Krm8 Ism Ch11

Chapter

11

Location

DISCUSSION QUESTIONS 1. Answers depend on the specific organizations and industries selected by the teams. Some expected tendencies for manufacturers are: Favorable labor climate Proximity to markets

Textiles, furniture, consumer electronics Paper, plastic pipe, cars, heavy metals, and food processing Quality of life High technology and research firms Proximity to suppliers and Paper mills, food processors, and cement manufacturers resources Proximity to company’s Feeder plants and certain product lines in computer other facilities manufacturing industry For service providers, the usually dominant location factor is proximity to customers, which is related to revenues. Other factors that also can be crucial are transportation costs and proximity to markets (such as for distribution centers and warehouses), location of competitors, and site-specific factors such as retail activity and residential density for retailers. Data collection relates to the factors selected, which can be collected with onsite visits or from consultants, chambers of commerce, governmental agencies, banks, and the like. For locations in other countries, additional information is needed about differences in political differences, labor laws, tax laws, regulatory requirements, and cultural differences. It is also important to assess how much control the home office should retain, and the extent to which new techniques will be accepted. 2. The “rust belt” city has made long-term investments in the stadium, roads, zoning, and planning to the benefit of the baseball team (an entertainment service). Leaving the rust belt city leaves the city with these long-term obligations with no means to pay for them. For example, when General Motors closed a large facility in a small community, the results were so devastating that the community sued GM for damages. Retailers in the vicinity have built facilities and operate stores that may not be viable any longer if the team moves. Baseball fans also may not be too sympathetic with the baseball owner.

Location z CHAPTER 11 z

273

PROBLEMS 1. Preference matrix location for A, B, C, or D Location Factor 1. Labor climate 2. Quality of life 3. Transportation system 4. Proximity to markets 5. Proximity to materials 6. Taxes 7. Utilities Total

Factor Weight 5 30 5 25 5 15 15 100

A 5 2 3 5 3 2 5

25 60 15 125 15 30 75 345

Factor Score for Each Location B C 4 20 3 15 3 90 5 150 4 20 3 15 3 75 4 100 2 10 3 15 5 75 5 75 4 60 2 30 350 400

D 5 1 5 4 5 4 1

25 30 25 100 25 60 15 280

Location C, with 400 points. 2. John and Jane Darling Location Factor 1. Rent 2. Quality of life 3. Schools 4. Proximity to work 5. Proximity to recreation 6. Neighborhood security 7. Utilities Total

Factor Weight 25 20 5 10 15 15 10 100

A 3 2 3 5 4 2 4

Factor Score for Each Location B C 75 1 25 2 50 40 5 100 5 100 15 5 25 3 15 50 3 30 4 40 60 4 60 5 75 30 4 60 4 60 40 2 20 3 30 310 320 370

D 5 4 1 3 2 4 5

125 80 5 30 30 60 50 380

Location D, the in-laws’ downstairs apartment, is indicated by the highest score. This points out a criticism of the technique: the Darlings did not include or give weight to a relevant factor. 3. Jackson or Dayton locations Jackson — $250(30,000) − [$1,500,000 + ($50 × 30,000)] = $7,500,000 − $3,000,000 = $4,500,000 Dayton — $250(40,000) − [$2,800,000 + ($85 × 40,000)] = $10,000,000 − $6,200,000 = $3,800,000 Jackson yields higher total profit contribution per year.

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4. Fall-Line, Inc. a. Plot of total costs (in $ millions) versus volume (in thousands) 18 16 Aspen 14 12

Medicine Lodge

Broken Bow

10 8 Wounded Knee 6 4 2 0 0 10 20 30 40 Medicine Lodge Broken Bow

50 60 70 80 Volume Wounded Knee

b. Medicine Lodge is the lowest-cost location for volumes up to 25,000 pairs per year. Broken Bow is the best choice over the range of 25,000 to 44,000 pairs per year. Wounded Knee is the lowest-cost location for volumes over 44,000 pairs per year. Aspen is not the low-cost location at any volume. c. Aspen — $500(60,000) − [$8,000,000 + ($250 × 60,000)] = $30,000,000 − $23,000,000 = $7,000,000 Medicine Lodge — $350(45,000) − [$2,400,000 + ($130 × 45,000)] = $15,750,000 − $8,250,000 = $7,500,000 Broken Bow — $350(43,000) − [$3,400,000 + ($90 × 43,000)] = $15,050,000 − $7,270,000 = $7,780,000 Wounded Knee— $350(40,000) − [$4,500,000 + ($65 × 40,000)] = $14,000,000 − $7,100,000 = $6,900,000

d. Aspen would surpass Broken Bow when the Aspen profit is $7,780,000. $500Q − ($8,000,000 + ($250Q)} = $7,780,000 $250Q = 15,780,000 Q = 63,120 Aspen would be the best location if sales would exceed 63,120 pairs per year.

Location z CHAPTER 11 z

5.

275

Wiebe Trucking, Inc. a. Plot of total costs (in $ millions) versus volume (in thousands) 9

8

5,000,000 + 4.65 Q Denver 7

6

5

3,500,000 + 7.25 Q Salt Lake City

4,200,000 + 6.25 Q 4 Santa Fe 3 0

200

400 Volume

600

800

576.9

b. For up to 576,923 shipments per year, Salt Lake City is the best location. Beyond that, Denver is the best location. 6. Sam’s Bagels Expected annual profits from “Downtown” location: 30,000(3.25 – 1.50) – 12,000 = $40,500 Expected annual profits from “Suburban” location: 25,000(2.85 – 1.00) – 8,000 = $38,250 Recommend “Downtown” location. 7. Distance between three points Point A = (20, 20) Point B = (50, 10) Point C = (50, 60) a. Euclidean distance

d AB = ( x A − x B ) 2 + ( y A − y B ) 2

dAB = (20 − 50)2 + (20 − 10 )2

dAC

= (900 + 100 ) . = 3162 ( = 20 − 50)2 + (20 − 60 )2 = (900 + 1600 ) = 50.0

dBC = (50 − 50 )2 + (10 − 60 )2 = ( 0 + 2500 ) = 50

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b. Rectilinear distances dAB = x A − xB + yA − yB dAB = 30 + 10 = 40 dBC = 0 + 50 = 50 dAC = 30 + 40 = 70

8. Centura High School

Inputs Solver - Center of Gravity Enter data in yellow shaded areas. Enter the names of the towns and the coordinates (x and y) and population (or load, l) of each town.

City/Town Name Boelus Cairo Dannebrog

Center-of-Gravity Coordinates

x 106.72 106.68 106.77

y 46.31 46.37 46.34

l 228 737 356

1321

lx 24332.16 78623.16 38010.12 0 0 140965.4

x* y*

106.71 46.35

ly 10558.68 34174.69 16497.04 0 0 61230.41

Location z CHAPTER 11 z

9. The address shown on the map below seems to be a reasonable choice – 548 Main Avenue, Fargo ND

277

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z

10.

Inputs Solver - Center of Gravity Enter data in yellow shaded areas. Enter the names of the towns and the coordinates (x and y) and population (or load, l) of each town.

