assignment problem.pdf

8/10/2019 Assignment Problem.pdf

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1

06IP/ IM74 OPERATIONS RESEARCH

, 4:

(By Dr.G.Rajendra, Prof & HOD (IEM), Dr. AIT, Bangalore 560 056)

The assignment problem is a special case of transportation problem in which the objective is to

assign m jobs or workers to n machines such that the cost incurred is minimized.

1 2

1

2

T C I (I,= 1,2,). T

( ) .

T

.

T 1.

11 12 1

21 22 2

1 2


2/55

2

T I C.

T .

T 1

H .

D A

S. N. T A1 T

T

2 T

I . T

.

3 T

M+N1

M

N

T

4 T

T

5 I

I


3/55

3

( )

S I : C

.

S II: D

N

) I N = (= )

) I N


4/55

4

S VII)

. T ()

.

N: H

1.

T A B C . T

. F .

M

J

A 19 28 31

B 11 17 16

C 12 15 13

:

S 1:

R M

0 9 12

0 6 5

0 3 1

C M

0 6 11

0 3 4

0 0 0


5/55

5

N H

0 6 11

0 3 4

0 0 0

H,

T 3 3, , N

N,

.

0 3 8

0 0 1

3 0 0

T N=

0 3 8

0 0 1

3 0 0

T A = 19

B = 17

C = 13

49


6/55

6

2

S

I II III IV V

1 11 17 8 16 20

2 9 7 12 6 15

3 13 16 15 12 16

4 21 24 17 28 26

5 14 10 12 11 15

S:

R M

3 9 0 8 12

3 1 6 0 9

1 4 3 0 4

4 7 0 11 9

4 0 2 1 5

C M

2 9 0 8 8

2 1 6 0 1

0 4 3 0 0

3 7 0 11 5

3 0 2 1 1

N

54

2 9 0 8 8

2 1 6 0 1

0 4 3 0 0

3 7 0 11 5

3 0 2 1 1


7/55

7

T 1,

.

1 9 0 8 7

1 1 6 0 0

0 4 3 0 0

2 7 0 11 4

2 0 2 1 0

A N

0 8 0 7 6

1 1 6 0 0

0 4 3 0 0

1 6 0 10 3

2 0 2 1 0

H, N=

N,

0 8 0 7 6

1 1 6 0 0

0 4 3 0 0

1 6 0 10 3

2 0 2 1 0

A

1 I = 11

2 IV = 6

3 V = 16

4 III = 17

5 II = 10

40


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8

3

U , ) )

R M

C

JOB

MECHANIC

1 2 3 4 5

A 10 3 3 2 8

B 9 7 8 2 7

C 7 5 6 2 4

D 3 5 8 2 4

E 9 10 9 6 10

8 1 1 0 6

7 5 6 0 5

5 3 4 0 2

1 3 6 0 2

3 4 3 0 4

7 0 0 0 4

6 4 5 0 3

4 2 3 0 0

0 2 5 0 02 3 2 0 2


9/55

9

D

H, N, 4 5

T, . 2 .

N= ,

A 2 = 3

B 4 = 2C 5 = 4

D 1 = 3

E 3 = 9

21 R. 21

9 0 0 2 6

6 2 2 0 3

4 0 1 0 0

0 0 3 0 0

2 1 0 0 2

7 0 0 0 4

6 4 5 0 3

4 2 3 0 0

0 2 5 0 0

2 3 2 0 2

9 0 0 2 6

6 2 2 0 3

4 0 1 0 0

0 0 3 0 0

2 1 0 0 2


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10

4

J 4 4 . T

. T . 1 3,

3 4. D H .

J

1 2 3 4

1 R. 50 R.50 R.20

2 R.70 R.40 R.20 R.30

3 R.90 R.30 R.50

4 R.70 R.20 R60 R70

R M

30 30 0

50 20 0 10

60 0 20

50 0 40 50

C

0 30 0

20 20 0 10

30 0 20

20 0 40 50

N

34

T 10


11/55

11

0 40 0

10 20 0 0

20 0 20

10 0 40 40N

3=4

T 10

0 50 0

10 20 0 0

10 0 10

0 0 30 30

N=

T , .

0 50 0

10 20 0 0

10 0 10

0 0 30 30

1 4 = 20

2 3 = 20

3 2 = 30

4 1 = 70

140

414, 232

T


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5

A ,

. J

F 1 M

T

+1 1. T

(

12

, F.

