location strategic considerations in facility location access to markets, ie eu nissan, toyota...

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


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.


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


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


Erie


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


Erie


Philadelphia

Scranton

Uniontown

State College



Weighted Score


Erie


Philadelphia

Scranton

Uniontown

State College



WS = (25 x 4)

Weighted Score


Erie


Philadelphia

Scranton

Uniontown

State College



WS = (25 x 4) + (20 x 3)

Weighted Score


Erie


Philadelphia

Scranton

Uniontown

State College



WS = (25 x 4) + (20 x 3) + (20 x 3)

Weighted Score


Erie


Philadelphia

Scranton

Uniontown

State College



WS = (25 x 4) + (20 x 3) + (20 x 3) + (15 x4) + (10 x 1) + (10 x 5)

Weighted Score


Erie


Philadelphia

Scranton

Uniontown

State College



WS = 340

Weighted Score

LocatioLocationnHealth-WatchHealth-WatchErie

A(50, 185)


Philadelphia

Scranton

Uniontown

North

0

50

100

150

200

y (

miles)

x (miles)50 100 150 200 250 300

East

State CollegeB (175, 100)


A(50, 185)


Philadelphia

Scranton

Uniontown

North

0

50

100

150

200

y (

miles)

x (miles)50 100 150 200 250 300

East


Euclidean distanceEuclidean distance

dAB = ( xA - xB )2 + ( yA - yB )2


A(50, 185)


Philadelphia

Scranton

Uniontown

North

0

50

100

150

200

y (

miles)

x (miles)50 100 150 200 250 300

East



dAB = (50 - 175 )2 + (185 - 100 )2


A(50, 185)


Philadelphia

Scranton

Uniontown

North

0

50

100

150

200

y (

miles)

x (miles)50 100 150 200 250 300

East



dAB = 151.2 miles


A(50, 185)


Philadelphia

Scranton

Uniontown

North

0

50

100

150

200

y (

miles)

x (miles)50 100 150 200 250 300

East


151.2 miles151.2 miles


A(50, 185)


Philadelphia

Scranton

Uniontown

North

0

50

100

150

200

y (

miles)

x (miles)50 100 150 200 250 300

East



Rectilinear distanceRectilinear distance

dAB = | xA - xB | + | yA - yB |


A(50, 185)


Philadelphia

Scranton

Uniontown

North

0

50

100

150

200

y (

miles)

x (miles)50 100 150 200 250 300

East




dAB = | 50 - 175 | + | 185 - 100 |


A(50, 185)


Philadelphia

Scranton

Uniontown

North

0

50

100

150

200

y (

miles)

x (miles)50 100 150 200 250 300

East




dAB = 210 miles


A(50, 185)


Philadelphia

Scranton

Uniontown

North

0

50

100

150

200

y (

miles)

x (miles)50 100 150 200 250 300

East



210 miles210 miles

LocatioLocationn

Figure 9.3

Health-WatchHealth-WatchErie A (50, 185) North

0

50

100

150

200

y (m

iles)


Philadelphia

Scranton

Uniontown

x (miles)50 100 150 200 250 300

East



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


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)


(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



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)


AA (2.5, 4.5)(2.5, 4.5) 22



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)


AA (2.5, 4.5)(2.5, 4.5) 22

5.5 - 2.5 = 35.5 - 2.5 = 3



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)


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



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)


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



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)


AA (2.5, 4.5)(2.5, 4.5) 22 3 + 0 = 33 + 0 = 3 66

2 * 3 = 62 * 3 = 6



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)


AA (2.5, 4.5)(2.5, 4.5) 22 3 + 0 = 33 + 0 = 3 66



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)


AA (2.5, 4.5)(2.5, 4.5) 22 3 + 0 = 33 + 0 = 3 66EE (8, 5)(8, 5) 1010



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)


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



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)


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



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)


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



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


(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)


(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


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)


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


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)



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



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


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)



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


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)



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


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



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


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



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


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* =



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


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



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


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



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



Figure 9.6

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



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



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



$62 (20,000)$62 (20,000)



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



$62 (20,000) = $1,240,000$62 (20,000) = $1,240,000



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



$62 (20,000) = $1,240,000$62 (20,000) = $1,240,000



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


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


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



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


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



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


B best


A

DBC

(20, 1390)

(20, 1200)

(20, 1060)

(20, 980)

A best

6.25



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


LocatioLocationn

A

DBC

(20, 1390)

(20, 1200)

(20, 1060)

A best

6.25



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


14.3


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



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


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

)




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.


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


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


Setting up the Initial TableauSetting up the Initial Tableau

Example 9.6



PlantWarehouse

1 2 3

Phoenix

Atlanta

Create a row for each plant and a column for each warehouse

Example 9.6


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



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


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

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