (2.5, 2.5)(2.5, 2.5)CC (5.5, 4.5)(5.5, 4.5)DD (5, 2)(5, 2)EE (8, 5)(8, 5)FF (7, 2)(7, 2)GG (9, 2.5)(9, 2.5)
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) CensusCensus Population PopulationTractTract ((xx,,yy)) ((ll)) lxlx lyly
AA (2.5, 4.5)(2.5, 4.5) 22 55 99BB (2.5, 2.5)(2.5, 2.5) 55 12.512.5 12.512.5CC (5.5, 4.5)(5.5, 4.5) 1010 5555 4545DD (5, 2)(5, 2) 77 3535 1414EE (8, 5)(8, 5) 1010 8080 5050FF (7, 2)(7, 2) 2020 140140 4040GG (9, 2.5)(9, 2.5) 1414 126126 3535
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) CensusCensus Population PopulationTractTract ((xx,,yy)) ((ll)) lxlx lyly
AA (2.5, 4.5)(2.5, 4.5) 22 55 99BB (2.5, 2.5)(2.5, 2.5) 55 12.512.5 12.512.5CC (5.5, 4.5)(5.5, 4.5) 1010 5555 4545DD (5, 2)(5, 2) 77 3535 1414EE (8, 5)(8, 5) 1010 8080 5050FF (7, 2)(7, 2) 2020 140140 4040GG (9, 2.5)(9, 2.5) 1414 126126 3535
TotalsTotals 6868 453.5453.5205.5205.5
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) CensusCensus Population PopulationTractTract ((xx,,yy)) ((ll)) lxlx lyly
AA (2.5, 4.5)(2.5, 4.5) 22 55 99BB (2.5, 2.5)(2.5, 2.5) 55 12.512.5 12.512.5CC (5.5, 4.5)(5.5, 4.5) 1010 5555 4545DD (5, 2)(5, 2) 77 3535 1414EE (8, 5)(8, 5) 1010 8080 5050FF (7, 2)(7, 2) 2020 140140 4040GG (9, 2.5)(9, 2.5) 1414 126126 3535
TotalsTotals 6868 453.5453.5205.5205.5
x* =
y* =
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) CensusCensus Population PopulationTractTract ((xx,,yy)) ((ll)) lxlx lyly
AA (2.5, 4.5)(2.5, 4.5) 22 55 99BB (2.5, 2.5)(2.5, 2.5) 55 12.512.5 12.512.5CC (5.5, 4.5)(5.5, 4.5) 1010 5555 4545DD (5, 2)(5, 2) 77 3535 1414EE (8, 5)(8, 5) 1010 8080 5050FF (7, 2)(7, 2) 2020 140140 4040GG (9, 2.5)(9, 2.5) 1414 126126 3535
TotalsTotals 6868 453.5453.5205.5205.5
x* =
y* =
453.568
205.568
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) CensusCensus Population PopulationTractTract ((xx,,yy)) ((ll)) lxlx lyly
AA (2.5, 4.5)(2.5, 4.5) 22 55 99BB (2.5, 2.5)(2.5, 2.5) 55 12.512.5 12.512.5CC (5.5, 4.5)(5.5, 4.5) 1010 5555 4545DD (5, 2)(5, 2) 77 3535 1414EE (8, 5)(8, 5) 1010 8080 5050FF (7, 2)(7, 2) 2020 140140 4040GG (9, 2.5)(9, 2.5) 1414 126126 3535
TotalsTotals 6868 453.5453.5205.5205.5
x* =
y* =
453.568
205.568
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) CensusCensus Population PopulationTractTract ((xx,,yy)) ((ll)) lxlx lyly
AA (2.5, 4.5)(2.5, 4.5) 22 55 99BB (2.5, 2.5)(2.5, 2.5) 55 12.512.5 12.512.5CC (5.5, 4.5)(5.5, 4.5) 1010 5555 4545DD (5, 2)(5, 2) 77 3535 1414EE (8, 5)(8, 5) 1010 8080 5050FF (7, 2)(7, 2) 2020 140140 4040GG (9, 2.5)(9, 2.5) 1414 126126 3535
TotalsTotals 6868 453.5453.5205.5205.5
x* = 6.67
y* = 2.96
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
North
B
A CE
GFD
(2.5, 4.5) [2]
(2.5, 2.5) [5] (5, 2)
[7](7, 2) [20]
(9, 2.5) [14]
(8, 5) [10]
(5.5, 4.5) [10]
x (miles) East1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
0
yy (
miles)
(m
iles) x* = 6.67
y* = 2.96
LocatioLocationnHealth-WatchHealth-Watch
Center of Gravity ApproachCenter of Gravity Approach
Figure 9.6
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
Fixed CostsFixed Costs Variable CostsVariable Costs Total CostsTotal CostsCommunityCommunity per Yearper Year per Unitper Unit (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $62$62BB $300,000$300,000 $38$38CC $500,000$500,000 $24$24DD $600,000$600,000 $30$30