. T

M .

.

.

F.2. I

) ;

.

H

. T


13/55

F 2. N

M 8

15 12

10 M

12 M

18 17

T ,

R

M 7 5 11

8 5 0 M

5 M 0 9

0 M 0 4

5 4 1 M

13

.

6 12 1

7 M 10

5 14 M

12 16 15

14 M 13

H

0

3

M

3

0


14/55

14

C

N, 45

T

N, 45 T

N=

M 3 5 7 0

8 1 0 M 3

5 M 0 5 M

0 M 0 0 3

5 0 1 M 0

M 3 5 7 0

8 1 0 M 3

5 M 0 5 M

0 M 0 0 3

5 0 1 M 0

M 2 5 6 0

7 0 0 M 3

4 M 0 4 M

0 M 1 0 3

2 0 1 M 0

M 2 5 2 0

3 0 0 M 3

0 M 0 0 M

0 M 1 0 3

2 0 1 M 0

M 2 5 2 0

3 0 0 M 3

0 M 0 0 M0 M 1 0 3

2 0 1 M 0


15/55

T

,

F 3. S

6.

F

;

J M

M1

J1

J2

J3

J4

5

8

4

10

H

15

F. 3 1

.

P

. T

M2 M3

7 11

5 9

7 10

4 8

4

.


16/55

16

R

0 2 6 1

3 0 4 1

0 3 6 37 1 5 0

C

0 2 2 1

3 0 0 1

0 3 2 3

7 1 1 0

D

0 2 2 1

3 0 0 1

0 3 2 3

7 1 1 0

N 34

T 1,

0 1 1 1

4 0 0 2

0 2 1 3

7 0 0 0

N

34

T 1,

0 0 0 0

5 0 0 2

0 1 0 2

8 0 0 0

N=


17/55

17

4=4

0 0 0 0

5 0 0 2

0 1 0 2

8 0 0 0

J1 M4 = 6

J2M2 = 5

J3M1 = 4

J4M3 = 823

A

0 0 0 0

5 0 0 2

0 1 0 2

8 0 0 0

J1 M1 = 5

J2M2 = 5

J3M3 = 10

J4M4 = 3

23


18/55

18

7

A 5 R.

(=1,2,3,5) (=1,2,3,). A 5 5

.

JOB

M

1 2 3 4 5

1 5 11 10 12 4

2 2 4 6 3 5

3 3 12 5 14 6

4 6 14 4 11 75 7 9 8 12 8

S,

S 1: C O

1

T

JOB

M

1 2 3 4 5

1 5 11 10 12 4

2 2 4 6 3 5

3 3 12 5 14 6

4 6 14 4 11 7

5 7 9 8 12 8


19/55

19

S2: = ()

I 14. U

. T

.

JOB

M

1 2 3 4 5

1 9 3 4 2 10

2 12 10 8 11 9

3 11 2 9 0 8

4 8 0 10 3 7

5 7 5 6 2 6

E

C11= 5 (14) = 9

S 3: U .. . T

H .

7 1 2 0 8

4 2 0 3 1

11 2 9 0 8

8 0 10 3 7

5 3 4 0 4


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20

3 1 2 0 7

0 2 0 3 0

7 2 9 0 74 0 10 3 6

1 3 4 0 3

N=3, =55

N,

.

2 1 1 0 6

0 3 0 4 0

6 2 8 0 6

3 0 9 3 5

0 3 3 0 2

N=4 =55

N

T 1

2 1 0 0 5

1 4 0 5 0

6 2 7 0 5

3 0 8 3 4

0 3 2 0 1


21/55

21

N=,

2 1 0 0 5

1 4 0 5 0

6 2 7 0 5

3 0 8 3 4

0 3 2 0 1

N

13 = 10

25 = 5

34 = 14

42 = 14

51 = 7

50


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22

7

A 5 5 . C

,

( 1000 ) .

A B C D E

1 32 38 40 28 40

2 40 24 28 21 36

3 41 27 33 30 37

4 22 38 41 36 36

5 29 33 40 35 39

F .

:

T . T ,

. T ..,

41. T

.

A B C D E

1 9 3 1 13 1

2 1 17 13 20 5

3 0 14 8 11 4

4 19 3 0 5 5

5 12 8 1 6 2

U H .


