8.7 Insurance company of Latin America (ILA) is considered opening an office in the

US the two cities under consideration are Philadelphia and New York. The factor ratings

(higher scores are better) for two cities are given in the following table. In which city

should ILA locate?

Factor Weight Philadelphia New York

Customer convenience .25 70 80

Bank accessibility .20 40 90

Computer support .20 85 75

Rental costs .15 90 55

Labor costs .10 80 50

Taxes .10 90 50

Solution:

Factor Philadelphia Score New York Score

Customer convenience .25 x 70 = 17.5 .25 x 80 = 20

Bank accessibility .20 x 40 = 8 .20 x 90 = 18

Computer support .20 x 85 = 17 .20 x 75 = 15

Rental costs .15 x 90 = 13.5 .15 x 55 = 8.25

Labor costs .10 x 80 = 8 .10 x 50 = 5

Taxes .10 x 90 = 9 .10 x 50 = 5

Total Score 73 71.25

Then, Philadelphia is chosen to place new office because got better score.

8.14 An American consulting firm is planning to expand globally by opening a new

office in one of four countries: Germany, Italy, Spain, or Greece. The chief partner

entrusted with the decision, L.Wayne Shell, has identified eight critical success factors

(CSFs) that he view as essential for the success of consultancy. He used a rating

system of 1 (least desirable country) to 5 (most desirable) to evaluate are each CSF.

Which country should be selected for the new office?

Critical Success Factor

Candidate country ratings

Weight German

yItaly Spain Greece

Level of education

Number of consultants .05 5 5 5 2

National literacy rate .05 4 2 1 1

Political aspects

Stability of government 0.2 5 5 5 2

Product liability laws 0.2 5 2 3 5

Environmental regulations 0.2 1 4 1 3

Social and cultural aspects

Similarity in language 0.1 4 2 1 1

Acceptability of consultants 0.1 1 4 4 3

Economic factor

Incentives 0.1 2 3 1 5

Solution:

Critical

Success Factor

Candidate country ratings

Germany Score Italy Score Spain Score Greece Score

Level of education

Number of

consultants .05 x 5 = 0.25 .05 x 5 = 0.25 .05 x 5 = 0.25 .05 x 2 = 0.1

National .05 x 4 = 0.2 .05 x 2 = 0.1 .05 x 1 = 0.05 .05 x 1 = 0.05

literacy rate

Political aspects

Stability of

government0.2 x 5 = 1 0.2 x 5 = 1 0.2 x 5 = 1 0.2 x 2 = 0.4

Product liability

laws0.2 x 5 = 1 0.2 x 2 = 0.4 0.2 x 3 = 0.6 0.2 x 5 = 1

Environmental

regulations0.2 x 1 = 0.2 0.2 x 4 = 0.8 0.2 x 1 = 0.2 0.2 x 3 = 0.6

Social and cultural aspects

Similarity in

language0.1 x 4 = 0.4 0.1 x 2 = 0.2 0.1 x 1 = 0.1 0.1 x 1 = 0.1

Acceptability of

consultants0.1 x 1 = 0.1 0.1 x 4 = 0.4 0.1 x 2 = 0.4 0.1 x 3 = 0.3

Economic factor

Incentives 0.1 x 2 = 0.2 0.1 x 3 = 0.3 0.1 x 1 = 0.1 0.1 x 5 = 0.5

Total Score 3.35 3.45 2.7 3.05

Italy was chosen for new office

8.16 The fixed and variable costs for three potential manufacturing plant sites for a

rattan chair weaver are shown:

Site Fixed Cost per Year Variable Cost per Unit

1 $ 500 $11

2 1000 7

3 1700 4

a) Over what range of production is each location optimal?

b) For a production of 200 units, which site is the best?