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
Fixed CostsFixed Costs Variable CostsVariable Costs Total CostsTotal CostsCommunityCommunity per Yearper Year per Unitper Unit (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $62$62BB $300,000$300,000 $38$38CC $500,000$500,000 $24$24DD $600,000$600,000 $30$30
For 20,000 unitsFor 20,000 units
Total Variable CostsTotal Variable Costs
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
Fixed CostsFixed Costs Variable CostsVariable Costs Total CostsTotal CostsCommunityCommunity per Yearper Year per Unitper Unit (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $62$62BB $300,000$300,000 $38$38CC $500,000$500,000 $24$24DD $600,000$600,000 $30$30
For 20,000 unitsFor 20,000 units
Total Variable CostsTotal Variable Costs
$62 (20,000)$62 (20,000)
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
Fixed CostsFixed Costs Variable CostsVariable Costs Total CostsTotal CostsCommunityCommunity per Yearper Year per Unitper Unit (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $62$62BB $300,000$300,000 $38$38CC $500,000$500,000 $24$24DD $600,000$600,000 $30$30
For 20,000 unitsFor 20,000 units
Total Variable CostsTotal Variable Costs
$62 (20,000) = $1,240,000$62 (20,000) = $1,240,000
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
Fixed CostsFixed Costs Variable CostsVariable Costs Total CostsTotal CostsCommunityCommunity per Yearper Year per Unitper Unit (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $62$62 $1,390,000$1,390,000BB $300,000$300,000 $38$38CC $500,000$500,000 $24$24DD $600,000$600,000 $30$30
For 20,000 unitsFor 20,000 units
Total Variable CostsTotal Variable Costs
$62 (20,000) = $1,240,000$62 (20,000) = $1,240,000
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
Fixed CostsFixed Costs Variable CostsVariable Costs Total CostsTotal CostsCommunityCommunity per Yearper Year per Unitper Unit (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $62$62 $1,390,000$1,390,000BB $300,000$300,000 $38$38CC $500,000$500,000 $24$24DD $600,000$600,000 $30$30
For 20,000 unitsFor 20,000 units
Total Variable CostsTotal Variable Costs
$62 (20,000) = $1,240,000$62 (20,000) = $1,240,000
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
Fixed CostsFixed Costs Variable CostsVariable Costs Total CostsTotal CostsCommunityCommunity per Yearper Year per Unitper Unit (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $62$62 $1,390,000$1,390,000BB $300,000$300,000 $38$38 $1,060,000$1,060,000CC $500,000$500,000 $24$24 $ 980,000$ 980,000DD $600,000$600,000 $30$30 $1,200,000$1,200,000
For 20,000 unitsFor 20,000 units
LocatioLocationn
Q (thousands of units)
0
200
400
600
800
1000
1200
1400
1600
2 4 6 8 10 12 14 16 18 20 22
An
nu
al cost
(th
ou
san
ds o
f d
ollars
) Break-Even AnalysisBreak-Even Analysis
Fixed CostsFixed Costs Total CostsTotal CostsCommunityCommunity per Yearper Year (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $1,390,000$1,390,000BB $300,000$300,000 $1,060,000$1,060,000CC $500,000$500,000 $ 980,000$ 980,000DD $600,000$600,000 $1,200,000$1,200,000
LocatioLocationn
Q (thousands of units)
0
200
400
600
800
1000
1200