City/Town Name Standard Products National Products Golf Cart, Inc. ACME Corp. Speedy Electronics

x 40.15 40.21 7 40.14 8 40.18 2 40.19 3

y 122.264

l 4000

lx 160600

ly 489056

122.28

3000

120651

366840

122.236

7000

281036

855652

122.21

2000

80364

244420

122.196

1000 17000

40193 682844

122196 2078164

x*

40.17

y*

122.24

Center-of-Gravity Coordinates

latitude longitud e

11. Val’s Pizza Treating the southwest corner of the plot as the origin and estimating the coordinates, Point A location (1.00, 1.75), demand = 4000 Point B location (3.75, 2.00), demand = 1000 Point C location (4.75, 2.50), demand = 1000 Point D location (5.00, 0.00), demand = 1000 Point E location (0.75, 0.50), demand = 500 a. x * =

∑ li xi i

∑ li i

and y* =

∑ li yi i

∑ li i

Location z CHAPTER 11 z

x* =

279

( 4000 × 1.00 ) + (1000 × 3.75) + (1000 × 4.75) + (1000 × 5.00 ) + (500 × 0.75) ( 4000 + 1000 + 1000 + 1000 + 500 )

17,875 = 2.38 7500 ( 4000 × 1.75) + (1000 × 2.00 ) + (1000 × 2.50 ) + (1000 × 0.00 ) + (500 × 0.50 ) y* = ( 4000 + 1000 + 1000 + 1000 + 500 ) 11750 = 1.57 y* = 7500

x* =

Val’s should start looking for locations at about 30th and “O” streets, say at (2.5, 1.5). b. Rectilinear load-distance score. Assuming Val’s location at (2.5, 1.5). Location Point A Point B Point C Point D Point E

Load 4000 1000 1000 1000 500

Distance 1.75 1.75 3.25 4.00 2.75

ld score 7000 1750 3250 4000 1375 17,375

c. Rectilinear distance from Val’s (at 2.5, 1.5) to the farthest point D (5.0, 0.0) is 4 miles. At two minutes per mile, the travel time is eight minutes. 12. Davis, California, Post Office a. Center of Gravity ∑ li xi ∑ li yi x* = i and y* = i ∑ li ∑ li i

i

(6 × 2) + (3 × 6) + (3 × 8) + (3 × 13) + (2 × 15) + (7 × 6) + (5 × 18) + (3 × 10) (6 + 3 + 3 + 3 + 2 + 7 + 5 + 3) 285 = 8.9 x* = 32 (6 × 8) + (3 × 1) + (3 × 5) + (3 × 3) + (2 × 10) + (7 × 14) + (5 × 1) + (3 × 3) y* = (6 + 3 + 3 + 3 + 2 + 7 + 5 + 3) 207 = 65 y* = . 32 x* =

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b. Load distance scores Mail Source Point 1 2 3 4 5 6 7 M

Round Trips per Day (l) 6 3 3 3 2 7 5 3

xyCoord (2, 8) (6, 1) (8, 5) (13, 3) (15, 10) (6, 14) (18, 1) (10, 3)

Load-distance to M: (10, 3) 6(8 + 5) = 78 3(4 + 2) = 18 3(2 + 2) = 12 3(3 + 0) = 9 2(5 + 7) = 24 7(4 + 11) = 105 5(8 + 2) = 50 3(0 + 0) = 0 Total = 296

Load-distance to CG: (8.9, 6.5) 6(6.9 + 1.5) = 50.4 3(2.9 + 5.5) = 25.2 3(0.9 + 1.5) = 7.2 3(4.1 + 3.5) = 22.8 2(6.1 + 3.5) = 19.2 7(2.9 + 7.5) = 72.8 5(9.1 + 5.5) = 73.0 3(1.1 + 3.5) = 13.8 Total = 284.4

13. Paramount a. Euclidean distance

d AB = ( x A − x B ) 2 + ( y A − y B ) 2

dAB = (100 − 400 )2 + (200 − 100 )2 dAB

= (90,000 + 10,000 ) = 316.2

dBC = ( 400 − 100)2 + (100 − 100 )2 dBC

= (90,000) = 300

dAC = (100 − 100 )2 + (200 − 100 )2 dAC

= (10,000 ) = 100

Location A —A 4000($3)(0) —B 3000($1)(316.2) —C 4000($3)(100)

= = =

$0 $ 948,600 $1,200,000 $2,148,600

Location B —A 4000($3)(316.2) —B 3000($1)(0) —C 4000($3)(300)

= = =

$3,794,400 $0 $3,600,000 $7,394,400

Location C —A 4000($3)(100) —B 3000($1)(300) —C 4000($3)(0)

= = =

$1,200,000 $ 900,000 $0 $2,100,000← lowest transportation cost

Location z CHAPTER 11 z

b. Rectilinear distances dAB = x A − xB + yA − yB dAB = 100 − 400 + 200 − 100 dAB = 400 dBC = 400 − 100 + 100 − 100 dBC = 300 dAC = 100 − 100 + 200 − 100 dAC = 100

Location A —A 4000($3)(0) —B 3000($1)(400) —C 4000($3)(100)

= = =

$0 $1,200,000 $1,200,000 $2,400,000

Location B —A 4000($3)(400) —B 3000($1)(0) —C 4000($3)(300)

= = =

$4,800,000 $0 $3,600,000 $8,400,000

Location C —A 4000($3)(100) —B 3000($1)(300) —C 4000($3)(0)

= = =

$1,200,000 $ 900,000 $0 $2,100,000← Location C is again indicated

c. Center of gravity (133.33, 144.44) ∑ li xi ∑ li yi * * i x = and y = i l ∑i ∑ li i

i

(100 × $12,000) + (400 × $3,000) + (100 × $12,000) ( 27,000 ) 3,600,000 x* = = 133.33 27,000 (200 × $12,000) + (100 × $3,000) + (100 × $12,000) y* = ( 27,000 ) 3,900,000 y* = = 144.44 27,000 x* =

281

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14. Personal computer manufacturer From port at Los Angeles: To Chicago: $0.0017/mile 1,800 miles To Atlanta: $0.0017/mile 2,600 miles To New York: $0.0017/mile 3,200 miles

= = =

$3.06/unit $4.42/unit $5.44/unit

From port at San Francisco: To Chicago: $0.0020/mile 1,700 miles To Atlanta: $0.0020/mile 2,800 miles To New York: $0.0020/mile 3,000 miles

= = =

$3.40/unit $5.60/unit $6.00/unit

Now we use the load-distance method to evaluate each port, where ld = Σi lidi Cost of port at Los Angeles: $3.06(10,000) + $4.42(7,500) + $5.44(12,500) = $131,750 Cost of port at San Francisco: $3.40(10,000) + $5.60(7,500) + $6.00(12,500) = $151,000 Therefore, the more cost-effective city is Los Angeles. 15. Optimal shipping pattern is: Source

Destination $4

El Paso New York City Demand

Omaha

Atlanta

$5 8,000

$3

$6 4,000

$7

8,000

2,000

8,000

10,000

Capacity

Seattle

12,000 $9 10,000

4,000

22,000

Ship 8000 cases from El Paso to Omaha @ $5: $40,000 Ship 4000 cases from El Paso to Seattle @ $6: $24,000 Ship 8000 cases from New York City to Atlanta @ $3: $24,000 Ship 2000 cases from New York City to Omaha @ $7: $14,000 Minimum transportation costs $102,000 This solution can be obtained with Tutor 11.4 of OM Explorer, using a dummy as the fourth destination with no demand, and a dummy for the third source with a capacity of 0. Just unprotect the worksheet to put in the names of the cities, and hide the columns and rows of the dummies. The results follow:

Location z CHAPTER 11 z

283

Tutor - Transportation Method Enter data in yellow shaded areas.

