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 Textiles, furniture, consumer electronics Proximity to markets Paper, plastic pipe, cars, heavy metals, and food

processing Quality of life High technology and research firms

Proximity to suppliers and resources

Paper mills, food processors, and cement manufacturers

Proximity to company’s other facilities

Feeder plants and certain product lines in computer 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 on-site 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 CHAPTER 11 273

PROBLEMS 1. Preference matrix location for A, B, C, or D Factor Factor Score for Each Location Location Factor Weight A B C D 1. Labor climate 5 5 25 4 20 3 15 5 25 2. Quality of life 30 2 60 3 90 5 150 1 30 3. Transportation system 5 3 15 4 20 3 15 5 25 4. Proximity to markets 25 5 125 3 75 4 100 4 100 5. Proximity to materials 5 3 15 2 10 3 15 5 25 6. Taxes 15 2 30 5 75 5 75 4 60 7. Utilities 15 5 75 4 60 2 30 1 15

Total 100 345 350 400 280

Location C, with 400 points. 2. John and Jane Darling Factor Factor Score for Each Location Location Factor Weight A B C D 1. Rent 25 3 75 1 25 2 50 5 125 2. Quality of life 20 2 40 5 100 5 100 4 80 3. Schools 5 3 15 5 25 3 15 1 5 4. Proximity to work 10 5 50 3 30 4 40 3 30 5. Proximity to recreation 15 4 60 4 60 5 75 2 30 6. Neighborhood security 15 2 30 4 60 4 60 4 60 7. Utilities 10 4 40 2 20 3 30 5 50

Total 100 310 320 370 380

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( , ) [$2, , ($85 , )] $10, , $6, ,

$3, ,40 000 800 000 40 000 000 000 200 000

800 000− + × = −

=

Jackson yields higher total profit contribution per year.

274 PART 3 Managing Value Chains

4. Fall-Line, Inc.

a. Plot of total costs (in $ millions) versus volume (in thousands)

14

12

10

8

6

4

2

20 40 60 80

18

16

010 30 50 700

Medicine Lodge BrokenBow

Wounded Knee Volume

Aspen

Medicine Lodge Broken Bow

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( , ) [$8, , ($250 , )] $30, , $23, ,

$7,60 000 000 000 60 000 000 000 000 000

000 000− + × = −

= ,

Medicine Lodge —

$350( ) [$2, , ($130 , )] $15, $8, ,

$7,45,000 400 000 45 000 750,000 250 000

500 000− + × = −

= ,

Broken Bow —

$350( ) [$3, , ($90 , )] $15, $7, ,

$7,43,000 400 000 43 000 050,000 270 000

780 000− + × = −

= ,

Wounded Knee—

$350( ) [$4, , ($65 , )] $14, $7, ,

$6,40,000 500 000 40 000 000,000 100 000

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.


5. Wiebe Trucking, Inc.

a. Plot of total costs (in $ millions) versus volume (in thousands)

3

4

5

6

7

8

9

0 200 400 600 800Volume

4,200,000 + 6.25Santa Fe

5,000,000 + 4.65 Denver

3,500,000 + 7.25 Salt Lake City

576.9

Q Q

Q

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 22 )()( BABAAB yyxxd −+−=

dAB = − + −

= +=

( ) ( )

( )

20 50 20 10

900 1003162

2 2

.

dBC = − + −

= +=

( ) ( )

( )

50 50 10 60

0 250050

2 2

dAC = − + −

= +=

( ) ( )

( )

20 50 20 60

900 160050 0

2 2

.


b. Rectilinear distances d x x y yAB A B A B= − + −

ddd

AB

BC

AC

= + =

= + =

= + =

30 10 400 50 5030 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 x y l lx ly Boelus 106.72 46.31 228 24332.16 10558.68 Cairo 106.68 46.37 737 78623.16 34174.69 Dannebrog 106.77 46.34 356 38010.12 16497.04 0 0 0 0 1321 140965.4 61230.41 Center-of-Gravity Coordinates x* 106.71 y* 46.35


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


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 x y l lx ly Standard Products 40.15 122.264 4000 160600 489056

National Products 40.21

7 122.28 3000 120651 366840

Golf Cart, Inc. 40.14

8 122.236 7000 281036 855652

ACME Corp. 40.18

2 122.21 2000 80364 244420

Speedy Electronics

40.193 122.196 1000 40193 122196

17000 682844 2078164

Center-of-Gravity Coordinates x* 40.17 latitude

y* 122.24longitude

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. xl x

l

i ii

ii

* =∑

∑ and y

l y

l

i ii

ii

* =∑

∑


x

x

y

y

*

*

*

*

. . . . .