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23

R

8 2 0 12 0

0 16 12 19 4

0 14 8 11 419 3 0 5 5

11 7 0 5 1

C

8 0 0 7 0

0 14 12 14 4

0 12 8 6 4

19 1 0 0 5

11 5 0 0 1

D

N=4 55

N,

. T 4

8 0 0 7 0

0 10 8 10 0

0 8 4 2 0

19 1 0 0 5

11 5 0 0 1

N=,


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24

8 0 0 7 0

0 10 8 10 0

0 8 4 2 0

19 1 0 0 511 5 0 0 1

1B = 38

2A = 40

3E = 37

4C = 41

5D = 35

191

8

A . T

;

:

T : I II III IV

A S (R) 60,000 50,000 40,000 30,000

F : ,

, :

S: A B C D

P: 7 5 5 4

I ,

, , ,

.


25/55

25

:

S 1

B R. 10000/

:

S 10

S P 6 5 4 3

I II III IV

7 A 42 35 28 21

5 B 30 25 20 15

5 C 30 25 20 15

4 D 24 20 16 12

T 11=

= 76=42

I

S 2:

B 1. T :

I II III IV

A 42 35 28 21

B 30 25 20 15

C 30 25 20 15

D 24 20 16 12

S 3: .. 42.

. T


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26

I II III IV

A 0 7 14 21

B 12 17 22 27

C 12 17 22 27D 18 22 26 30

N, H

,

R

0 7 14 21

0 5 10 15

0 5 10 15

0 4 8 12

C

0 3 6 9

0 1 2 3

0 1 2 3

0 0 0 0

D

0 3 6 9

0 1 2 3

0 1 2 3

0 0 0 0

N, 24

T 1


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27

0 2 5 8

0 0 1 2

0 0 1 2

0 0 0 0

N, 34

T 1

0 2 4 7

0 0 0 1

0 0 0 1

0 0 0 0

N=, 4=4,

0 2 4 7

0 0 0 1

0 0 0 1

0 0 0 0

AI

BII

CIII

DIV


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28

9:

A C

. G

, .

S (R. 000 P)

P 1 2 3 4

A 50 68 49 62

B 60 70 51 74

C 55 67 53 70

D 58 65 54 69

P (R. 000 P)

P 1 2 3 4

A 49 60 45 61

B 55 63 45 69

C 52 62 49 68

D 55 64 48 66

:

N, .

P =

P

1 2 3 4

A 1 8 4 1

B 5 7 6 5

C 3 5 4 2

D 3 1 6 3


29/55

29

N , .. 8

.

7 0 4 7

3 1 2 3

5 3 4 6

5 7 2 5

U H

R

7 0 4 7

2 0 1 2

2 0 1 3

3 5 0 3

C

5 0 4 5

0 0 1 0

0 0 1 1

1 5 0 1

D

5 0 4 5

0 0 1 0

0 0 1 1

1 5 0 1

N=,


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30

5 0 4 5

0 0 1 0

0 0 1 1

1 5 0 1

A2

B4

C1

D3

11

A . C

() 5 , . O

. F

.

D J JD

F N. D A F N. D A

1 7.00 AM 8.00 AM 101 8.00 AM 9.15 AM

2 8.00 AM 9.00 AM 102 8.30 AM 9.45 AM

3 1.30 PM 2.30 P.M 103 12.00 NOON 1.15 PM

4 6.30AM 7.30 PM 104 5.30 PM 6.45 PM

, .

:

S1 D,

15 = 1.


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31

T 1: D

F 101 102 103 104

1 96 98 112 38

2 92 94 108 34

3 70 72 86 108

4 50 52 66 88

S, 5

T 1 101 24 (96 ) 8.00 AM 8.00 AM

. 1 8.00 8.00

5

.