Wholesaler

Atlanta

Distribution Center Omaha 4

El Paso

Seattle

Capacity

5

6

8,000

4,000

3

7

9

New York City

8,000

2,000

Requirements

8,000

10,000

4,000

$24,000

$54,000

$24,000

Costs

12,000 10,000

Total Cost

22,000 22,000

$102,000

16. Placing a warehouse at 2568 Sunset Blvd., West Columbia, SC 29169 will result in a load distance score of 77,043 miles.

17. Pelican Company a. The sum of requirements equals the sum of demands, so no dummy plant or warehouse is needed. The capacity is fully utilized and the demand is fully satisfied. The following shows an optimal solution found with Tutor 11.4, where the quantities are in thousands of gallons. Tutor - Transportation Method Enter data in yellow shaded areas.

Wholesaler

Distribution Center B C

A 1.3

1.4

1.3

1.5

1 2

D

Capacity

1.8

1.6

1.8

1.6

50

50

40

10

20

1.6

1.4

1.7

1.5

10

50

3

70 60

180 Requirements Costs Total Cost

40

60

30

50

$52

$85

$53

$75

180

$265

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b. Total cost of the preceding solution (in $000) is (50 × 1.4) + (40 × 1.3) + (30 × 1.8) + (10 × 1.4) + (50 × 1.5) = $265 18. Acme Company The optimal solution follows. The total transportation costs are: [(60,000 × $1) + (20,000 × $3) + (50,000 × $1) + (10,000 × $4) + (20,000 × $3) +

(40,000 × $1) + (50,000 × $2)] = $410,000

Factory F1 F2 F3 F4 Demand

Shipping Cost ($/case) to Warehouse W1

W3

W2

W4

$1

$3

60,000

20,000

$2

$2

$1

$4

$5

50,000 $1

10,000 $3

$1

20,000

40,000

$5

$4

$1 $5

$2

$4

Capacity

W5 $5

$6 80,000

$4

$5 60,000

50,000 60,000

70,000

60,000 50,000

50,000

30,000

40,000

250,000

Location z CHAPTER 11 z

285

These results can be obtained from OM Explorer, this time using the Transportation Method solver (with the larger problem size, Tutor 10.4 cannot be used): Solver Transportation Method Destinations W1

W2

W3

W4

W5

Capacity

1 2 1 5

3 2 5 2

4 1 1 4

5 4 3 5

6 5 1 4

80,000 60,000 60,000 50,000

60,000

70,000

50,000

30,000

40,000

250,000

Sources F1 F2 F3 F4 Reqt's

Destinations W1

W2

W3

W4

W5

Capacity

Sources F1 F2 F3 F4

60,000 0 0 0

10,000 10,000 0 50,000

0 50,000 0 0

10,000 0 20,000 0

0 0 40,000 0

80,000 60,000 60,000 50,000

Reqt's

60,000

70,000

50,000

30,000

40,000

250,000

Totals

$60,000 $150,000 $50,000 $110,000 $40,000 $410,000

19. Giant Farmer Company Buffalo location-optimal solution: Plant

Miami 7

Chicago Houston Buffalo Requirements

Distribution Center Denver Lincoln 2

40

4

Capacity

5

45

55 3

Jackson

1

100 5

2

35 6

75 9

7

4 80

50

30

255 70

Total optimal cost = $82,500.

90

45

50

255

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Atlanta location-optimal solution: Shipping cost to Distribution Centers ($/case)

Plant

Miami $7

Chicago

Denver $2

Lincoln $4

55

45

$3

Houston

$1

$2

$5

70

$2 75

40

$10

$8

70

Demand ( ×100)

Jackson $5

100

35

Atlanta

Capacity ( × 100)

90

45

$3 10

80

50

255

Total optimal cost = $57,500. The new plant should be located in Atlanta because the total cost is lower.

20.

Ajax International Company Using the Transportation Method solver, the optimal solution is found to be: Destinations W1

W2

W3

W4

W5

Dummy

Capacity

1 2 1 5

3 2 5 2

3 1 1 4

5 4 3 5

6 5 1 4

0 0 0 0

50,000 80,000 80,000 40,000

45,000 30,000

30,000

35,000

50,000 60,000

250,000

Sources F1 F2 F3 F4 Reqt's

Destinations W1

Dummy

Capacity

0 5,000 30,000 0

0 5,000 0 45,000 50,000 0 0 10,000

50,000 80,000 80,000 40,000

35,000

50,000 60,000

250,000

W2

W3

W4

Sources F1 F2 F3 F4

45,000 0 0 0 0 0 0 30,000

0 30,000 0 0

Reqt's

45,000 30,000

30,000

Totals

W5

$45,000 $60,000 $30,000 $110,000 $50,000

$0 $295,000

Location z CHAPTER 11 z

287

Total cost = ($45,000 + $60,000 + $30,000 + $20,000 + $90,000 + $50,000) = $295,000

21. Ajax International Company: Further Analysis Once again using Transportation Method solver, we get the optimal solution shown in the output that follows. With this solution: Total cost, revised problem = $45,000 + $60,000 + $30,000 + $140,000 + $200,000 = $475,000 Total cost, original problem = $295,000 The logistics manager should receive a budget increase of ($475,000 – $295,000) = $180,000 for increased transportation costs. By shifting the shipping pattern, the increase in costs is less than the $210,000 requested. Destinations W1

W2

W3

W4

W5

Dummy

Capacity

1 2 5

3 2 2

3 1 4

5 4 5

6 5 4

0 0 0

50,000 80,000 90,000 ---

45,000

30,000

30,000

35,000

50,000 30,000

220,000

W1

W2

W3

W4

Sources F1 F2 F4

45,000 0 0

0 0 30,000

0 30,000 0

Reqt's

45,000

30,000

30,000

Sources F1 F2 F4 --Reqt's

Destinations

Totals

Dummy

Capacity

0 35,000 0

0 5,000 0 15,000 50,000 10,000

50,000 80,000 90,000

35,000

50,000 30,000

220,000

W5

$45,000 $60,000 $30,000 $140,000 $200,000

$0 $475,000

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22. Giant Farmer Company: Further Analysis—Memphis Plant The optimal solution is shown following. The total costs are $66,500. Because total shipping costs are higher with the Memphis location, this would not change the decision in Problem 19.

Supplier Chicago

Shipping cost to Distribution Centers ($/case) Miami $7

Demand ( × 100)

Lincoln $4

65

35

$3

Houston Memphis

Denver $2 $1

Jackson $5

100 $5

$2

25 $3 70

75

50

$11

$6

$5 80

10

70

90

Capacity ( × 100)

45

50

255

Total optimal cost = $66,500.