, .

. . . . .

.

=× + × + × + × + ×

+ + + +

= =

=× + × + × + × + ×

+ + + +

= =

( ) ( ) ( ) ( ) ( )

( )

( ) ( ) ( ) ( ) ( )

( )

4000 100 1000 3 75 1000 4 75 1000 5 00 500 0 754000 1000 1000 1000 500

17 8757500

2 38

4000 175 1000 2 00 1000 2 50 1000 0 00 500 0 504000 1000 1000 1000 500

117507500

157

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 Load Distance ld score Point A 4000 1.75 7000 Point B 1000 1.75 1750 Point C 1000 3.25 3250 Point D 1000 4.00 4000 Point E 500 2.75 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

xl x

l

i ii

ii

* =∑

∑ and y

l y

l

i ii

ii

* =∑

∑

x

x

y

y

*

*

*

*

.

.

=×( ) + ×( ) + ×( ) + ×( ) + ×( ) + ×( ) + ×( ) + ×( )

+ + + + + + +( )

= =

=×( ) + ×( ) + ×( ) + ×( ) + ×( ) + ×( ) + ×( ) + ×( )

+ + + + + + +( )

= =

6 2 3 6 3 8 3 13 2 15 7 6 5 18 3 106 3 3 3 2 7 5 3

28532

89

6 8 3 1 3 5 3 3 2 10 7 14 5 1 3 36 3 3 3 2 7 5 3

20732

65


b. Load distance scores

Mail Source Point

Round Trips per Day (l)

xy- Coord

Load-distance to M: (10, 3)

Load-distance to CG: (8.9, 6.5)

1 6 (2, 8) 6(8 + 5) = 78 6(6.9 + 1.5) = 50.4 2 3 (6, 1) 3(4 + 2) = 18 3(2.9 + 5.5) = 25.2 3 3 (8, 5) 3(2 + 2) = 12 3(0.9 + 1.5) = 7.2 4 3 (13, 3) 3(3 + 0) = 9 3(4.1 + 3.5) = 22.8 5 2 (15, 10) 2(5 + 7) = 24 2(6.1 + 3.5) = 19.2 6 7 (6, 14) 7(4 + 11) = 105 7(2.9 + 7.5) = 72.8 7 5 (18, 1) 5(8 + 2) = 50 5(9.1 + 5.5) = 73.0 M 3 (10, 3) 3(0 + 0) = 0 3(1.1 + 3.5) = 13.8 Total = 296 Total = 284.4

13. Paramount

a. Euclidean distance 22 )()( BABAAB yyxxd −+−=

d

d

AB

AB

= − + −

= +=

( ) ( )

( )

100 400 200 100

90 000 10 000316 2

2 2

, ,.

d

d

BC

BC

= − + −

==

( ) ( )

( )

400 100 100 100

90 000300

2 2

,

d

d

AC

AC

= − + −

==

( ) ( )

( )

100 100 200 100

10 000100

2 2

,

Location A

— A 4000($3)(0) = $0 — B 3000($1)(316.2) = $ 948,600 — C 4000($3)(100) = $1,200,000 $2,148,600

Location B — A 4000($3)(316.2) = $3,794,400 — B 3000($1)(0) = $0 — C 4000($3)(300) = $3,600,000 $7,394,400

Location C — A 4000($3)(100) = $1,200,000 — B 3000($1)(300) = $ 900,000 — C 4000($3)(0) = $0 $2,100,000← lowest transportation cost


b. Rectilinear distances d x x y yAB A B A B= − + −

dddddd

AB

AB

BC

BC

AC

AC

= − + −

=

= − + −

=

= − + −

=

100 400 200 100400400 100 100 100300100 100 200 100100

Location A — A 4000($3)(0) = $0 — B 3000($1)(400) = $1,200,000 — C 4000($3)(100) = $1,200,000 $2,400,000

Location B — A 4000($3)(400) = $4,800,000 — B 3000($1)(0) = $0 — C 4000($3)(300) = $3,600,000 $8,400,000

Location C — A 4000($3)(100) = $1,200,000 — B 3000($1)(300) = $ 900,000 — C 4000($3)(0) = $0 $2,100,000← Location C is again

indicated c. Center of gravity (133.33, 144.44)

xl x

l

i ii

ii

* =∑

∑ and y

l y

l

i ii

ii

* =∑

∑

x

x

y

y

*

*

*

*

$12, $3, $12,,

, ,,

.

$12, $3, $12,,

, ,,

.

