Water Network Design

3.2

~ ™  €  Œ  Ž   ‘

- —  ‘  a  L E 1 i G H 0 E 3 Y 5  ‡ ˆ < '  p 1 P M l

m E ‡ ˆ  <  f _ U 7 ½ v w  Z ’ E i N 7

1. 1 i V ! Q K ^{  E @ ? 7 Ç “ Q “ , E P}

2. : R a E ¯ I t 7 V 9  I E P

3. b Q R 1 i V ! Q a < v w 9 L M E ? ? ³ / 7 “ , E P

'  I R U 7 S ? T U š Z 7

„ 4 u = : 7

(a) !  “ E 2 ^  ! ? G  P

3.2 … ž † ‰ Ÿ § ¨ © ª « ¬ 43

(b) b R 1 i V ! Q G > h E K  ^{) *} G  { n P

(c) b R 1 i V ! Q " : € E  ^{@ l} ! 2 ^{d E ³ / ? P}

(d) b R 1 i V ! Q K a ^ , ^{³ / ! ? E  { P}

(e) I R i ™ E ; < 0 P

? U 7 O  > 7

(a) ¬ Q 5 ¡ a v E # E 3 e P

(b) ¬ ^  a v E ! ) ? _ P

(c) ¬ V ! Q K ^{   L G > h G  X Y P}

U 7 E Z [ 7  ‘  !  < y < U | }  Q R K L M E ! 

^ _ E „ 4 < ?  o 7

(a) K C ^  ^{! E > ? P}

(b) K = M ^{  E  = P}

44 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

3.3

~ ‹  €  • – ¢ £

1 F _ : 3 4 E l m p  1 i V ! Q ?  ^{7 Q p % < 4 f _ 6}

!  ` ^ _ % S ?  p  R F G < 1 i V ! Q (Ä 3.2 )K ^ 

(Ä 3.3 )<  Q 6 ½ ~ \ Q R s t  (Mixer)< ? F ( ^{k  ´ ¬ R V W}

 “ E ! ) — f  Q  ^{< 6   Q  E  ‘ Q a =   <  Q 6}

  \ Q R  V  (Splitter)< Z E 7 k  ’ ) ! © A Q E !  Q R  V E V < P Ä 3.4 p Q R " # ^{w E ` ^ _ <   ^ _ a  l !  “ ? }

I $ ! < ! ^{! > . ( @  ?  I Q R ( & <} B ^{V   V < I a ©}

A F G 7 6  !   Q E : \ # E S ] w P a <  U E a b <

I R ` ^ _ !  Ç \ $ ^{e E Ô _ < 4 Z E F _ k  G  E a b b}

R d l ? : U 6 E d l 4 m  5 P { n 7 P

) 3.2 ` ^ _ (Superstructure)

Water Using S Unit M

From Other Water Using

Unit

To Other Water Using

Unit From

FreshWater Supplied From

Storage Tank

Storage To Tank Environment To

Micn^load out

qi in qii n

in

3.3 … œ † ‰ Ÿ ˜ ™ ¦ § 45

) 3.3 ` ^ _ (Superstructure)

Storage S Tank

M From Water Using Unit

To Water Using Unit From Other

Storage Tank ’

out

in To Other

Storage Tank ’

) 3.4 " # ^{w E ` ^ _}

46 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

3.4

~ ‹  š › œ  ž œ ¨ © Ÿ   Œ ¨ © ¡  

( Indices, Sets, Parameters, and Variables)

1  7 ² V ` ^ _  , D < 4 ` ^ _  , D % ^% 9 i N ` ^ _

a < : \ a v ^. p ^  < x ? { n 7  ? { n a v E ^   ­ < : ? v

w 9  V  ? E P  < f g : ¡ E n @  k @ < '  f g U 7 E '

e ª x 7 „ , : R a E < j (indices)9 3 t (sets)9 : R k @ (parameters)

?  : R n @ (¼ „ # O n @  0-1n @ )(variables)9 1 2 k  ’ — 3.4.1

_ - 3.4.4_ P

3.4.1

” • – ^! — ^B ˜ ™

(Indies and Sets)

  ^" E [ < j 7 ? U 6 d  E < j < + š : i7 1 i V ! Q

9 c 7 ! 2 ^{d 2 ^ ... Z < © A [ < j . / Ò 3.1 = 4  U 7 a :}

V E ^# É k @  n @ « ” > R [ < j P

* 3.1 [ < j  3 t . /

c ∈ C ^{: \} ! 2 ^{d 2 ^ 6 3 t}

e ∈ E ^K ! 2 ^{d > . — c £ E 2 ^ 6 3 t}

i ∈ I^{c : \ # O 7 1 i V ! Q 6 3 t} i ∈ I^{b : \}  ^{7 1 i V ! Q 6 3 t}

i ∈ Ip ^  p " : \ V ! Q 6 3 t

n ∈ N ^{: \ 0  6 3 t}

n ∈ N^{− j M 8 Q R 0  < : \ 0  6 3 t}

p ∈ P ^{: \  6 3 t}

s ∈ S ^{: \   6 3 t}

s ∈ Sp : \   p" E ^{  6 3 t}

w ∈ W ^{: \ }  ^{!  “ 6 3 t}

47

3.4.2

 œ ^$

(Parameters)