23. Chambers Corporation (using Transportation Method Solver) a. Alternative 1 (Portland) Destinations AT

CO

LA

SE

Capacity

Baltimore Milwaukee Portland

0.35 0.55 0.85

0.20 0.15 0.60

0.85 0.70 0.30

0.75 0.65 0.10

6,000 6,000 6,000

Reqt's

5,000

3,000

6,000

4,000

18,000

AT

CO

LA

SE

Capacity

Sources Baltimore Milwaukee Portland

5,000 0 0

1,000 2,000 0

0 4,000 2,000

0 0 4,000

6,000 6,000 6,000

Reqt's

5,000

3,000

6,000

4,000

18,000

$1,750.00 $500.00 $3,400.00

$400.00

$6,050.00

Sources

Destinations

Totals

Location z CHAPTER 11 z

289

b. Alternative 2 (San Antonio) Destinations AT

CO

LA

SE

Capacity

Baltimore Milwaukee San Antonio

0.35 0.55 0.55

0.20 0.15 0.40

0.85 0.70 0.40

0.75 0.65 0.55

6,000 6,000 6,000

Reqt's

5,000

3,000

6,000

4,000

18,000

AT

CO

LA

SE

Capacity

Sources Baltimore Milwaukee San Antonio

5,000 0 0

1,000 2,000 0

0 0 6,000

0 4,000 0

6,000 6,000 6,000

Reqt's

5,000

3,000

6,000

4,000

18,000

$1,750.00 $500.00 $2,400.00 $2,600.00

$7,250.00

Sources

Destinations

Totals

c. Alternative 3 (Portland and San Antonio) Destinations AT

CO

LA

SE

Capacity

Baltimore Milwaukee Portland San Antonio

0.35 0.55 0.85 0.55

0.20 0.15 0.60 0.40

0.85 0.70 0.30 0.40

0.75 0.65 0.10 0.55

6,000 6,000 3,000 3,000

Reqt's

5,000

3,000

6,000

4,000

18,000

AT

CO

LA

SE

Capacity

5,000 0 0 0

1,000 2,000 0 0

0 3,000 0 3,000

0 1,000 3,000 0

6,000 6,000 3,000 3,000

5,000

3,000

6,000

4,000

18,000

$1,750.00 $500.00 $3,300.00

$950.00

$6,500.00

Sources

Destinations Sources Baltimore Milwaukee Portland San Antonio

Reqt's Totals

Alternative 1 (Portland) with a minimum total cost of $605,000 is the best. Alternative 2 (San Antonio) has a minimum total cost of $725,000. Alternative 3 (Portland and San Antonio) has a minimum total cost of $650,000.

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CASE: INDUSTRIAL REPAIR. Inc. * Analysis of the current situation

Using the mileage solver, we determined that based on last year’s data, the costs at 26 Arbor St. location are as follows. • • • •

Mileage cost = 29,338 miles (one-way) *2 (to make two-way)* $2/mile =$117,352 Travel Time (technician expense) = 33,555 minutes (one-way) *2 (to make two-way)*$150/hour * 1 hour/60 minutes = $167,773 Total transportation related costs = $117,352 + $167,773 = $285,125 Analyzing the results of the Mileage Solver, 34% of all trips to customers were within 30 minutes or less.

Question 1

Using the customer data available on Student CD-ROM, determine the best location if IR decides to use only one facility. Be sure to report on the net present value (NPV) using a ten year horizon for this relocation and the percentage of repairs that are within 30 minutes of the chosen location. Note: with this option we must pay $100,000 (which we depreciate using ten year straight-line depreciation). • • •

The best location we found is 16 Hart Ave, Meriden, CT 6450 The one-way mileage and travel time are 25,690 miles and 29,194 minutes, respectively. This results in a total transportation related cost of $248,731. Analyzing the results of the Mileage Solver, 52% of all trips to customers were 30 minute or less.

To use the Financial Solver, we must determine the marginal costs and investments for this proposal. We must invest an extra $100,000 in year 0, and the reduction in expenses is $36,393 (or $285,125 $248,731). Plugging this into the Financial Solver, we get a NPV of $45,979.

*

This case was prepared by Dr. Brooke Saladin, Wake Forest University, as a basis for classroom discussion.

Location z CHAPTER 11 z

291

Inputs Solver - Financial Analysis Enter data in yellow shaded areas. Use the dropdown list to set depreciation type. If you use straight-line depreciation, use the spinner control to set number of years in the horizon Investment amount Starting year Depreciation type Years Discount rate Tax Rate (as percent) Year Revenue Expenses: Variable Expenses: Fixed Depreciation (D) Pre-tax income Taxes (40%) Net Operating Income (NOI) Total Cash Flow (NOI + D)

$100,000 0 StraightLine

Net Present Value Internal Rate of Return

$45,978 22.4%

Payback Period

3.87

years

10 12.0% 40% 1

2

3

4

5

6

(36,393) (36,393) (36,393) (36,393) (36,393) (36,393)

7

8

9

10

(36,393) (36,393) (36,393) (36,393)

10,000 26,393 10,557

10,000 26,393 10,557

10,000 26,393 10,557

10,000 26,393 10,557

10,000 26,393 10,557

10,000 26,393 10,557

10,000 26,393 10,557

10,000 26,393 10,557

10,000 26,393 10,557

10,000 26,393 10,557

15,836

15,836

15,836

15,836

15,836

15,836

15,836

15,836

15,836

15,836

$25,836

$25,836

$25,836

$25,836

$25,836

$25,836

25,836

25,836

25,836

25,836

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Question 2

Using the customer data available on Student CD-ROM, determine the best location for the new site if IR decides to use two facilities (retaining the existing site for the first one). Be sure to report on the NPV using a ten year horizon for this relocation and the percentage of repairs that are within 30 minutes of the chosen locations. • • •

The best location we found is 240 Kimberly Ave., New Haven, CT 6519 (along with our present location of 26 Arbor St). The one-way mileage and travel time are 19,459 miles and 22,921 minutes, respectively. This results in a Total transportation related cost of $192,442. Analyzing the results of the Mileage Solver, 66% of all trips to customers were 30 minute or less.

To use the Financial Solver, we must determine the marginal costs and investments for this proposal. We must invest an extra $100,000 in year 0 and the reduction in expenses is $22,682 or $285,125 - $192,442 $70,000 (the operating cost for an additional facility). Plugging this into the Financial Solver, we get a NPV of -$502.

Location z CHAPTER 11 z

293

Inputs Solver - Financial Analysis Enter data in yellow shaded areas. Use the dropdown list to set depreciation type. If you use straight-line depreciation, use the spinner control to set number of years in the horizon Investment amount Starting year Depreciation type Years Discount rate Tax Rate (as percent) Year Revenue Expenses: Variable Expenses: Fixed Depreciation (D) Pre-tax income Taxes (40%) Net Operating Income (NOI) Total Cash Flow (NOI + D)

$100,000 0 StraightLine

Net Present Value Internal Rate of Return

-$502 11.9%

Payback Period

5.68

years

10 12.0% 40% 1

2

3

4

5

6

7

8

9

10

(22,682) (22,682) (22,682) (22,682) (22,682) (22,682) (22,682) (22,682) (22,682) (22,682) 10,000 12,682 5,073

10,000 12,682 5,073

10,000 12,682 5,073

10,000 12,682 5,073

10,000 12,682 5,073

10,000 12,682 5,073

10,000 12,682 5,073

10,000 10,000 12,682 12,682 5,073 5,073

10,000 12,682 5,073

7,609

7,609

7,609

7,609

7,609

7,609

7,609

7,609 7,609

7,609

$17,609

$17,609

$17,609

$17,609

$17,609

$17,609

17,609

17,609 17,609

17,609

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Question 3 What should Andrew recommend? Provide an explanation for supporting the recommendation.