=×( ) + ×( ) + ×( )

= =

=×( ) + ×( ) + ×( )

= =

( )

( )

100 000 400 000 100 00027 000

3 600 00027 000

133 33

200 000 100 000 100 00027 000

3 900 00027 000

144 44


14. Personal computer manufacturer From port at Los Angeles: To Chicago: $0.0017/mile 1,800 miles = $3.06/unit To Atlanta: $0.0017/mile 2,600 miles = $4.42/unit To New York: $0.0017/mile 3,200 miles = $5.44/unit

From port at San Francisco: To Chicago: $0.0020/mile 1,700 miles = $3.40/unit To Atlanta: $0.0020/mile 2,800 miles = $5.60/unit To New York: $0.0020/mile 3,000 miles = $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:

SourceDestination

Omaha SeattleAtlantaCapacity

El Paso

New York City

Demand

$4

$38,000

8,000

$5

$72,000

10,000

8,000$6

$9

4,000

4,000

22,000

12,000

10,000

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:


Tutor - Transportation MethodEnter data in yellow shaded areas.

Distribution CenterWholesaler Atlanta Omaha Seattle Capacity

4 5 6El Paso 8,000 4,000 12,000

3 7 9New York City 8,000 2,000 10,000

22,000Requirements 8,000 10,000 4,000 22,000

Costs $24,000 $54,000 $24,000

Total Cost $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 MethodEnter data in yellow shaded areas.

Distribution CenterWholesaler A B C D Capacity

1.3 1.4 1.8 1.61 50 50

1.3 1.5 1.8 1.62 40 10 20 70

1.6 1.4 1.7 1.53 10 50 60

180Requirements 40 60 30 50 180

Costs $52 $85 $53 $75

Total Cost $265


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:

000,410$)]2$000,50()1$000,40(

)3$000,20()4$000,10()1$000,50()3$000,20()1$000,60[(=×+×

+×+×+×+×+×

FactoryShipping Cost ($/case) to Warehouse

W1Capacity

F1

Demand

$1

$2

60,000 250,000

80,000

60,000$1

60,000

F2

F3

W2$3

$2

70,000

$5

W3$4

$160,000

50,000

$1

W4$5

$420,000

30,000

$3

$550,000

F4$2 $4 $5

W5$6

$5

40,000

$1

$4

50,000 10,000

20,000 40,000

50,000


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

DestinationsW1 W2 W3 W4 W5 Capacity

SourcesF1 1 3 4 5 6 80,000F2 2 2 1 4 5 60,000F3 1 5 1 3 1 60,000F4 5 2 4 5 4 50,000

Reqt's 60,000 70,000 50,000 30,000 40,000 250,000

DestinationsW1 W2 W3 W4 W5 Capacity

SourcesF1 60,000 10,000 0 10,000 0 80,000F2 0 10,000 50,000 0 0 60,000F3 0 0 0 20,000 40,000 60,000F4 0 50,000 0 0 0 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:

PlantDistribution Center

MiamiCapacity

Chicago

Requirements

7

340

70 255

100

756

80

Houston

Buffalo

Denver2

1

50

90

9

Lincoln4

545

45

7

Jackson5

2

50

4

255

35

30

55

Total optimal cost = $82,500.


Atlanta location-optimal solution:

Plant

Shipping cost to Distribution Centers

Miami

Capacity

Chicago

Demand ( 100)

$7

$3

70 255

100

75$2

80

Houston

Atlanta

Denver$2

$1

10

90

$10

Lincoln$4

$545

45

$8

Jackson$5

$2

50

$335

70

55

($/case)( 100)

40

×

×

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:

DestinationsW1 W2 W3 W4 W5 Dummy Capacity

SourcesF1 1 3 3 5 6 0 50,000F2 2 2 1 4 5 0 80,000F3 1 5 1 3 1 0 80,000F4 5 2 4 5 4 0 40,000

Reqt's 45,000 30,000 30,000 35,000 50,000 60,000 250,000


SourcesF1 45,000 0 0 0 0 5,000 50,000F2 0 0 30,000 5,000 0 45,000 80,000F3 0 0 0 30,000 50,000 0 80,000F4 0 30,000 0 0 0 10,000 40,000

Reqt's 45,000 30,000 30,000 35,000 50,000 60,000 250,000

Totals $45,000 $60,000 $30,000 $110,000 $50,000 $0 $295,000


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 CapacitySources

F1 1 3 3 5 6 0 50,000F2 2 2 1 4 5 0 80,000F4 5 2 4 5 4 0 90,000--- ---

Reqt's 45,000 30,000 30,000 35,000 50,000 30,000 220,000


SourcesF1 45,000 0 0 0 0 5,000 50,000F2 0 0 30,000 35,000 0 15,000 80,000F4 0 30,000 0 0 50,000 10,000 90,000