1400
1600
2 4 6 8 10 12 14 16 18 20 22
An
nu
al cost
(th
ou
san
ds o
f d
ollars
) Break-Even AnalysisBreak-Even Analysis
Fixed CostsFixed Costs Total CostsTotal CostsCommunityCommunity per Yearper Year (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $1,390,000$1,390,000BB $300,000$300,000 $1,060,000$1,060,000CC $500,000$500,000 $ 980,000$ 980,000DD $600,000$600,000 $1,200,000$1,200,000 A
DBC
(20, 1390)
(20, 1200)
(20, 1060)
(20, 980)
LocatioLocationn
A
DBC
(20, 1390)
(20, 1200)
(20, 1060)
(20, 980)
A best
Break-even pointBreak-even point
Q (thousands of units)
0
200
400
600
800
1000
1200
1400
1600
2 4 6 8 10 12 14 16 18 20 22
An
nu
al cost
(th
ou
san
ds o
f d
ollars
) Break-Even AnalysisBreak-Even Analysis
Fixed CostsFixed Costs Total CostsTotal CostsCommunityCommunity per Yearper Year (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $1,390,000$1,390,000BB $300,000$300,000 $1,060,000$1,060,000CC $500,000$500,000 $ 980,000$ 980,000DD $600,000$600,000 $1,200,000$1,200,000
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
B best
Break-even pointBreak-even point
A
DBC
(20, 1390)
(20, 1200)
(20, 1060)
(20, 980)
A best
6.25
Break-even pointBreak-even point
Q (thousands of units)
0
200
400
600
800
1000
1200
1400
1600
2 4 6 8 10 12 14 16 18 20 22
An
nu
al cost
(th
ou
san
ds o
f d
ollars
)Fixed CostsFixed Costs Total CostsTotal Costs
CommunityCommunity per Yearper Year (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $1,390,000$1,390,000BB $300,000$300,000 $1,060,000$1,060,000CC $500,000$500,000 $ 980,000$ 980,000DD $600,000$600,000 $1,200,000$1,200,000
14.3
C best
(20, 980)
B best
Break-even pointBreak-even point
LocatioLocationn
A
DBC
(20, 1390)
(20, 1200)
(20, 1060)
A best
6.25
Break-even pointBreak-even point
Q (thousands of units)
0
200
400
600
800
1000
1200
1400
1600
2 4 6 8 10 12 14 16 18 20 22
An
nu
al cost
(th
ou
san
ds o
f d
ollars
) Break-Even AnalysisBreak-Even Analysis
14.3
Fixed CostsFixed Costs Total CostsTotal CostsCommunityCommunity per Yearper Year (Fixed + Variable)(Fixed + Variable)
AA $150,000$150,000 $1,390,000$1,390,000BB $300,000$300,000 $1,060,000$1,060,000CC $500,000$500,000 $ 980,000$ 980,000DD $600,000$600,000 $1,200,000$1,200,000
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
Q (thousands of units)
0
200
400
600
800
1000
1200
1400
1600
2 4 6 8 10 12 14 16 18 20 22
A best B best C best
Break-even pointBreak-even point
6.25 14.3
A
DBC
(20, 1390)
(20, 1200)
(20, 1060)
(20, 980)
An
nu
al cost
(th
ou
san
ds o
f d
ollars
)
Break-even pointBreak-even point
LocatioLocationnBreak-Even AnalysisBreak-Even Analysis
Q (thousands of units)
0
200
400
600
800
1000
1200
1400
1600
2 4 6 8 10 12 14 16 18 20 22
A best B best C best
Break-even point
6.25 14.3
A
DBC
(20, 1390)
(20, 1200)
(20, 1060)
(20, 980)
An
nu
al c
ost
(th
ou
san
ds
of
do
llars
)
Break-even point
Example 9.5
(A) (B)
$150,000 + $62Q = $300,000 + $38QQ = 6,250 units
$300,000 + $38Q = $500,000 + $24QQ = 14,286 units
(B) (C)
Break-Even Quantities
Locating a facility in a Network
• Location of each facility in the network
• Allocation of work throughout the network
• Capacity may be affected by allocations
• Transportation Method
Locating a faclitiy within a network of facilities.