F 1 102 (98) 8.00 8.30 = 24

+30

F 1 103 (112 ) 8.00 12.00 = 24

+4 =112

F 1 104 (38 )8.00 5.30 =

9 +30 = 38

T F 2 101 (9.00 8.00

) =23 = 92

F 2 102 (9.00 8.30 ) = 23

+30 = 94

F 2 103 (9.00 12.00 ) = 24

+3 = 108

F 2 104 (9.00 5.30 ) = 8

+30 = 34


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32

T F 3 101 (2.30 8.00

) =17 + 30 = 70

F 3 102 (2.30 8.30 ) = 18

= 72

F 3 103 (2.30 12.00 ) =

21 + 30 = 86

F 3 104 (2.30 5.30 ) =

24+3= 108

T F 4 101 (7.30 8.00

) =12 +30 = 50

F 4 102 (7.30 8.30 ) = 13

= 52

F 4 103 (7.30 12.00 ) =

16 + 30 = 66

F 4 104 (7.30 5.30 ) =

22= 88

T 2:

F 101 102 103 104

1 87 85 71 49

2 91 89 75 53

3 113 111 97 75

4 37 35 21 95


33/55

33

A

S, 5

T 101 1 21 + 45 (87 ) 9.15 AM

7.00 AM 1 . 101 D 9.15 D

7.00 1 5

.

F 101 2 (91 ) 9.15 D D 8.00 = 22 +45

F 101 3 (113 ) 9.15 D D 1.30 = 28

+15 = 113 F 101 4 (38 ) 9.15 D D 6.30 = 9

+15 = 37

T F 102 1 (9.45 D 7.00

) =21 +15 = 85

F 102 2 (9.45 D D 8.00 ) = 22 +

15 = 89 F 102 3 (9.45 D D 1.30 ) = 27

+45 = 111

F 102 4 (9.45 D D 6.30 ) = 8

+45 = 35

F N. A() F N. D (D)

101 9.15 AM 1 7.00 AM

102 9.45 AM 2 8.00 AM

103 1.15 PM 3 1.30 PM

104 6.45 PM 4 6.30AM


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34

T F 103 1 (1.15 D 7.00

) =17 + 45 = 71

F 103 2 (1.15 D D 8.00 ) = 18 +

45 = 75

F 103 3 (1.15 D D 1.30 ) = 24

+15 = 97

F 103 4 (1.15 D D 6.30 ) = 5 +

15 = 21

T F 104 1 (6.45 D 7.00

) =12 + 15 = 49

F 104 2 (6.45 D D 8.00 ) = 13 +

15 = 53

F 104 3 (6.45 D D 1.30 ) =18

+45 = 75

F 104 4 (6.45 D D 6.30 ) = 23 + 45 = 95

S 3: T 1

T 2 * .

T 3:

F 101 102 103 104

1 87* 85* 71* 38

2 91* 89* 75 34

3 70 72 86 75

4 37* 35* 21* 88


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35

U H

0 0 0 0

12 8 8 0

0 0 28 50

4 0 0 100

T

F 1103

F 2104F 3101

F 4102


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36

I (

),

T .

I , .

T .

1:

A .

T ( ):

M

J

1 2 3 4 5

1 2.5 5.0 1.0 6 1.0

2 2.0 5.0 1.5 7 3.0

3 3.0 6.5 2.0 9 4.5

4 3.5 7.0 2.0 9 4.5

5 4.0 7.0 3.0 9 6.0

6 6.0 9.0 5.0 10 6.0

S .

:

T 65, . S

. J 6 . T

.


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37

M

J

1 2 3 4 5 6

1 2.5 5.0 1.0 6 1.0 0

2 2.0 5.0 1.5 7 3.0 03 3.0 6.5 2.0 9 4.5 0

4 3.5 7.0 2.0 9 4.5 0

5 4.0 7.0 3.0 9 6.0 0

6 6.0 9.0 5.0 10 6.0 0

T, H .

R M

2.5 5.0 1.0 6 1.0 0

2.0 5.0 1.5 7 3.0 0

3.0 6.5 2.0 9 4.5 0

3.5 7.0 2.0 9 4.5 0

4.0 7.0 3.0 9 6.0 0

6.0 9.0 5.0 10 6.0 0

R

C

0.5 0 0 0 0 0

0 0 0.5 1 2.0 0

1.0 1.5 1.0 3 3.5 0

1.5 2.0 1.0 3 3.5 0

2.0 2.0 2.0 3 5.0 0

4.0 4.0 4.0 4 5.0 0

N=3, =55, N, 1.0


38/55

38

0.5 0 0 0 0 1

0 0 0.5 1 2.0 1

0 0.5 0 2 3.5 1

0.5 1.0 0 2 3.5 11.0 1.0 1.0 2 5.0 0

3.0 3.0 3.0 3 5.0 0

N=5, =66, N

T 1

.