Reqt's 45,000 30,000 30,000 35,000 50,000 30,000 220,000

Totals $45,000 $60,000 $30,000 $140,000 $200,000 $0 $475,000


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

Shipping cost to Distribution Centers

Miami

Capacity

Chicago$7

$3

70 255

100

75$3

80

Houston

Memphis

Denver$2

$1

10

90

$11

Lincoln$4

$535

45

$6

Jackson$5

$2

50

$525

70

65

($/case)( 100)

50

Demand( 100)×

×

Total optimal cost = $66,500. 23. Chambers Corporation (using Transportation Method Solver)

a. Alternative 1 (Portland)

DestinationsAT CO LA SE Capacity

SourcesBaltimore 0.35 0.20 0.85 0.75 6,000Milwaukee 0.55 0.15 0.70 0.65 6,000Portland 0.85 0.60 0.30 0.10 6,000

Reqt's 5,000 3,000 6,000 4,000 18,000


SourcesBaltimore 5,000 1,000 0 0 6,000Milwaukee 0 2,000 4,000 0 6,000Portland 0 0 2,000 4,000 6,000

Reqt's 5,000 3,000 6,000 4,000 18,000

Totals $1,750.00 $500.00 $3,400.00 $400.00 $6,050.00


b. Alternative 2 (San Antonio)


SourcesBaltimore 0.35 0.20 0.85 0.75 6,000Milwaukee 0.55 0.15 0.70 0.65 6,000San Antonio 0.55 0.40 0.40 0.55 6,000

Reqt's 5,000 3,000 6,000 4,000 18,000


SourcesBaltimore 5,000 1,000 0 0 6,000Milwaukee 0 2,000 0 4,000 6,000San Antonio 0 0 6,000 0 6,000

Reqt's 5,000 3,000 6,000 4,000 18,000

Totals $1,750.00 $500.00 $2,400.00 $2,600.00 $7,250.00 c. Alternative 3 (Portland and San Antonio)


SourcesBaltimore 0.35 0.20 0.85 0.75 6,000Milwaukee 0.55 0.15 0.70 0.65 6,000Portland 0.85 0.60 0.30 0.10 3,000San Antonio 0.55 0.40 0.40 0.55 3,000

Reqt's 5,000 3,000 6,000 4,000 18,000


SourcesBaltimore 5,000 1,000 0 0 6,000Milwaukee 0 2,000 3,000 1,000 6,000Portland 0 0 0 3,000 3,000San Antonio 0 0 3,000 0 3,000

Reqt's 5,000 3,000 6,000 4,000 18,000

Totals $1,750.00 $500.00 $3,300.00 $950.00 $6,500.00

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.


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.


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 $100,000 Net Present Value $45,978 Starting year 0 Internal Rate of Return 22.4% Depreciation type

Straight-Line Payback Period 3.87 years

Years 10 Discount rate 12.0% Tax Rate (as percent) 40%

Year 1 2 3 4 5 6 7 8 9 10 Revenue Expenses: Variable (36,393) (36,393) (36,393) (36,393) (36,393) (36,393) (36,393) (36,393) (36,393) (36,393)Expenses: Fixed Depreciation (D) 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000Pre-tax income 26,393 26,393 26,393 26,393 26,393 26,393 26,393 26,393 26,393 26,393Taxes (40%) 10,557 10,557 10,557 10,557 10,557 10,557 10,557 10,557 10,557 10,557Net Operating Income (NOI) 15,836 15,836 15,836 15,836 15,836 15,836 15,836 15,836 15,836 15,836Total Cash Flow (NOI + D) $25,836 $25,836 $25,836 $25,836 $25,836 $25,836 25,836 25,836 25,836 25,836


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.


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 $100,000 Net Present Value -$502 Starting year 0 Internal Rate of Return 11.9% Depreciation type

Straight-Line Payback Period 5.68 years

Years 10 Discount rate 12.0% Tax Rate (as percent) 40% Year 1 2 3 4 5 6 7 8 9 10Revenue Expenses: Variable (22,682) (22,682) (22,682) (22,682) (22,682) (22,682) (22,682) (22,682) (22,682) (22,682)Expenses: Fixed Depreciation (D) 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000Pre-tax income 12,682 12,682 12,682 12,682 12,682 12,682 12,682 12,682 12,682 12,682Taxes (40%) 5,073 5,073 5,073 5,073 5,073 5,073 5,073 5,073 5,073 5,073Net Operating Income (NOI) 7,609 7,609 7,609 7,609 7,609 7,609 7,609 7,609 7,609 7,609Total Cash Flow (NOI + D) $17,609 $17,609 $17,609 $17,609 $17,609 $17,609 17,609 17,609 17,609 17,609


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

(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.