On the basis of the NPV analysis, it appears that we should simply relocate our facility since that outcome has a positive net present value and the two location model has a negative net present value. However, let us examine a boxplot comparing the one-way travel times under each option. Plot of one-way travel time for three scenarios

240 Kimberly Ave along with present location

16 Hart Ave

Use current location only

0

20

40

60

80

(The scale is in minutes. The center dots indicate the mean one-way travel time for that scenario. The left vertical line in the boxes is the 25th percentile; the middle vertical line is the 50th percentile, and; the right vertical line is the 75th percentile.) It is clear that the two location option has significant travel time advantages over the other options. As noted in the case, the proximity to the customer is becoming an increasingly important factor in attracting and retaining customers. The two location option provides a better competitive position, and it would only take an increase of a marginal $13,711 to make the two alternatives equal regarding NPV.

Location z CHAPTER 11 z

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CASE: R. U. Reddie for Location A. Overview Rhonda Reddie, owner and CEO of a company that manufactures wardrobes for stuffed animals, is faced with the prospect of sizeable demand increases in the near future with insufficient capacity to take advantage of it. Expanding capacity at her existing plants is not an option for various reasons. Consequently, she must decide if it is a good idea to increase capacity by purchasing a new plant. If the answer is yes, then she must decide where the plant should be located. The two options she would consider are St. Louis and Denver. B. Purpose This case was written to provide the student with enough data to analyze the decisions Reddie must make, using tools such as linear programming and net present values. Reddie has a number of concerns regarding the quality of the data she has to work with, which offers the opportunity for students to do sensitivity analysis with the models. Students learn where the cost figures come from that are used in the cash flow analysis and net present value calculations. In this case, the location decision will affect the cost of goods sold because of differing cost factors at each location which affect the distribution patterns in the supply network. In addition, the capital costs of the plant and equipment differ by location, as does the cost of the land. Consequently, the location decision affects annual operating costs, the extent of the capital investment, and hence the financial results as represented by the net present value of the investment. Instructors can use the case to demonstrate the cross-functional aspects of these major decisions in practice. C. Linear Programming Models Appendix A contains the linear programming models for Denver and St. Louis in matrix form. The models determine the optimal shipping pattern if Denver or St. Louis are the chosen locations. The objective function value is the optimal cost of goods sold for the entire network of plants with a given option for the new fourth plant. The demand data are the “most likely” estimates given in the case. Students will have to determine the objective function coefficients, which consist of the variable production cost per unit at a plant plus the transportation cost to ship one unit from the plant to one of the destinations in the supply chain. The distribution cost is $0.0005: The actual cost to ship to another destination will depend on the number of miles the unit must be shipped. For example, the cost to produce one unit in Cleveland and ship it to Boston is $3.00 + $0.0005 (650 miles) = $3.325.

Appendix A contains two models for each location option because the new plant can only produce 500,000 units the first year, and the demand increases for the first year are less than those projected for years 2 and beyond. In the second year the new plant can produce 900,000 units. The capacity of the network with the new plant is sufficient to handle any foreseeable contingencies. These models must be used a number of times to analyze the issues in the case.

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D. Optimal Distribution Plans for each Location There are actually two distribution plans for each location: One for year 1 and another for years 2 and beyond. The tables below provide the optimal distribution plans and costs. Denver

From

To

Year 1

Years 2 to 10

Boston

Boston St. Louis

80 220

140 60

Cleveland

Cleveland St. Louis

200 200

260 140

Chicago

Chicago St. Louis Denver

370 20 110

430 70 NONE

Denver

Denver St. Louis

500 NONE

670 230

The Total Cost of Goods Sold ($000)for the Denver alternative is: Year 1 $5790 Years 2 – 10 $6606.25 per year St. Louis

From

To

Year 1

Years 2 to 10

Boston

Boston Denver Chicago

80 220 NONE

140 NONE 60

Cleveland

Cleveland Chicago

200 200

260 140

Chicago

Chicago Denver

170 330

230 270

St. Louis

St. Louis Denver

440 60

500 400

The Total Cost of Goods Sold ($000)for the St. Louis alternative is: Year 1 $5935.50 Years 2 – 10 $6689.50 per year Several things can be noted at this stage. First, on the basis of variable costs (COGS) alone, Denver seems to be the best choice. However, as we shall see later, other financial considerations must be made. Second, the distribution assignments (i.e., which warehouses must be serviced by each plant) differ slightly in going from the first to the second years. If they are not changed, the lowest costs will not be realized. Also, the distribution plans for Denver are quite different than those for St. Louis. The implication is that the location decision affects the distribution assignments of all plants in the network, not just the new plant being added to the network. Appendix B contains the linear programming solutions, which show not only the optimal

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297

distribution plans but also the shadow prices and constraint ranges that are useful for decision making. E. Net Present Value One important measure of the viability of a location decision involving capital outlays is the use of a net present value (NPV) criterion. However, in this case we must compute incremental cash flows because the new plant is to be used as a member of an existing network of plants. The only measures of cash flow we get here is the total system COGS with and without the new investment. The case gives the COGS for a Status Quo (without the new plants) solution so that these incremental costs attributable to the new investment can be computed. For example, the Denver alternative will generate the following incremental COGS ($000):

Year 1 Years 2-10

Denver $5790 $6606

-

Status Quo $4692 $4554

= =

Incremental COGS $1098 $2052

The revenue flows due to the addition of a new plant are the same regardless of the location. In year 1, 400 (000) additional units can be sold at a price of $8 per unit, for an incremental addition of $3200. In years 2 and beyond, 700 (000) additional units will generate $5600 in incremental revenues. Given the assumptions regarding taxes, depreciation, and the data on capital costs, land costs, and annual fixed costs listed in the case, a spreadsheet can be constructed to compute the NPV for each alternative. NOTE: The terminal value of the project is 50% of the combined land and plant and equipment costs, while the tax is 40% of the terminal value of the project net of the initial land cost. The NPV calculations for the two alternatives are given in Appendix C. Note that now St. Louis appears to be the better alternative. The NPV for Denver is $936.35 versus the NPV for St. Louis of $1058.62. The reason for this switch is that Denver’s capital costs are higher than St. Louis’, enough to offset it’s advantage in annual COGS. St. Louis is the better investment while Denver would require less annual operating capital. F. Sensitivity Analysis The case raised some questions about the quality of the data used to make this important decision. The models can be used to explore the implications of errors in the data used in the analysis. In each case taken separately, the question is whether the decision to go to St. Louis would be reversed. Demand Changes Equally Divided for Each Destination

In this analysis, the following issue is raised: If forecast errors are in the range of + 10% across the board, will the location decision be affected? Running the linear programming model for years 2 to 10 for each alternative and recalculating the incremental revenue and COGS for the conditions of 10% increases and 10% decreases, we find the following NPV results:

