Answer set 4



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Operations and Production Management MGMT 405 Answer set 4




MGMT 405 Operations and Production Management

Answer set 4



(Reference chapters 8– William J. Stevenson-2007, ninth edition)

Problems and Answers

1. Green Valley Milis produces carpet at plants in St. Louis and Richmond. The carpet is then shipp to two outlets, located in Chicago and Atlanta. The cost per ton of shipping carpet from each of th two plants to the two warehouses is as follows:

To

From Chicago Atlanta




St. louis $ 40 65

Richmond 70 30

The plant at St. Louis can supply 250 tons of carpet per week; the plant at Richmond can supply 400 ton per week. The Chicago outlet has a demand of 300 tons per week, and the outlet at Atlanta. dernands 350 tons per week. The company wants to know the nunıher of tons of carpet to ship from each plant to each outlet in order to minimize the total shipping cost. Solve this transportation problem.


Answer:


To

From Chicago Atlanta Supply




St. louis $ 40 65 250

Richmond 70 30 400

Demand 300 350 650\650


To

From Chicago Atlanta Supply




St. louis $ 40 65 250 (25)

Richmond 70 30 400 (40)

Demand 300 350

(30) (35)




To

From Chicago Atlanta Supply




St. louis $ 40 65 250 (25)

Richmond 70 30 /350 400/350 (40)

Demand 300 350/350

(30) (35)


Richmond → Atlanta =350*30=10500


To

From Chicago Supply




St. louis $ 40 250 (25)

Richmond 70/50 50/50 (40)

Demand 300/50

(30)


Richmond → Chicago =50*70=3500


To

From Chicago Supply




St. louis $ 40/250 250 (25)




Demand 250

(30)


St. louis → Chicago =250*40=10000
Total= $ 24,000

2. Given a transportation problem wıth the following costs, supply, and demand, find the optimal solution:


To (Cost)

From 1 2 3 supply

A $ 6 7 4 100

B $ 5 3 6 180

C $ 8 5 7 200

Demand 135 175 170



ANSWER:


To (Cost)

From 1 2 3 supply

A $ 6 7 4 100 (2)

B $ 5 3/175 6 180 (2)

C $ 8 5 7 200 (2)

Demand 135 175 170 480\480

(1) (2) (2)


B → 2 =175*3 =525


To (Cost)

From 1 3 supply

A $ 6 4/100 100 (2)

B $ 5 6 5 (1)

C $ 8 7 200 (1)

Demand 135 170

(1) (2)



A → 3 =100*4 =400



To (Cost)

From 1 3 supply

B 5/5 6 5 (1)

C 130/ 8 7/70 200 (1)

Demand 130 70

(3) (1)



B → 1 =5*5 =25

C → 1 =130*8 =1040

C → 3 =70*7 =490

Total= 2,480

  1. A plant has four operators to be assigned to four machines. The time (minutes) required by each worker to produce a product on each machine is shown in the following table:




Machine (min.)

Operator A B C D

1 10 12 9 11

2 5 10 7 8

3 12 14 13 11

4 8 15 11 9

Determine the optimal assignment and compute total minimum time.



ANSWER


10

12

9

11

5

10

7

8

12

14

13

11

8

15

11

9



Row and Column



1

0

0

2




0

2

2

3




1

0

2

0




0

4

3

1























1

0

0

2




0

2

2

3



1

0

2

0




0

4

3

1



















2

0

0

2




0

1

1

2




2

0

2

0




0

3

2

0



















C1=9

A2=5


B3=14

D4=9
Total=37 minutes



  1. The Omega pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the salespersons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each city is shown in the following table:










Region

Days














A

B

C

D

E




1

17

10

15

16

20

Sales

person


2

12

9

16

9

14

3

11

16

14

15

12




4

14

10

10

18

17




5

13

12

9

15

11

Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time.



Answer
Row reduction:




A

B

C

D

E

1

7

0

5

6

10

2

3

0

7

0

5

3

0

5

3

4

1

4

4

0

0

8

7

5

4

3

0

6

2

Coloumn reduction:

A

B

C

D

E

7

0

5

6

9

3

0

7

0

4

0

5

3

4

0

4

0

0

8

6

4

3

0

6

1





A

B

C

D

E




7

0

5

6

9



3

0

7

0

4




0

5

3

4

0




4

0

0

8

6



4

3

0

6

1






√

√












Final step is as follows:


A

B

C

D

E

6

0

5

5

8

3

1

8

0

4

0

6

4

4

0

4

0

0

7

5

3

3

0

5

0

















B → 1

C → 4

A → 3

D → 2

E → 5
Total= 51 days


  1. A company supplies three project A, B, and C in three different towns. Construction plant engineers of the company estimated weekly requirement truckloads as 72, 102, and 41 respectively. These projects can be supplied by the three plants 1, 2, and 3 with available amount of truckloads 56, 82 and 77 respectively. Conducting North west corner method:













Project










A

B

C




1

4

8

8

Plant

2

16

24

16




3

8

16

24


  1. Determine the dispatch program between the projects and plants.

  2. Calculate individual cost

  3. Calculate total minimum cost



ANSWER:











Project




Capacity







A

B

C







1

4

8

8

56

Plant

2

16

24

16

82




3

8

16

24

77

requirement

72

102

41

215/215












Project




Capacity







A

B

C







1

Apr-56

8

8

56

Plant

2

16/16*

24/66**

16

82




3

8

16/36***

24/41****

77

requirement

72

102

41

215/215

41-41=0- this is the final step.





© 2010/11, Sami Fethi, EMU, All Right Reserved, McGraw-Hill, 2007, 9. Ed.




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