Problem#1(10points). A manufacturer of cat towers wishes to locate a super assem

Question

Problem#1(10points). A manufacturer of cat towers wishes to locate a super assembly facility to meet their cat tower assembly needs for the next millennium. Currently, carpet, cylinders, yarn and fasteners are purchased in bulk from suppliers in North Haverbrook, Ogden, and Springfield in the quantities shown in the table. The super assembly facility would ship to distribution centers located in Seattle, Lubbock, Nashville, and Philadelphia. The locations of all of these cities on an x-y grid, transportation costs on a ton per mile basis, and total tonnage are all contained in the table A) Formulate model that will minimize the shipping costs to the super assembly center B) Solve the model and indicate where should the new super assembly facility be located and what is the total system shipping cost? Transportation Quantity Sources/Markets Cost $/ton mile in Tons Xn Yn (Fn) (Dn) Supply North Haverbrook Ogden Springfield Market Seattle Lubbock Nashville 1.2 1.4 650 450 400 700 250 225 1.200 600 825 2.25 2.25 2.25 300 200 500 500 50 450 800 950 1,200 300 250 1,100 Philadelphia 2.25

Explanation / Answer

Answer:

Here using the center of gravity model for supply we will locate the location of plant and then using the load distance technique calculate the load distance and cost

Source/Markets

Transportation Cost$/ton Mile (Fn)

Quantity in Tons (Dn)

xn

yn

x coordinate for new plant

y coordinate for new plant

Distance from proposed site

Load distance

Shipping Cost

Supply

A

B

C

D

x=(x1*B1+x2*B2+x3*B3+x4*B4+x5*B5+x6*B6+x7*B7)/(B1+B2+B3+B4+B5+B6+B7)

y=(y1*B1+y2*B2+y3*B3+y4*B4+y5*B5+y6*B6+y7*B7)/(B1+B2+B3+B4+B5+B6+B7)

d=sqrt of(square of (xn-x)+square of (yn-y))

l=B*d

SC=l*A

North Haverbrook

1.1

650

700

1200

549.17

825.00

404.20

262727.6

289000.39

Ogden

1.2

450

250

600

374.34

168451.3

202141.62

Springfield

1.4

400

250

825

299.17

119668

167535.2

Market

Seattle

2.25

300

50

1200

624.34

187300.9

421426.93

Lubbock

2.25

200

450

300

534.28

106856.9

240427.92

Nashville

2.25

500

800

250

627.33

313664.1

705744.24

Philadelphia

2.25

500

950

1100

486.10

243048.2

546858.43

Total Shipping cost

Here using the center of gravity model for supply we will locate the location of plant and then using the load distance technique calculate the load distance and cost

Source/Markets

Transportation Cost$/ton Mile (Fn)

Quantity in Tons (Dn)

xn

yn

x coordinate for new plant

y coordinate for new plant

Distance from proposed site

Load distance

Shipping Cost

Supply

A

B

C

D

x=(x1*B1+x2*B2+x3*B3+x4*B4+x5*B5+x6*B6+x7*B7)/(B1+B2+B3+B4+B5+B6+B7)

y=(y1*B1+y2*B2+y3*B3+y4*B4+y5*B5+y6*B6+y7*B7)/(B1+B2+B3+B4+B5+B6+B7)

d=sqrt of(square of (xn-x)+square of (yn-y))

l=B*d

SC=l*A

North Haverbrook

1.1

650

700

1200

549.17

825.00

404.20

262727.6

289000.39

Ogden

1.2

450

250

600

374.34

168451.3

202141.62

Springfield

1.4

400

250

825

299.17

119668

167535.2

Market

Seattle

2.25

300

50

1200

624.34

187300.9

421426.93

Lubbock

2.25

200

450

300

534.28

106856.9

240427.92

Nashville

2.25

500

800

250

627.33

313664.1

705744.24

Philadelphia

2.25

500

950

1100

486.10

243048.2

546858.43

Total Shipping cost

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