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10% Increase 10% Decrease

Denver $3243.52 -$1608.01

St. Louis $3196.47 -$1324.34

If demands are 10 percent higher, Denver is best. However, if demands are 10 percent lower, St. Louis is best but the NPVs are negative. The question of how confident Reddie is about the forecasts should be discussed. If there is a good chance of the lower demands materializing, the whole issue of capacity expansion should be revisited. Shift in Market Concentration to the West

The question is whether the location decision is affected by a shift in the demand concentration to the West. The linear programming models must be revised and rerun to reflect the different demand pattern, where St. Louis is now 550 (000) and Denver is now 820 (000). The NPVs are now: Denver: $3281.30 St. Louis: $3036.94 While both alternatives yield good returns, Denver is now a little better than St. Louis. The reason is that the Denver location is particularly well positioned since the preponderance of the new demands are projected for that city. The COGS goes down relative to St. Louis, thereby offsetting Denver’s larger capital costs. Changes in the COGS Estimates for Each Alternative

How sensitive is the solution to the estimates in the variable production costs and the transportation costs for Denver and St. Louis. Would an error of 10% make a difference? In this analysis the linear programming models must be modified (both the first year and the years 2 to 10 models) to reflect the changes to the objective function values for the variables associated with the new plants only. New incremental cash flows must be computed and used in a NPV analysis. The resulting NPVs are: 10% Increase in COGS 10% Decrease in COGS

Denver -$27.28 $1,898.49

St. Louis $ 102.65 $2,020.36

If the estimates for the COGS of each alternative both increase or decrease, the decision to go to St. Louis is still unchanged. However, if the estimates for the COGS for Denver were supposed to be 10% lower than the base case while the estimates for St. Louis were supposed to be 10% higher, then the decision is clearly to go to Denver. The instructor can discuss the costs that make up “variable “ production costs and why there may be errors in estimating them. Such costs would include: • • • •

Materials (a function of the negotiated prices with suppliers; actual quality) Labor (available skills and productivity, training, wage packages) Machine costs (power, repair, speeds, quality) Changeover (actual run sizes, product mix)

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299

In addition, actual transportation costs will also vary depending on the chosen mode of transportation (rail, truck, air) and the reliability of the carrier. Considerations in the mode choice depend on whether speed, on-time delivery, or costs are the most important consideration in distribution. This analysis shows that estimating the COGS accurately is important for this decision. Changes in the Estimates of Fixed Annual Costs for Each Alternative

A similar conclusion can be drawn regarding the annual fixed costs. In this analysis only the spreadsheet containing the NPV analysis need be revised and recalculated because the linear programming models do not contain annual fixed costs. The category “annual fixed costs” includes administration, utilities not directly associated with producing a unit of product, insurance, and any other overhead cost that does not vary with output. Would the decision to go to St. Louis be changed if there were errors of 10 % in the annual fixed costs for each alternative? The NPVs are: 10% Increase in Fixed Costs 10% Decrease in Fixed Costs

Denver $ 742.01 $1,130.69

St. Louis $ 793.61 $1,323.63

We see that if the fixed costs for Denver used in the base case should have been 10% lower, while the fixed costs for St. Louis in the base case should have been 10% higher, the decision would now be to go to Denver. Otherwise, if both estimates were low or high, the decision would not change. The instructor can discuss the various cost elements that comprise annual fixed costs and the potential for estimation errors in situations such as this one. Reducing Production in Cleveland

Reddie is contemplating cutting back production by 50 (000) units annually from years 2 and beyond for Cleveland. This option is feasible from a capacity perspective so long as a new plant is in the system. This decision can be approached without rerunning any of the models in the following way. The shadow price and the right-hand-side range for Cleveland’s capacity from the base solution (most likely demands) for each alternative are useful (See Appendix B). The “new” change in COGS equals the “old” change in COGS plus 50 times the shadow price on Cleveland capacity. For example, using the solution for Denver (years 2 – 10) in the base case (Appendix B), and the NPV for the Denver base case (Appendix C), we get: New change in COGS = $2052 + 50($1.100) = $2107. This estimate can now be used in the NPV model to get the desired results. Denver: $771.74

St. Louis: $890.27

We see that the St. Louis alternative would be better than Denver.

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F. Conclusions The sensitivity analysis demonstrated that the following data are critical to the decision at hand: (1) demand increase, (2) forecast of a market shift, and (3) estimates of the COGS and fixed costs. Any reasonable errors in these data could cause a reversal of the decision. Reddie must be confident in the accuracy of the data before going further.

Finally, the case raised some non-quantitative factors in this decision. The instructor should press the students as to how they would reconcile these factors, particularly since two of the three favor Denver. One way to rationalize the decision is to use a preference matrix where each alternative can be scored subjectively across all the major criteria. For example, using the base case in which St. Louis had the best NPV, we might have the following matrix where a score of 5 is excellent and a 1 is poor: Factor

Weight

Workforce availability Environmental restrictions Supplier availability NPV

0.20 0.10 0.20 0.50

Denver

4 2 5 4 4.0

St. Louis

2 3 3 5 3.8

With this arbitrary example, Denver would get the nod for the new plant. Obviously, the analysis depends on the scores and weights.