Solution:

a) Location optimal

Site 1

Total cost = $500 + $11(200) = $2700

Site 2

Total cost = $1000 + $7(200) = $2400

Site 3

Total cost = $1700 + $4(200) = $2500

a) From graph we know that if the production unit is lower than 125 units site 1 is

the best, for the production cost higher than 125 units between 233.33 units

sites 2 is the best, and for production cost higher than 233.33 units it best for

site 3

b) The best production of 200 units

The crossover point for Site 2 and Site 1

1000 + 7(x) = 500 + 11(x)

4(x) = 500

x = 125

The crossover point for Site 2 and Site 3

1000 + 7(x) = 1700 + 4(x)

3(x) = 700

x = 233.33

According to the graph the best plant side for 200 units’ production is on plant

side 2

8.17 Peter Billington Stereo, Inc., supplies car radios to auto manufacturers and is

going to open new plant. The company is undecided between Detroit and Dallas as the

site. The fixed costs in Dallas are lower due to cheaper land costs, but the variable cost

in Dallas are higher because shipping distances would increase. Given the following

costs, perform an analysis of the volume over which location is preferable:

Dallas Detroit

Fixed costs $600,000 $800,00

Variable costs $28/radio $22/radio

Total cost = $600000 + $28(x) = $800000 + $22(x)

6(x) = $200000

x = 33333.33 units

From the graph, the production below 33333 units Dallas is the best. But for production

exceeding 33333 units production Detroit is the best.

8.20 The following table gives the map coordinates and the shipping loads for a set of

cities that we wish to connect through a central hub. Near which map coordinates

should the hub be located?

City Map Coordinate(x,y) Shipping Load

A (5,10) 5

B (6,8) 10

C (4,9) 15

D (9,5) 5

E (7,9) 15

F (3,2) 10

G (2,6) 5

Solution:

x – coordinate of the central of gravity:

= (5)(5)+(6)(10)+ (5)(5)+(4)(15)+ (9)(5)+(7)(15)+ (3)(10)+(2)(5) = 335

5+10+15+5+15+10+5 65

= 5.15

y – coordinate of the center of gravity:

= (10)(5)+(8)(10)+ (9)(5)+(5)(15)+ (5)(5)+(9)(15)+ (2)(10)+(6)(5) = 475

5+10+15+5+15+10+5 65

= 7.31

The location for central hub on map coordinate is (5.15, 7.31)

8.21 A chain of home health care firms in Louisiana needs to locate a central office

from which to conduct internal audits and other periodic reviews of its facilities. These

facilities are scattered throughout the state, as detailed in the following table. Each site,

except for Houma, will be visited three times each year by a team of workers, who will

drive from the central office to the site. Houma will be visited five times a year. Which

coordinates represent a good central location for this office?

City Map Coordinates

x y

Covington 9.2 3.5

Donaldsonville 7.3 2.5

Houma 7.8 1.4

Monroe 5.0 8.4

Natchitoches 2.8 6.5

New Iberia 5.5 2.4

Opelousas 5.0 3.6

Ruston 3.8 8.5

Solution:

x – coordinate of the central of gravity:

= (9.2)(3)+(7.3)(3)+ (7.8)(5)+(5.0)(3)+ (2.8)(3)+(5.5)(3)+ (5.0)(3)+(3.8)(3)

3+3+5+3+3+3+3+3

= 154.8 = 5.95

26

y – coordinate of the central of gravity:

= (3.5)(3)+(2.5)(3)+ (1.4)(5)+(8.4)(3)+ (6.5)(3)+(2.4)(3)+ (3.6)(3)+(8.5)(3)

3+3+5+3+3+3+3+3

= 113.2 = 4.35

26

Coordinate (5.95, 4.35) is the best location to setup a new office.

C.1 Find an initial solution to the following transportation problem

To

FromLos Angeles Calgary City Supply

Mexico City $ 6 $ 18 $ 8 100

Detroit $ 17 $ 13 $ 19 60

Ottawa $ 20 $ 10 $ 24 40

Demand 50 80 70

a) Use the northwest – corner method. What is its total cost?

b) Use the intuitive lowest – cost approach. What is its total cost?

c) Using the stepping – stone method, find the optimal solution. Compute the total

cost.

Solution:

a) Northwest – Corner method

To

FromLos Angeles Calgary City Supply

Mexico City

$ 6

50

$ 18

50

$ 8

100

Detroit

$ 17 $ 13

30

$ 19

30

60

Ottawa

$ 20 $ 10 $ 24

40

40

Demand 50 80 70 200

Total cost = (50) ($6) + (50) ($18) + (30) ($18) + (30) ($19) + (40) ($24) = $3120

b) Intuitive Lowest – cost approach

To

FromLos Angeles Calgary City Supply

Mexico City

$ 6

50

$ 18 $ 8

50

100

Detroit

$ 17 $ 13

40

$ 19

20

60

Ottawa

$ 20 $ 10

40

$ 24

40

Demand 50 80 70 200

Total cost = (50) ($6) + (50) ($8) + (20) ($19) + (40) ($13) + (40) ($10) = $2000

c) The Stepping – Stone method

To

From

Los Angeles

(A)