Facilities may work independently (chain ofrestaurants) or interact (warehouses).
Interaction between facilities requires solving of:- location- allocation (allocating work between facilities)- capacity (reallocationg of work affect the capacity)
Transportation Model
1. Create a row for each plant2. Create a column for each warehouse3. Create a single column for plant capacity 4. Create a single row for warehouse demand.5. Split cells where plant and warehouse, rows
and columns intersect6. Place price per unit in half of each split cell7. Place estimated capacities and demand
figures for each plant and warehouse.
Transportation Model
8. Create a dummy warehouses if total capacity is greater than total demand.
8.1 Demand for the dummy warehouse should equal Total capacity – Total demand so as to raise total demand to equal total capacity.
8.2 Split the new intersection cells as in step 5 for dummy column
8.3 use a price of $ 0.00 per unit in the split cells9. Create a dummy plant if total demand is greater
than total capacity9.1 Capacity for the dummy plant should equal Total demand –
Total capacity so as to raise Total capacity to equal total demand
9.2 Split the new intersection cell as in step5 for the dummy row9.3 Set the price per unit to the cost to the company for stock
outs. If unknown or all stock out cost are equal allow price to be $0.00
Transportation Model
10. Solve model by placing the amount each plant should send each warehouse in the unused half of the split cells where
10.1 Total capacity of each plant is fully used
10.2 Total demand for each warehouse is fully met
10.3 Where total cost to met 10.1 and 10.2 is at a minimum.
Tools to solve Transportation Model
• Trial and Error• Linear Programming (supplement
I)– Simplex Method Max. non Zero shipments = Sum of
plants + sum of warehouse -1
LocatioLocationnTransportation MethodTransportation Method
LocatioLocationnTransportation MethodTransportation Method
Setting up the Initial TableauSetting up the Initial Tableau
Example 9.6
LocatioLocationnTransportation MethodTransportation Method
Setting up the Initial TableauSetting up the Initial Tableau
PlantWarehouse
1 2 3
Phoenix
Atlanta
Create a row for each plant and a column for each warehouse
Example 9.6
LocatioLocationnTransportation MethodTransportation Method
Setting up the Initial TableauSetting up the Initial TableauAdd a column for plant capacities and a row for warehouse demand
PlantWarehouse
Capacity1 2 3
Requirements
Phoenix
Atlanta
400
500
900900200 400 300
Example 9.6
LocatioLocationnTransportation MethodTransportation Method
Setting up the Initial TableauSetting up the Initial Tableau
PlantWarehouse
Capacity1 2 3
Requirements
Phoenix
Atlanta
5.0 6.0 5.4
7.0 4.6 6.6
400
500
900900200 400 300
Figure 9.8
Insert costs into the shipping route option cells
LocatioLocationnTransportation MethodTransportation Method
LocatioLocationnTransportation MethodTransportation Method
Interpreting the Optimal SolutionInterpreting the Optimal Solution
Figure 9.9
Mile-High Beer— Mile-High Beer— Solved Problem Solved Problem
22
Boulder
Break-evenpoint
Fort Collins
2.67
Break-even Break-even pointpoint
Barrels of beer per year (in hundred thousands)
10
8
6
4
2
0 1 2 3 4 5 6
Lo
cati
on
co
st (
in m
illio
ns
of
do
llars
)
Figure 9.10
Denver
Golden
Arid CompanyArid Company—Solved —Solved Problem 4Problem 4
Figure 9.11
SourceDestination
Capacity
$4.37 $4.25 $4.8912,000
10,000
18,000
40,0006,000 22,000 12,000
$4.00 $5.00 $5.27
$4.13 $4.50 $3.75
Demand
Battle Creek
Cherry Creek
Dee Creek
12,000
6,000 4,000
6,000 12,000
Worchester Rochester Dorchester