 1 _ k a b U 7 a : ¡ E P 1 ’ ¢ < j ¡ „ 4 u : s ‘ E k @

< + š 7 C_ic,maxⁱⁿ 6  ! G ‘ 1 i V ! Q i 0 < ! 2 ^{d 2 ^ c E K  S}

) * 6 G  G  7 Q R 9 „ , E “ , _ = 4 © f k @ 6 , m   ^ £

< š 6 2.2 :  P

* 3.2 : R k @

C_ic,maxⁱⁿ ! G ‘ 1 i V ! Q i0 < ! 2 ^{d 2 ^ cK  S ) * 6 G ( G }

C_ic,max^out ! V c 1 i V ! Q i< ! 2 ^{d 2 ^ cK  S ) * 6 > h G }

C_wc !  “ w: € ! 2 ^{d 2 ^ cE G }

M_icn^load  0  n 1 i V ! Q ia < ! 2 ^{d 2 ^ cE ? ? ³ /}

Q^min_i 1 i V ! Q i S @ ^* K = ! @ ?

Q^max_i 1 i V ! Q i S @ ^* K  ! @ ?

Q^max_s ^{  s K  E @ ?}

Y_in^st. ∈ {0, 1},= 1^{6  1 i V ! Q} i  0  n c  ; <

Y_in^end ∈ {0, 1},= 1^{6  1 i V ! Q} i  0  n ^  ^{; <}

Z^cyc. ∈ {0, 1}, = 0^{6  p Q 5 ; <} ,= 1^{6  p 2 c ; <}

Δi ^{1 i V ! Q c  ; <  ^  ; < E 0 } ›

3.4.3

  ^$

(Variables)

1 _ k a b „ 4 n @ < j U 7 s > E n @ < ¼ „ Q 3 E # O n @ 

  E 0 − 1^{n @ <  2 V W E : R n @ P}

0 − 1^{n @} (binary variable)< 7 6  Q R ^%  ^  N V ^  E   n @

< ^Q @ _ ? ] ^  — 0^ 1^{ u 6 Q < \ j} 0 − 1^{n @ E ^ } V 7} 0^{x 7}

1^{P + š 7 } y_wi = 1^{0 < 6  m !  “} W )  1 i V ! Q iE a v 7

  E =  y_wi = 1^{0 < 6  m !  “} W )  1 i V ! Q i E a v 7

48 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

V ^  E P 4 # O n @ (continuous variable)< 7  Q , h — " : \ S ] - @ A r  }  E ^ } < p ^# É  — N Z — 0 ^{E @ _ < © f} 0 − 1^{n @}

 # O n @ š 6 :  =

* 3.3 # O n @

cⁱⁿ_icn  0  n 1 i V ! Q i a < ! 2 ^{d 2 ^ cE G ‘ G }

c^out_icn  0  n 1 i V ! Q i a < ! 2 ^{d 2 ^ cE > h G }

cⁱⁿ_scn  0  n ^{  s a <} ! 2 ^{d 2 ^ cE G ‘ G }

c^out_scn  0  n ^{  s a <} ! 2 ^{d 2 ^ cE > h G }

q_inⁱⁿ  0  n G ‘ 1 i V ! Q i E Š ) ?

q_in^out  0  n V c 1 i V ! Q i E Š ) ?

q_iin ^{1 i V ! Q} i  Q R 1 i V ! Q i^ E Š ) ?

q_isn 1 i V ! Q i ^{  s E Š ) ?}

q_ien 1 i V ! Q i c £ e E Š ) ?

q_sn  0  n ^{  s E  Š ?}

q_snⁱⁿ  0  n G ‘ ^{  s E Š ) ?}

q_sn^out  0  n V c ^{  s E Š ) ?}

q_sin  0  n ^{  s  1 i V ! Q iE}

q_ss^_n  0  n ^{  s   Q R   s E Š ) ?}

q_win  0  n !  “ w 1 i V ! Q iE Š ) ?

y_∗n  0  n E 0 − 1^{n @}

*∈{ si, is, ss^, ii^}

∀i ∈ I, s ∈ S

49

3.6

^{& ' ‹}

(Constraints)

3.6.1

¤ ¥ ¦ § ¨ © ^{5 0 1 3 4}

(Flow Rate Balance for Water-using Unit)