0.5 0 0 0 0 2

0 0 0.5 1 2.0 2

0 0.5 0 2 3.5 2

0.5 1.0 0 2 3.5 2

0 0 0 1 5.0 0

2.0 2.0 2.0 2 5.0 0

N=5, =6, N, 1

.

0.5 0 0 0 0 2

0 0 0.5 0 1.0 2

0 0.5 0 1 2.5 2

0.5 1.0 0 1 2.5 2

0 0 0 0 4.0 0

2.0 2.0 2.0 1 4.0 0


39/55

39

T N=

.

0.5 0 0 0 0 2

0 0 0.5 0 1.0 2

0 0.5 0 1 2.5 2

0.5 1.0 0 1 2.5 2

0 0 0 0 4.0 0

2.0 2.0 2.0 1 4.0 0

M 1 J5 = 1

M 2 J2 = 5

M 3 J1 = 3

M 4 J3 = 2

M 5 J4 = 9

M 6 J6 = 6

26


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40

2.

M T C 5 5

. T . A 5 .

T

L L

A B C D E

1 300 290 280 290 210

2 250 310 290 300 200

3 180 190 300 190 180

4 320 180 190 240 170

5 270 210 190 250 160

6 190 200 220 190 140

7 220 300 230 180 160

8 200 190 260 210 180

S;

T 85, , 3

.

T

L L

A B C D E F G H

1 300 290 280 290 210 0 0 0

2 250 310 290 300 200 0 0 0

3 180 190 300 190 180 0 0 0

4 320 180 190 240 170 0 0 0

5 270 210 190 250 160 0 0 0

6 190 200 220 190 140 0 0 0

7 220 300 230 180 160 0 0 0

8 200 190 260 210 180 0 0 0


41/55

41

O

.

R

300 290 280 290 210 0 0 0

250 310 290 300 200 0 0 0

180 190 300 190 180 0 0 0

320 180 190 240 170 0 0 0

270 210 190 250 160 0 0 0

190 200 220 190 140 0 0 0

220 300 230 180 160 0 0 0

200 190 260 210 180 0 0 0

S, (0) .

C

120 110 90 110 70 0 0 0

70 130 100 120 60 0 0 0

0 10 110 10 40 0 0 0

140 0 0 60 30 0 0 0

90 30 0 70 20 0 0 0

10 20 30 10 0 0 0 0

40 120 40 0 20 0 0 0

20 10 70 30 40 0 0 0


42/55

42

T1 G = 0

T2 F = 0

T3 A = 180

T4 B = 180

T5 C = 190T6 E = 140

T7 D = 180

T8 H = 0

870

120 110 90 110 70 0 0 0

70 130 100 120 60 0 0 0

0 10 110 10 40 0 0 0

140 0 0 60 30 0 0 0

90 30 0 70 20 0 0 0

10 20 30 10 0 0 0 0

40 120 40 0 20 0 0 0

20 10 70 30 40 0 0 0


43/55

43

()

T

.

S .

H ( ) ,

.. I .

H . P

(

).

S 9 ) I =1,

I , . T

. I , I I . T

=

.

A, . I

=1 I . ( )

1.

T

F

C12 C1

C21 C2

C1 C2


44/55

44

1:

G ,

.

:

R

C

T

F

A1 A2 A3 A4 A5

A1 2 5 7 1

A2 6 3 8 2

A3 8 7 4 7

A4 12 4 6 5

A5 1 3 2 8

A1 A2 A3 A4 A5

A1 1 4 6 0

A2 4 1 6 0

A3 4 3 0 3

A4 8 0 2 1

A5 0 2 1 7

A1 A2 A3 A4 A5

A1 1 3 6 0

A2 4 0 6 0

A3 4 3 0 3

A4 8 0 1 1

A5 0 2 0 7


45/55

45

N=, 5=55

A1A5A1, A2A3A4A2

C = 1+3+4+4+1=13

A A1, A5

A1, A2,A3 A4

.

S 2:

(1) 1 12, 43, 45,

L 15 12 42 45

T A1A2A3A4A5A1

T 2+3+4+5+1 =15H R.2.

15 12 1 42 45

. T R 2.