Use current location only

16 Hart Ave

240 Kimberly Ave along with present location

0 20 40 60 80


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.


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 80 140 St. Louis 220 60 Cleveland Cleveland 200 260 St. Louis 200 140 Chicago Chicago 370 430 St. Louis 20 70 Denver 110 NONE Denver Denver 500 670 St. Louis NONE 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 80 140 Denver 220 NONE Chicago NONE 60 Cleveland Cleveland 200 260 Chicago 200 140 Chicago Chicago 170 230 Denver 330 270 St. Louis St. Louis 440 500 Denver 60 400

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


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): Denver Status Quo Incremental COGS Year 1 $5790 - $4692 = $1098 Years 2-10 $6606 - $4554 = $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:


Denver St. Louis 10% Increase $3243.52 $3196.47 10% Decrease -$1608.01 -$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:

Denver St. Louis 10% Increase in COGS -$27.28 $ 102.65 10% Decrease in COGS $1,898.49 $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)


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:

Denver St. Louis 10% Increase in Fixed Costs $ 742.01 $ 793.61 10% Decrease in Fixed Costs $1,130.69 $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.


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 Denver St. Louis

Workforce availability 0.20 4 2 Environmental restrictions 0.10 2 3 Supplier availability 0.20 5 3 NPV 0.50 4 5

4.0 3.8

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

Denver LP Year 1 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 RHV

Min-Z 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 3.4 3.75 4.15 3.85 3.65 3.575 3.15 Z <=/=>

=

B 1 1 1 1 1 < 400 CL 1 1 1 1 1 < 400 CH 1 1 1 1 1 < 500 D 1 1 1 1 1 < 500 BDEM 1 1 1 1 = 80 CLDEM 1 1 1 1 = 200 CHDEM 1 1 1 1 = 370 SLDEM 1 1 1 1 = 440 DDEM 1 1 1 1 = 610

Denver LP Years 2-10

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 RHV Min-Z 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 3.4 3.75 4.15 3.85 3.65 3.575 3.15 Z <=/=>

=

B 1 1 1 1 1 < 400 CL 1 1 1 1 1 < 400 CH 1 1 1 1 1 < 500 D 1 1 1 1 1 < 900 BDEM 1 1 1 1 = 140 CLDEM 1 1 1 1 = 260 CHDEM 1 1 1 1 = 430 SLDEM 1 1 1 1 = 500 DDEM 1 1 1 1 = 670

St. Louis LP Year 1

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 RHV Min-Z 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 3.4 3.75 3.65 3.35 3.2 3.05 3.475 Z <=/=

>=

B 1 1 1 1 1 < 400 CL 1 1 1 1 1 < 400 CH 1 1 1 1 1 < 500 SL 1 1 1 1 1 < 500 BDEM 1 1 1 1 = 80 CLDEM 1 1 1 1 = 200 CHDEM 1 1 1 1 = 370 SLDEM 1 1 1 1 = 440 DDEM 1 1 1 1 = 610

St. Louis LP Years 2-10

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 RHV

Min-Z 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 3.4 3.75 3.65 3.35 3.2 3.05 3.475 Z <=/=>

=

B 1 1 1 1 1 < 400 CL 1 1 1 1 1 < 400 CH 1 1 1 1 1 < 500 SL 1 1 1 1 1 < 900 BDEM 1 1 1 1 = 140 CLDEM 1 1 1 1 = 260 CHDEM 1 1 1 1 = 430 SLDEM 1 1 1 1 = 500 DDEM 1 1 1 1 = 670

Appendix A


Denver LP Year 1 Denver LP Years 2-10 Results Results Solver - Linear Programming Solver - Linear Programming Solution Solution

Variable Label

Variable Value

Original Coefficient

Coefficient Sensitivity

Variable Label

Variable Value



B-B 80.0000 3.8000 0 B-B 140.0000 3.8000 0 B-CL 0.0000 4.1250 0.0250 B-CL 0.0000 4.1250 0.0250 B-CH 0.0000 4.3000 0.0500 B-CH 0.0000 4.3000 0.0500 B-SL 220.0000 4.4000 0 B-SL 60.0000 4.4000 0 B-D 0.0000 4.8000 0.0500 B-D 0.0000 4.8000 0.8250