Appendix A Denver LP Year 1 Min-Z

B CL CH D BDEM CLDEM CHDEM SLDEM DDEM

B-B 3.8

B-CL 4.125

1

1

B-CH 4.3

1

B-SL 4.4

1

B-D 4.8

CL-B 3.325

CL-CL 3

CL-CH 3.175

CL-SL 3.3

CL-D 3.7

CH-B 3.75

CH-CL 3.425

CH-CH 3.25

CH-SL 3.4

CH-D 3.75

D-B 4.15

D-CL 3.85

D-CH 3.65

D-SL 3.575

D-D 3.15

1 1

1

1

1

1 1

1

1 1

1

1

1

1 1 1

1 1

1

1 1

1

1

1

1

1 1

1

1 1

1

1 1

1 1

1

RHV Z = < < < < = = = = =

400 400 500 500 80 200 370 440 610

Denver LP Years 2-10 Min-Z

B CL CH D BDEM CLDEM CHDEM SLDEM DDEM

B-B 3.8

B-CL 4.125

1

1

B-CH 4.3

1

B-SL 4.4

1

B-D 4.8

CL-B 3.325

CL-CL 3

CL-CH 3.175

CL-SL 3.3

CL-D 3.7

CH-B 3.75

CH-CL 3.425

CH-CH 3.25

CH-SL 3.4

CH-D 3.75

D-B 4.15

D-CL 3.85

D-CH 3.65

D-SL 3.575

D-D 3.15

1 1

1

1

1

1 1

1

1 1

1

1

1

1 1 1

1 1

1

1 1

1

1

1

1

1

1

1 1

1

1 1

1

1 1

1

RHV Z = < < < < = = = = =

400 400 500 900 140 260 430 500 670

St. Louis LP Year 1 Min-Z

B CL CH SL BDEM CLDEM CHDEM SLDEM DDEM

B-B 3.8

1

B-CL 4.125

1

B-CH 4.3

1

B-SL 4.4

1

B-D 4.8

CL-B 3.325

CL-CL 3

CL-CH 3.175

CL-SL 3.3

CL-D 3.7

CH-B 3.75

CH-CL 3.425

CH-CH 3.25

CH-SL 3.4

CH-D 3.75

SL-B 3.65

SL-CL 3.35

SL-CH 3.2

SL-SL 3.05

SL-D 3.475

1 1

1

1

1

1 1

1

1 1

1

1

1

1 1 1

1 1

1

1 1

1

1

1

1

1

1

1 1

1

1 1

1

1 1

1

RHV Z = < < < < = = = = =

400 400 500 500 80 200 370 440 610

St. Louis LP Years 2-10 Min-Z

B CL CH SL BDEM CLDEM CHDEM SLDEM DDEM

B-B

B-CL

B-CH

B-SL

B-D

CL-B

CL-CL

CL-CH

CL-SL

CL-D

CH-B

CH-CL

CH-CH

3.8

4.125

4.3

4.4

4.8

3.325

3

3.175

3.3

3.7

3.75

3.425

3.25

1

1

1

1

CHSL 3.4

CH-D

SL-B

SL-CL

SL-CH

SL-SL

SL-D

3.75

3.65

3.35

3.2

3.05

3.475

1 1

1

1

1

1 1

1

1 1

1 1

1

1 1 1

1

1

1

1 1

1

1 1

1 1

1

1

1 1

1

1

1

1 1

1

RHV Z = < < < < = = = = =

400 400 500 900 140 260 430 500 670

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Appendix B Denver LP Year 1

Denver LP Years 2-10

Results

Results

Solver - Linear Programming

Solver - Linear Programming

Solution

Solution

Variable Label B-B B-CL B-CH B-SL B-D CL-B CL-CL CL-CH CL-SL CL-D CH-B CH-CL CH-CH CH-SL CH-D D-B D-CL D-CH D-SL D-D

Variable Value 80.0000 0.0000 0.0000 220.0000 0.0000 0.0000 200.0000 0.0000 200.0000 0.0000 0.0000 0.0000 370.0000 20.0000 110.0000 0.0000 0.0000 0.0000 0.0000 500.0000

Original Coefficient 3.8000 4.1250 4.3000 4.4000 4.8000 3.3250 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 4.1500 3.8500 3.6500 3.5750 3.1500

Coefficient Sensitivity 0 0.0250 0.0500 0 0.0500 0.6250 0 0.0250 0 0.0500 0.9500 0.3250 0 0 0 1.9500 1.3500 1.0000 0.7750 0

Variable Label B-B B-CL B-CH B-SL B-D CL-B CL-CL CL-CH CL-SL CL-D CH-B CH-CL CH-CH CH-SL CH-D D-B D-CL D-CH D-SL D-D

Variable Value 140.0000 0.0000 0.0000 60.0000 0.0000 0.0000 260.0000 0.0000 140.0000 0.0000 0.0000 0.0000 430.0000 70.0000 0.0000 0.0000 0.0000 0.0000 230.0000 670.0000

Original Coefficient 3.8000 4.1250 4.3000 4.4000 4.8000 3.3250 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 4.1500 3.8500 3.6500 3.5750 3.1500

Coefficient Sensitivity 0 0.0250 0.0500 0 0.8250 0.6250 0 0.0250 0 0.8250 0.9500 0.3250 0 0 0.7750 1.1750 0.5750 0.2250 0 0

Constraint Label B CL CH D BDEM CLDEM CHDEM SLDEM DDEM

Original RHV 400 400 500 500 80 200 370 440 610

Slack or Surplus 100 0 0 0 0 0 0 0 0

Shadow Price 0 -1.1000 -1.0000 -1.6000 3.8000 4.1000 4.2500 4.4000 4.7500

Constraint Label B CL CH D BDEM CLDEM CHDEM SLDEM DDEM

Original RHV 400 400 500 900 140 260 430 500 670

Slack or Surplus 200 0 0 0 0 0 0 0 0

Shadow Price 0 -1.1000 -1.0000 -0.8250 3.8000 4.1000 4.2500 4.4000 3.9750

5790 Objective Function Value: Sensitivity Analysis and Ranges

Objective Function Value: 6606.25 Sensitivity Analysis and Ranges

Objective Function Coefficient Variable Label B-B B-CL B-CH B-SL B-D CL-B CL-CL CL-CH CL-SL CL-D CH-B CH-CL CH-CH CH-SL CH-D D-B D-CL D-CH D-SL D-D

Lower Limit No Limit 4.1000 4.2500 3.7750 4.7500 2.7000 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 4.1500 3.8500 3.6500 3.5750 3.1500

Constraint Label B CL CH D BDEM CLDEM CHDEM SLDEM DDEM

Lower Limit 300 300 480 480 4.43379E-11 -1.02318E-10 150 220 500

Original Coefficient 3.8000 4.1250 4.3000 4.4000 4.8000 3.3250 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 4.1500 3.8500 3.6500 3.5750 3.1500

Objective Function Coefficient

Upper Limit 4.4250 No Limit No Limit 4.4250 No Limit No Limit 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 4.1500 3.8500 3.6500 3.5750 3.1500

Variable Label B-B B-CL B-CH B-SL B-D CL-B CL-CL CL-CH CL-SL CL-D CH-B CH-CL CH-CH CH-SL CH-D D-B D-CL D-CH D-SL D-D

Lower Limit No Limit 4.1000 4.2500 3.7750 3.9750 2.7000 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 4.1500 3.8500 3.6500 3.5750 3.1500

Right-Hand-Side Values Original Upper Value Limit 400 No Limit 400 620 500 720 500 610 80 180.0000001 200 300 370 390 440 540 610 630

Constraint Label B CL CH D BDEM CLDEM CHDEM SLDEM DDEM

Lower Limit 200 260 430 700 0 200 370 440 610

Original Coefficient 3.8000 4.1250 4.3000 4.4000 4.8000 3.3250 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 4.1500 3.8500 3.6500 3.5750 3.1500

Upper Limit 4.4250 No Limit No Limit 4.4250 No Limit No Limit 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 4.1500 3.8500 3.6500 3.5750 3.1500

Right-Hand-Side Values Original Upper Value Limit 400 No Limit 400 460 500 560 900 960 140 340 260 400 430 500 500 700 670 870

Location z CHAPTER 11 z

Appendix B

St. Louis LP Year 1

St. Louis LP Years 2-10

Results

Results

Solver - Linear Programming

Solver - Linear Programming

Solution

Solution

Variable Label B-B B-CL B-CH B-SL B-D CL-B CL-CL CL-CH CL-SL CL-D CH-B CH-CL CH-CH CH-SL CH-D SL-B SL-CL SL-CH SL-SL SL-D

Variable Value 80.0000 0.0000 0.0000 0.0000 220.0000 0.0000 200.0000 200.0000 0.0000 0.0000 0.0000 0.0000 170.0000 0.0000 330.0000 0.0000 0.0000 0.0000 440.0000 60.0000

Original Coefficient 3.8000 4.1250 4.3000 4.4000 4.8000 3.3250 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 3.6500 3.3500 3.2000 3.0500 3.4750

Coefficient Sensitivity 0 0 0 0.0250 0 0.6500 0 0 0.0500 0.0250 1.0000 0.3500 0 0.0750 0 1.1750 0.5500 0.2250 0 0