1 3 6 0

4 0 6 0

4 3 0 3

8 0 1 1

0 2 0 7

1 3 6 0

4 0 6 0

4 3 0 3

8 0 1 1

0 2 0 7


46/55

46

2

A 5 ,

. T

:

T I

A B C D E

A 4 7 3 4

B 4 6 3 4

C 7 6 7 5

D 3 3 7 7

E 4 4 5 7

?

:

U

R M

1 4 1 1

1 3 0 1

2 1 2 0

0 0 4 4

0 0 1 3

C

1 3 1 1

1 2 0 1

2 1 2 0

0 0 3 4

0 0 0 3


47/55

47

D

1 3 1 1

1 2 0 1

2 1 2 00 0 3 4

0 0 0 3

N, 45, 1

0 2 1 1

0 1 0 1

1 0 2 0

0 0 3 5

0 0 0 4

N=

0 2 1 1

0 1 0 1

1 0 2 0

0 0 3 5

0 0 0 4

ABDA, CEC, THE COST =4+3+5+3+5=20

I 2


48/55

48

S 12 15 35 32

0 2 1 1

0 1 0 1

1 0 2 0

0 0 3 5

0 0 0 4

AEBDA, CB, T

COST =4+3+6+3+5=21

N 32 31 41 42

0 2 1 1

0 1 0 1

1 0 2 0

0 0 3 5

0 0 0 4

AECA, BDB

COST= 4+3+7+3+5=22

NO E TR ITH SHIFITNG OF C15 TO C14 AND C24 TO C25

0 2 1 1

0 1 0 1

1 0 2 0

0 0 3 5

0 0 0 4

ADBECA COST=4+4+7+3+5=23


49/55

49

3

S P

1 2 3 4 5

1 20 4 10

2 20 5 10

3 4 5 6 5

4 10 6 2

5 10 5 2

4.

S

C12 =20, C13 =4, C14 =10, C23 =5, C34 =6, C25 =10, C35 =6, C45 =20 = C= C

I .

:

S1 C = ,

=

A

R :

16 0 6

15 0 5

0 1 2 1

8 4 0

8 3 0


50/55

50

C

15 0 6

15 0 5

0 0 2 18 4 0

7 3 0

D

15 0 6

15 0 5

0 0 2 1

8 4 0

7 3 0

N, 4=5 5

10 0 1

10 0 0

0 0 7 6

8 4 0

7 3 0

N , 45 7

3 0 1

3 0 0

0 0 14 13

1 4 0

0 3 0

N, 45 1


51/55

51

2 0 0

2 0 0

0 0 2 2

0 4 0 0 4 0

N=,

U

2 0 0

2 0 0

0 0 2 2

0 4 0

0 4 0

145231

C = 10+5+4+20+10 = R. 49/

A 5 ABCD &E () 5

A B C D E

A 7 6 8 4

B 7 8 5 6

C 6 8 9 7

D 8 5 9 8

E 4 7 7 8


52/55

52

R

3 2 4 0

4 3 0 1

0 2 3 13 0 4 3

0 3 3 1

C

3 0 4 0

4 1 0 1

0 2 3 1

3 0 2 3

0 3 1 1

N, 45, 1

3 0 4 0

4 0 0 0

0 2 3 0

3 0 1 2

0 3 0 1

N= 5=5


53/55

53

T

3 0 4 0

4 0 0 0

0 2 3 0

3 0 1 2

0 3 0 1

ACEA, BDB COST=6+7+4+5+5=27

U

3

00+0=0

4 00+0=0

4 00+0=0

00+1=1

00+0=0

00+0=0

2 3 00+0=0

3 02+1=3

1 2

00+0=0

3 00+0=0

1

DB


54/55

54

A C D E

A

00+0=0

4 00+0=0

B 4 0

0+0=0

0

0+0=0

C 00+0=0

3 00+0=0

E 00+0=0

00+0=0

1

, ,

1 .

A C D E

A

00+0=0

3 00+0=0

B 4 00+0=0

00+0=0

C 00+0=0

2 00+0=0

E 00+0=0

00+0=0

02+0=2

ED


55/55

A C E

A

00+0=0

00+0=0

B 4 00+0=0

00+0=0

C 00+4=0

00+0=0

CA

C E

A

00+0=0

B 00+0=0

00+0=0

BC

AE

T O A

AEDBCA

COST=4+8+5+8+6=31

, , , ,

, ,

&

assignment problem.pdf

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