Calgary

(B)

City

(C)Supply

Mexico City

(D)

$ 6

50

$ 18

50

$ 8

100

Detroit

(E)

$ 17 $ 13

30

$ 19

30

60

Ottawa

(F)$ 20 $ 10 $ 24

40

40

Demand 50 80 70 200

1 Mexico city – City = $8 - $18 + $13 - $19 = -$16

(Closed path = DC – DB + EB – EC)

2 Detroit – Los Angeles = $17 - $13 + $18 - $6 = $16

(Closed path = EA – EB + DB – DA)

3 Ottawa – Calgary = $10 - $24 + $19 - $13 = -$8

(Closed path = FB – FC + EC – EB)

4 Ottawa – Los Angeles = $20 - $24 + $19 - $13 + $18 - $6 = $14

To

From

Los Angeles

(A)

Calgary

(B)

City

(C)Supply

Mexico City

(D)

$ 6

50

$ 18 $ 8

100

50

Detroit

(E)

$ 17 $ 13

40

$ 19

20 60

Ottawa

(F)

$ 20 $ 10

40

$ 24

40

Demand 50 80 70 200

1 Mexico city – Calgary = $18 - $13 + $19 - $8 = $6

(Closed path = DB – EB + EC – DC)

2 Ottawa – City = $4 - $19 + $13 - $10 = -$12

(Closed path = FC – EC + EB – FB)

Complete analysis from stepping stone method base on Northwest Corner method and

Intuitive Lowest- Cost method, the lowest value is the best solution for this method.

Then, Mexico City – City path was chosen.

C.10 The Tara Tripp Clothing Group owns factories in three towns (W, Y, and Z) which

distribute to three Walsh retail dress shops in three other cities (A, B, and C). The

following table summarizes factory availabilities, projected store demand, and unit

shipping cost:

Walsh Clothing Group

To

FromDress Shop A Dress Shop B Dress Shop C

Factory

availability

Factory W

$ 4 $ 3 $ 3

35

Factory Y$ 6 $ 7 $6

50

Factory Z

$ 8 $ 2 $ 5

50

Store

demand30 65 40 135

a) Complete the analysis, determining the optimal solution for shipping at the

analysis at the Tripp Clothing Group

b) How do you know if it is optimal or not?

Solution:

a) Complete the analysis

To

From

Dress Shop A

(A)

Dress Shop B

(B)

Dress Shop C

(C)

Factory

availability

Factory W

(D)

$ 4

30

$ 3

5

$ 3

35

Factory Y

(E)

$ 6 $ 7

50

$6

50

Factory Z

(F)

$ 8 $ 2

10

$ 5

40

50

Store

demand30 65 40 135

Using Stepping-Stone method base on Northwest Corner method

1 Factory Y – Dress shop A = $6 - $7 + $3 - $4 = -$2

(Closed path = EA – EB + DB – DA)

2 Factory F – Dress Shop A = $8 - $2 + $7 - $3 + $4 = $14

(Closed path = FA – FB + EB – DB + DA)

3 Factory D – Dress shop C = $3 - $3 + $7 - $2 + $5 = $10

(Closed path = DC – DB + EB – FB + FC)

4 Factory E – Dress shop C = $6 - $7 + $2 - $5 = -$4

(Closed path = EC – EB + FB – FC)

To

From

Dress Shop A

(A)

Dress Shop B

(B)

Dress Shop C

(C)

Factory

availability

Factory W

(D)

$ 4

$ 3

15

$ 3

20

35

Factory Y

(E)

$ 6

30

$ 7 $6

20

50

Factory Z

(F)

$ 8 $ 2 $ 5 50

50

Store

demand30 65 40 135

Total cost = $2(50) + $3(15) + $3(20) + $6(20) +$6(30) = $505

Using Stepping-stone method base on Intuitive Lowest- Cost method

1 Factory Y – Dress shop B = $7 - $6 + $3 - $3 = $1

(Closed path = EB – EC + DC – DB)

From complete analysis, the lowest index cost savings using the Factory E – Dress

shop C path

b) Since Factory E – Dress shop C path is the lowest index, then it is optimal

solution