CL-B 0.0000 3.3250 0.6250 CL-B 0.0000 3.3250 0.6250 CL-CL 200.0000 3.0000 0 CL-CL 260.0000 3.0000 0 CL-CH 0.0000 3.1750 0.0250 CL-CH 0.0000 3.1750 0.0250 CL-SL 200.0000 3.3000 0 CL-SL 140.0000 3.3000 0 CL-D 0.0000 3.7000 0.0500 CL-D 0.0000 3.7000 0.8250 CH-B 0.0000 3.7500 0.9500 CH-B 0.0000 3.7500 0.9500

CH-CL 0.0000 3.4250 0.3250 CH-CL 0.0000 3.4250 0.3250 CH-CH 370.0000 3.2500 0 CH-CH 430.0000 3.2500 0 CH-SL 20.0000 3.4000 0 CH-SL 70.0000 3.4000 0 CH-D 110.0000 3.7500 0 CH-D 0.0000 3.7500 0.7750

D-B 0.0000 4.1500 1.9500 D-B 0.0000 4.1500 1.1750 D-CL 0.0000 3.8500 1.3500 D-CL 0.0000 3.8500 0.5750 D-CH 0.0000 3.6500 1.0000 D-CH 0.0000 3.6500 0.2250 D-SL 0.0000 3.5750 0.7750 D-SL 230.0000 3.5750 0 D-D

500.0000 3.1500 0 D-D

670.0000 3.1500 0

Constraint Label

Original RHV

Slack or Surplus

Shadow Price

Constraint Label

Original RHV

Slack or Surplus

Shadow Price

B 400 100 0 B 400 200 0 CL 400 0 -1.1000 CL 400 0 -1.1000 CH 500 0 -1.0000 CH 500 0 -1.0000

D 500 0 -1.6000 D 900 0 -0.8250 BDEM 80 0 3.8000 BDEM 140 0 3.8000

CLDEM 200 0 4.1000 CLDEM 260 0 4.1000 CHDEM 370 0 4.2500 CHDEM 430 0 4.2500 SLDEM 440 0 4.4000 SLDEM 500 0 4.4000 DDEM

610 0 4.7500 DDEM 670 0 3.9750

Objective Function Value: 5790 Objective Function Value: 6606.25 Sensitivity Analysis and Ranges Sensitivity Analysis and Ranges

Objective Function Coefficient Objective Function Coefficient

Variable Label

Lower Limit


Upper Limit

Variable Label

Lower Limit


Upper Limit

B-B No Limit 3.8000 4.4250 B-B No Limit 3.8000 4.4250 B-CL 4.1000 4.1250 No Limit B-CL 4.1000 4.1250 No Limit B-CH 4.2500 4.3000 No Limit B-CH 4.2500 4.3000 No Limit B-SL 3.7750 4.4000 4.4250 B-SL 3.7750 4.4000 4.4250 B-D 4.7500 4.8000 No Limit B-D 3.9750 4.8000 No Limit

CL-B 2.7000 3.3250 No Limit CL-B 2.7000 3.3250 No Limit CL-CL 3.0000 3.0000 3.0000 CL-CL 3.0000 3.0000 3.0000 CL-CH 3.1750 3.1750 3.1750 CL-CH 3.1750 3.1750 3.1750 CL-SL 3.3000 3.3000 3.3000 CL-SL 3.3000 3.3000 3.3000 CL-D 3.7000 3.7000 3.7000 CL-D 3.7000 3.7000 3.7000 CH-B 3.7500 3.7500 3.7500 CH-B 3.7500 3.7500 3.7500

CH-CL 3.4250 3.4250 3.4250 CH-CL 3.4250 3.4250 3.4250 CH-CH 3.2500 3.2500 3.2500 CH-CH 3.2500 3.2500 3.2500 CH-SL 3.4000 3.4000 3.4000 CH-SL 3.4000 3.4000 3.4000 CH-D 3.7500 3.7500 3.7500 CH-D 3.7500 3.7500 3.7500

D-B 4.1500 4.1500 4.1500 D-B 4.1500 4.1500 4.1500 D-CL 3.8500 3.8500 3.8500 D-CL 3.8500 3.8500 3.8500 D-CH 3.6500 3.6500 3.6500 D-CH 3.6500 3.6500 3.6500 D-SL 3.5750 3.5750 3.5750 D-SL 3.5750 3.5750 3.5750 D-D

3.1500 3.1500 3.1500 D-D

3.1500 3.1500 3.1500

Right-Hand-Side Values Right-Hand-Side Values Constraint

Label

Lower Limit

Original Value

Upper Limit

Constraint Label

Lower Limit

Original Value

Upper Limit

B 300 400 No Limit B 200 400 No Limit CL 300 400 620 CL 260 400 460 CH 480 500 720 CH 430 500 560

