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#$ false

while $ false and $ false do begin

#$ % ! "! & '

−

#$

−

'

(

#$

(

)

(

* + ,

(

- '

if

(

. ,

(

- ( #$ true [TEST OTTIMALITÀ]

else begin

* - ,

( (

/ '

#$

− (

#$

− (

'

-

(

0 ∈1 !"! 2 ( #$ true

else begin

#$ 1 3

(

! ∈1 !"! 2#

(

4 2' #$ ( end

end end end

[TEST ILLIMITATEZZA]

5

− −

# $ ! $

[ ] =

= 0 1

0 1

4

3 A

A B

6

7

[ ] =

= 0 1

0 1

4

3

A

A

B

−

=

1 0

0

1

1

B [ ] [ 0 0 ]

1 0

0 0 1

0 =

T

= u

[ ] 5

4 0 1 0

1

= − 5 − = −

c

8 * -

[ ] 4

1 0 3 0

2

= − 4 − = −

c

= 3

b 4 =

−

= =

4 1 4 1 1 0

0 1

1 1

A B A

h

1 4

11 1

= a

b

ϑ

=

= 4 3

21 2

a b

9 * $ ! $ = [ ] =

4 0

1 1

1

3

A

A

B

(2)

:

= −

−

4 / 1 0

4 / 1

1

1

B [ ] [ 0 5 / 4 ]

4 / 1 0

4 / 1 5 1

0 − = −

−

T

= u

[ ] 5 / 4

1 4 0 / 5 0

4

= 0 − − =

c

8 * -

[ ] 4 5 / 4 11 / 4

1 4 3 / 5 0

2

= − 4 − − = − + = −

c

[ ] =

= 0 4

1 1

1

3

A

A B

− =

= 3 / 4

4 / 13 3 4 4 / 1 0

4 / 1

b 1 − =

=

=

−

4 / 1

4 / 11 1 3 4 / 1 0

4 / 1 1

2 1

A B A

h

θ

=

= 11 13

12 1

a b

3

22 2

= a

b

9 * $ ! $ = [ ] =

4 1

1 3

1

2

A

A B

;

−

= −

−

11 / 3 11 / 1

11 / 1 11 /

1

4 B

[ ] [ 1 1 ]

11 / 3 11 / 1

11 / 1 11 / 5 4

4 = − −

−

− −

−

T

= u

[ ] 1

1 1 0 1

4

= 0 − − − =

c

8 * -

[ ] 1

0 1 1 1

3

= 0 − − − =

c

8 *

[ ] =

= 1 4

1 3

1

2

A

A B

− =

= −

= 5 / 11

11 / 13 3 4 11 / 3 11 / 1

11 / 1 11 / 4

1 2

x x

x

B

= =

0 0

4 3

x x x

F

<

=

[ ] =

= 0 1

0 1

4

3

A

A

B = =

−

= =

3 4 3 4 1 0

0

1

1

4

3

B b

x x x

B

− =

=

=

=

−

4 / 3

4 / 13 3 4 4 / 1 0

4 / 1

1

1

1

3

B b

x x x

B

[ ] =

= 0 4

1 1

1

3

A

A B

=

= 0

0

2 1

x x x

F

=

= 0

0

2 4

x x x

F

− =

= −

= 5 / 11

11 / 13 3 4 11 / 3 11 / 1

11 / 1 11 / 4

1 2

x x

x

B

= =

0 0

4 3

x x x

F

[ ] =

= 1 4

1 3

1

2

A

A B

>

7

* -+ + + #

x c x

F B c c b B c x

c T = B T − 1 + ( T F − T B − 1 ) F = cost + T

? * * θ

- * = @

0

|

| c h ϑ ≥

7 ! * ! ( #

h ϑ

T B T

B B b c B b c

c ~ ~ − 1 = − 1 +

B ~

(3)