Variable Label B-B B-CL B-CH B-SL B-D CL-B CL-CL CL-CH CL-SL CL-D CH-B CH-CL CH-CH CH-SL CH-D SL-B SL-CL SL-CH SL-SL SL-D

Variable Value 140.0000 0.0000 60.0000 0.0000 0.0000 0.0000 260.0000 140.0000 0.0000 0.0000 0.0000 0.0000 230.0000 0.0000 270.0000 0.0000 0.0000 0.0000 500.0000 400.0000

Original Coefficient 3.8000 4.1250 4.3000 4.4000 4.8000 3.3250 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 3.6500 3.3500 3.2000 3.0500 3.4750

Coefficient Sensitivity 0 0 0 0.0250 0 0.6500 0 0 0.0500 0.0250 1.0000 0.3500 0 0.0750 0 1.1750 0.5500 0.2250 0 0

Constraint Label B CL CH SL BDEM CLDEM CHDEM SLDEM DDEM

Original RHV 400 400 500 500 80 200 370 440 610

Slack or Surplus 100 0 0 0 0 0 0 0 0

Shadow Price 0 -1.1250 -1.0500 -1.3250 3.8000 4.1250 4.3000 4.3750 4.8000

Constraint Label B CL CH SL BDEM CLDEM CHDEM SLDEM DDEM

Original RHV 400 400 500 900 140 260 430 500 670

Slack or Surplus 200 0 0 0 0 0 0 0 0

Shadow Price 0 -1.1250 -1.0500 -1.3250 3.8000 4.1250 4.3000 4.3750 4.8000

Objective Function Value: 5935.5 Sensitivity Analysis and Ranges

Objective Function Value: 6689.5 Sensitivity Analysis and Ranges

Objective Function Coefficient Variable Label B-B B-CL B-CH B-SL B-D CL-B CL-CL CL-CH CL-SL CL-D CH-B CH-CL CH-CH CH-SL CH-D SL-B SL-CL SL-CH SL-SL SL-D

Lower Limit No Limit 4.1250 4.3000 4.3750 4.1500 2.6750 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.250 3.4000 3.7500 3.6500 3.3500 3.2000 3.0500 3.4750

Constraint Label B CL CH SL BDEM CLDEM CHDEM SLDEM DDEM

Lower Limit 300 300 400 440 4.43379E-11 30 200 220 390

Original Upper Coefficient Limit 3.8000 4.4500 4..1250 No Limit 4.3000 No Limit 4.4000 No Limit 4.8000 4.8000 3.3250 No Limit 3.0000 3.0000 3.1750 3.1750 3.3000 3.3000 3.7000 3.7000 3.7500 3.7500 3.4250 3.4250 3.2500 3.2500 3.4000 3.4000 3.7500 3.7500 3.6500 3.6500 3.3500 3.3500 3.2000 3.2000 3.0500 3.0500 3.4750 3.4750 Right-Hand-Side Values Original Upper Value Limit 400 No Limit 400 570 500 720 500 720 80 180 200 300 370 470 440 500 610 710

Objective Function Coefficient Variable Label B-B B-CL B-CH B-SL B-D CL-B CL-CL CL-CH CL-SL CL-D CH-B CH-CL CH-CH CH-SL CH-D SL-B SL-CL SL-CH SL-SL SL-D

Lower Limit No Limit 4.1250 3.6500 4.3750 4.8000 2.6750 3.0000 3.1750 3.3000 3.7000 3.7500 3.4250 3.2500 3.4000 3.7500 3.6500 3.3500 3.2000 3.0500 3.4750

Constraint Label B CL CH SL BDEM CLDEM CHDEM SLDEM DDEM

Lower Limit 200 260 300 700 0 200 370 440 610

Original Upper Coefficient Limit 3.8000 4.4500 4.1250 No Limit 4.3000 4.3000 4.4000 No Limit 4.8000 No Limit 3.3250 No Limit 3.0000 3.0000 3.1750 3.1750 3.3000 3.3000 3.7000 3.7000 3.7500 3.7500 3.4250 3.4250 3.2500 3.2500 3.4000 3.4000 3.7500 3.7500 3.6500 3.6500 3.3500 3.3500 3.2000 3.2000 3.0500 3.0500 3.4750 3.4750 Right-Hand-Side Values Original Upper Value Limit 400 No Limit 400 460 500 560 900 960 140 340 260 400 430 630 500 700 670 870

303

Appendix C Denver Location NPV⎯Most Likely Denver 0

1

2

3

4

5

6

7

8

9

10

Change in Revenues COGS Gross Profit

3200 1098 2102

5600 2052 3548

5600 2052 3548

5600 2052 3548

5600 2052 3548

5600 2052 3548

5600 2052 3548

5600 2052 3548

5600 2052 3548

5600 2052 3548

Depreciation Fixed Costs EBIT

1210 550 342

1210 550 1788

1210 550 1788

1210 550 1788

1210 550 1788

1210 550 1788

1210 550 1788

1210 550 1788

1210 550 1788

1210 550 1788

Taxes Profit After Tax

136.8 205.2

715.2 1072.8

715.2 1072.8

715.2 1072.8

715.2 1072.8

715.2 1072.8

715.2 1072.8

715.2 1072.8

715.2 1072.8

715.2 1072.8

1415.2

2282.8

2282.8

2282.8

2282.8

2282.8

2282.8

2282.8

2282.8

2282.8

Profit or Loss

Cash Flows

Add Back Depreciation Other Cash Flows Initial Plant & Equip Costs Land Cost Sale of New Plant Tax on Gain

12100 1200 6650 -2180

Free Cash Flow NPV @ 11%

1415.2 $936.35

2282.8

2282.8

2282.8

2282.8

2282.8

2282.8

2282.8

2282.8

6752.8

Location

z

CHAPTER 11

z

305

Appendix C St. Louis Location NPV⎯Most Likely St. Louis 0

1

2

3

4

5

6

7

8

9

10

Change in Revenues COGS Gross Profit

3200 1244 1956

5600 2135.5 3464.5

5600 2135.5 3464.5

5600 2135.5 3464.5

5600 2135.5 3464.5

5600 2135.5 3464.5

5600 2135.5 3464.5

5600 2135.5 3464.5

5600 2135.5 3464.5

5600 2135.5 3464.5

Depreciation Fixed Costs EBIT

1080 750 126

1080 750 1634.5

1080 750 1634.5

1080 750 1634.5

1080 750 1634.5

1080 750 1634.5

1080 750 1634.5

1080 750 1634.5

1080 750 1634.5

1080 750 1634.5

Taxes Profit After Tax

50.4 75.6

653.8 980.7

653.8 980.7

653.8 980.7

653.8 980.7

653.8 980.7

653.8 980.7

653.8 980.7

653.8 980.7

653.8 980.7

1155.6

2060.7

2060.7

2060.7

2060.7

2060.7

2060.7

2060.7

2060.7

2060.7

Profit or Loss

Cash Flows

Add Back Depreciation Other Cash Flows Initial Plant & Equip Costs Land Cost Sale of New Plant Tax on Gain

10800 800 5800 -2000

Free Cash Flow NPV @ 11%

1155.6 $1,058.62

2060.7

2060.7

2060.7

2060.7

2060.7

2060.7

2060.7

2060.7

5860.7