D 480 500 610 D 700 900 960 BDEM 4.43379E-11 80 180.0000001 BDEM 0 140 340

CLDEM -1.02318E-10 200 300 CLDEM 200 260 400 CHDEM 150 370 390 CHDEM 370 430 500 SLDEM 220 440 540 SLDEM 440 500 700 DDEM 500 610 630 DDEM 610 670 870

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

Variable Value



Variable Label

Variable Value



B-B 80.0000 3.8000 0 B-B 140.0000 3.8000 0 B-CL 0.0000 4.1250 0 B-CL 0.0000 4.1250 0 B-CH 0.0000 4.3000 0 B-CH 60.0000 4.3000 0 B-SL 0.0000 4.4000 0.0250 B-SL 0.0000 4.4000 0.0250 B-D 220.0000 4.8000 0 B-D 0.0000 4.8000 0

CL-B 0.0000 3.3250 0.6500 CL-B 0.0000 3.3250 0.6500 CL-CL 200.0000 3.0000 0 CL-CL 260.0000 3.0000 0 CL-CH 200.0000 3.1750 0 CL-CH 140.0000 3.1750 0 CL-SL 0.0000 3.3000 0.0500 CL-SL 0.0000 3.3000 0.0500 CL-D 0.0000 3.7000 0.0250 CL-D 0.0000 3.7000 0.0250 CH-B 0.0000 3.7500 1.0000 CH-B 0.0000 3.7500 1.0000

CH-CL 0.0000 3.4250 0.3500 CH-CL 0.0000 3.4250 0.3500 CH-CH 170.0000 3.2500 0 CH-CH 230.0000 3.2500 0 CH-SL 0.0000 3.4000 0.0750 CH-SL 0.0000 3.4000 0.0750 CH-D 330.0000 3.7500 0 CH-D 270.0000 3.7500 0 SL-B 0.0000 3.6500 1.1750 SL-B 0.0000 3.6500 1.1750

SL-CL 0.0000 3.3500 0.5500 SL-CL 0.0000 3.3500 0.5500 SL-CH 0.0000 3.2000 0.2250 SL-CH 0.0000 3.2000 0.2250 SL-SL 440.0000 3.0500 0 SL-SL 500.0000 3.0500 0 SL-D

60.0000 3.4750 0 SL-D 400.0000 3.4750 0

Constraint Label

Original RHV

Slack or Surplus

Shadow Price

Constraint Label

Original RHV

Slack or Surplus

Shadow Price

B 400 100 0 B 400 200 0 CL 400 0 -1.1250 CL 400 0 -1.1250 CH 500 0 -1.0500 CH 500 0 -1.0500 SL 500 0 -1.3250 SL 900 0 -1.3250

BDEM 80 0 3.8000 BDEM 140 0 3.8000 CLDEM 200 0 4.1250 CLDEM 260 0 4.1250 CHDEM 370 0 4.3000 CHDEM 430 0 4.3000 SLDEM 440 0 4.3750 SLDEM 500 0 4.3750 DDEM

610 0 4.8000 DDEM 670 0 4.8000

Objective Function Value: 5935.5 Objective Function Value: 6689.5 Sensitivity Analysis and Ranges

Sensitivity Analysis and Ranges

Objective Function Coefficient

Objective Function Coefficient

Variable Label

Lower Limit


Upper Limit

Variable Label

Lower Limit


Upper Limit

B-B No Limit 3.8000 4.4500 B-B No Limit 3.8000 4.4500 B-CL 4.1250 4..1250 No Limit B-CL 4.1250 4.1250 No Limit B-CH 4.3000 4.3000 No Limit B-CH 3.6500 4.3000 4.3000 B-SL 4.3750 4.4000 No Limit B-SL 4.3750 4.4000 No Limit B-D 4.1500 4.8000 4.8000 B-D 4.8000 4.8000 No Limit

CL-B 2.6750 3.3250 No Limit CL-B 2.6750 3.3250 No Limit CL-CL 3.0000 3.0000 3.0000 CL-CL 3.0000 3.0000 3.0000 CL-CH 3.1750 3.1750 3.1750 CL-CH 3.1750 3.1750 3.1750 CL-SL 3.3000 3.3000 3.3000 CL-SL 3.3000 3.3000 3.3000 CL-D 3.7000 3.7000 3.7000 CL-D 3.7000 3.7000 3.7000 CH-B 3.7500 3.7500 3.7500 CH-B 3.7500 3.7500 3.7500