[ ] =

= 0 1

0 1

4

3

A

A B

=

= 3

4

4 3

x x x

B

− =

=

=

=

−

4 / 3

4 / 13 3 4 4 / 1 0

4 / 1

~

1

1

1

~ 3

B b

x x x

B

[ ] =

= 0 4

1

~ 1

1

3

A

A B

=

= 0

0

2 1

x x x

F

=

= 0

0

2 4

x x x

F

#

[ ] 5

4 0 1 0

1

= − 5 − = −

c

ϑ

=

= 4 3

21 2

a b

4 15 4

) 3 5 (

1

0

−

=

− +

=

−

+

h

ϑ

T

B

B b c

c

4 15 4

/ 3

4 / ] 13 5 0

~

1

[

~

B

−

b = − = −

c

T

B

− =

= −

= 5 / 11

11 / 13 3 4 11 / 3 11 / 1

11 / 1 11 / 4

1 2

~

x x x

B

[ ] =

= 1 4

1

~ 3

1

2

A

A B

− =

=

=

=

−

4 / 3

4 / 13 3 4 4 / 1 0

4 / 1

1

1

1

3

B b

x x x

B

[ ] =

= 0 4

1 1

1

3

A

A B

#

[ ] 11 / 4

1 4 3 / 5 0

2

= − 4 − − = −

c = = θ

11 13

12 1

a b

4 7 28 11

) 13 4 ( 11 4

1

15

−

=

−

=

− +

−

=

−

+

h

ϑ

T

B

B b c

c

11 7 77 11

/ 5

11 / ] 13 5 4

~

1

[

~

B

−

b = − − = − = −

c

T

B

# $ ! $

−

− −

− −

.

[ ]

−

= −

−

= −

=

−

3 / 1 3 / 2

3 / 2 3 / 1 1

2 2

1

1

3

2

A B

A B

7

[ ] [ 1 0 / 3 8 / 3 ]

3 / 1 3 / 2

3 / 2 3 / 4 1

2 = −

−

= − u

T

[ ] 3

1 3 1 / 8 3 / 10

1

3 − =

−

−

−

= c

8 * -

−

= −

−

3 / 1 3 / 2

3 / 2 3 /

1

1 B

[ ] 10 / 3

0 3 1 / 8 3 / 10

4

= 0 − − = −

c

[ ] 8 / 3

1 3 0 / 8 3 / 10

5

= 0 − − =

c

A

6

(4)

5

− =

−

= −

1 1 1 1 3 / 1 3 / 2

3 / 2 3 /

b 1 =

−

−

= −

=

−

3 / 2

3 / 1 0 1 3 / 1 3 / 2

3 / 2 3 / 1

4 1

4

B A

A

3

14 1

= a

b

ϑ

=

= 3 / 2

24 2

a b

9 * $ ! $ [ ]

−

= −

= 2 0

1 1

4

2

A

A B

6

[ ] [ 0 1 ]

2 / 1 1

2 / 1 0 0

2 = −

−

= − u

T

[ ] 3 1 2

1 1 1 0

1

3 − = − + = −

−

−

−

= c

8 * -

−

= −

−

2 / 1 1

2 / 1

1

0 B

[ ] 5

1 1 2 0

3

= 4 − − =

c

[ ] 1

1 1 0 0

5

= 0 − − =

c

A

:

7

− =

−

= −

2 / 3

2 / 1 1 1 2 / 1 1

2 / 1 b 0

−

= −

−

−

= −

=

−

2 / 3

2 / 1 1

1 2 / 1 1

2 / 1 0

1 1

1

B A

A

0 $ !

1

≤ a

i

;

B *

C D - E

8 * E

C 8 * F D E

C D G H I D *

+ D G -- HE

(5)

<

J #

K

K

>

F )

7 K

K

7

7 K

− $ K − K −

7

J -

7 K

A A -

A

A

* A -+ +

K − K

(6)

0

6 4

2

5 5

4 3

6 3

2 1

5 3

2

4 2

1

≥

= +

+ +

= +

+

= +

+

x

x x

x x

x x

x

x x

x

:

; :

6

6 5

:

* # 1635! ! ;362 $ :

; :

6

6 5

:

; 3:

3:

6

6 5

:

*

5

* )5 I #

; 6

3:

3:

−53:

−53:

−: −

−

; 6

3:

3:

6 5

−: −

−

6

* )6 I 5#

; 6

3:

3:

−53:

−53:

−: −

−

3:

63:

3:

3:

53:

53:

:

(7)

:

* : I #

3:

63:

3:

3:

53:

53:

3:

63:

3:

3:

53:

53:

:

;

3:

63:

3:

3:

53:

53:

:

* , $ % &

9B9 A J7K78 @! =

* *

<

3:

63:

3:

3:

53:

53:

:

* # 1 ! 3 2 $

3 3:

<3

3 3:

3:

3:

3

<

3:

3:

$ % & B 7 + A $ )<+

Riferimenti

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