CH-CL 3.4250 3.4250 3.4250 CH-CL 3.4250 3.4250 3.4250 CH-CH 3.250 3.2500 3.2500 CH-CH 3.2500 3.2500 3.2500 CH-SL 3.4000 3.4000 3.4000 CH-SL 3.4000 3.4000 3.4000 CH-D 3.7500 3.7500 3.7500 CH-D 3.7500 3.7500 3.7500 SL-B 3.6500 3.6500 3.6500 SL-B 3.6500 3.6500 3.6500

SL-CL 3.3500 3.3500 3.3500 SL-CL 3.3500 3.3500 3.3500 SL-CH 3.2000 3.2000 3.2000 SL-CH 3.2000 3.2000 3.2000 SL-SL 3.0500 3.0500 3.0500 SL-SL 3.0500 3.0500 3.0500 SL-D 3.4750 3.4750 3.4750 SL-D 3.4750 3.4750 3.4750

Right-Hand-Side Values Right-Hand-Side Values Constraint

Label

Lower Limit

Original Value

Upper Limit

Constraint Label

Lower Limit

Original Value

Upper Limit

B 300 400 No Limit B 200 400 No Limit CL 300 400 570 CL 260 400 460 CH 400 500 720 CH 300 500 560 SL 440 500 720 SL 700 900 960

BDEM 4.43379E-11 80 180 BDEM 0 140 340 CLDEM 30 200 300 CLDEM 200 260 400 CHDEM 200 370 470 CHDEM 370 430 630 SLDEM 220 440 500 SLDEM 440 500 700 DDEM 390 610 710 DDEM 610 670 870

Appendix B

Appendix C

Denver Location NPV⎯Most Likely Denver

0 1 2 3 4 5 6 7 8 9 10Profit or Loss

Change in Revenues 3200 5600 5600 5600 5600 5600 5600 5600 5600 5600COGS 1098 2052 2052 2052 2052 2052 2052 2052 2052 2052Gross Profit

2102 3548 3548 3548 3548 3548 3548 3548 3548 3548

Depreciation 1210 1210 1210 1210 1210 1210 1210 1210 1210 1210Fixed Costs 550 550 550 550 550 550 550 550 550 550EBIT

342 1788 1788 1788 1788 1788 1788 1788 1788 1788

Taxes 136.8 715.2 715.2 715.2 715.2 715.2 715.2 715.2 715.2 715.2Profit After Tax

205.2 1072.8 1072.8 1072.8 1072.8 1072.8 1072.8 1072.8 1072.8 1072.8

Cash Flows

Add Back Depreciation 1415.2 2282.8 2282.8 2282.8 2282.8 2282.8 2282.8 2282.8 2282.8 2282.8Other Cash Flows Initial Plant & Equip Costs 12100 Land Cost 1200 Sale of New Plant 6650Tax on Gain

-2180

Free Cash Flow

1415.2 2282.8 2282.8 2282.8 2282.8 2282.8 2282.8 2282.8 2282.8 6752.8

NPV @ 11% $936.35


St. Louis Location NPV⎯Most Likely St. Louis

0 1 2 3 4 5 6 7 8 9 10Profit or Loss

Change in Revenues 3200 5600 5600 5600 5600 5600 5600 5600 5600 5600COGS 1244 2135.5 2135.5 2135.5 2135.5 2135.5 2135.5 2135.5 2135.5 2135.5Gross Profit

1956 3464.5 3464.5 3464.5 3464.5 3464.5 3464.5 3464.5 3464.5 3464.5

Depreciation 1080 1080 1080 1080 1080 1080 1080 1080 1080 1080Fixed Costs 750 750 750 750 750 750 750 750 750 750EBIT

126 1634.5 1634.5 1634.5 1634.5 1634.5 1634.5 1634.5 1634.5 1634.5

Taxes 50.4 653.8 653.8 653.8 653.8 653.8 653.8 653.8 653.8 653.8Profit After Tax

75.6 980.7 980.7 980.7 980.7 980.7 980.7 980.7 980.7 980.7

Cash Flows

Add Back Depreciation 1155.6 2060.7 2060.7 2060.7 2060.7 2060.7 2060.7 2060.7 2060.7 2060.7Other Cash Flows Initial Plant & Equip Costs 10800 Land Cost 800 Sale of New Plant 5800Tax on Gain

-2000

Free Cash Flow

1155.6 2060.7 2060.7 2060.7 2060.7 2060.7 2060.7 2060.7 2060.7 5860.7

NPV @ 11% $1,058.62

Appendix C

Krm8 Ism Ch11

Documents

Transcript of Krm8 Ism Ch11