) 3.5 1 i V ! Q E ` ^ _

50 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

- Ä 3.5 S M  1 i V ! Q E ` ^ _ <  G h   E  “ S ] \ 

´ © A 1 i V ! Q i^9 ^{  s< ?  }  ^{!  “ wP x  Q   < V}

c 1 i V ! Q E ! S ] ” ) ^# © f E 1 i V ! Q i^9 ^{  s< ?}

 > . ^# c £ a eP Ì (3.1)Í (3.2) T U 1 i V ! Q E ) ?  =  G

h   (Mixer) K > h   (Split) — 0  nP

q_inⁱⁿ = 

w∈W

q_win+

s∈S

q_sin+

i^∈I

q_iin ∀i ∈ I, n ∈ N (3.1) q_in^out = 

i^∈I

q_iin+

s∈S

q_isn+

e∈E

q_ien ∀i ∈ I, n ∈ N (3.2)

4 1 i V ! Q G > h ) ? E  Z { Ì (3.3) Í (3.4)  6 U 6 < 4

Y_in^st.K Y_in^end p 0 − 1^{k @ V  > 1 i V ! Q E c   ^  E 0  =}

 Y_in^st. = 1^{6  1 i V ! Q} i  0  n c  ; < P W l < Y_in^end = 1^B

p ; < C ^{± — 0  n< -   R F i 7 S  / I} " ^{n  1 i V ! Q}

i ; <  C ^{± 0 ! G > E Š ?  = P : ? < V ” \ # É E ! G ‘ N V}

c 1 i V ! Q < — V  ; < N ^  ^{E 0  0 P}

Q^min_i Y_in^st. ≤ qⁱⁿ_in ≤ Q^max_i Y_in^st. ∀i ∈ I, n ∈ N (3.3) Q^min_i Y_in^end ≤ q^out_in ≤ Q^max_i Y_in^end ∀i ∈ I, n ∈ N (3.4)

Ì (3.5) B p 1 i V ! Q E Š ) ?  = < i N ¥ \ ^# É  ^{ ! E ®}

¦  ˜ # P © a Δi ^{p 1 i V ! Q} ic   ^  ^{0  E} › ^@

q_inⁱⁿ = q_i,n+Δ^out _i ∀i ∈ I, n ∈ N (3.5)

51

3.6.2

¤ ¥ ¦ § ¨ © ⁵ ª ^{P 3 4}

(Contaminant Balance for Water-using Unit)

M 1 ) ?  = < 1 i V ! Q E > ?  =  7 v w  I E P Ì (3.6)T

(Flow Rate Balance for Storage Tank)

) 3.6 ^{  E ` ^ _}

52 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

 V    <  0  n 0 P

q_snⁱⁿ =

i∈I

q_isn+

s^∈S

q_ssn ∀s ∈ S, n ∈ N (3.10) q_sn^out =

i∈I

q_sin+

s^∈S

q_ssn ∀s ∈ S, n ∈ N (3.11)

4 Ì (3.12)B p I R ^{  s E ) ?  = <  0  n  E ! Š ?}

Z — ½ Q R 0  t − 1 ^{ E ?   — 0  n 0 ! G ‘   E ?}

? ( — 0  n 0 ! V c ^{  E ? P  a Zcyc. p 0 − 1k @ 6  : R}

E ; < U 7 =  Z^cyc. = 0^{0 6  p Q 5 ; < <   3 e Z   K} $ ⁷

¥ \ ^{ ! ? E = 4  Zcyc. = 00 6  p 2 c ; < < K} $ ^{   " E}

! Š ? ” Z —  R 2 c ; < ^  ^{E 0  N E  ? P}

q_sn = Z^cyc.q_sN |_n=1+q_s,n−1|_n>1+q_snⁱⁿ − q_sn^out ∀s ∈ S, n ∈ N (3.12)

4 ! ^{ —   " E Š ? ?  G (   E ) ? E  { < - Ì}

(3.13)Í (3.14) 6 U 6 P

q_sn≤ Q^max_s ∀s ∈ S, n ∈ N (3.13) Z^cyc.q_sN |n=1+qs,n−1 |n>1+qⁱⁿ_sn≤ Q^max_s ∀s ∈ S, n ∈ N (3.14)

3.6.4

^{   5} ª ^{P 3 4}

(Contaminant Balance for Storage Tank)

 ^{  a M 1  I ) ?  =  <  v w  I > ?  = P Ì (3.15)B}

T U ^{  s — 0  n  s t    E > ?  = P Ì (3.16) B p } 

53

n— 0  n E Š > ?  = P š } ^{  — W Q R 0  n W 0 \ G ‘}

 V c E ) ? < B i N G ( E ) ? p ¯ 9 ž # (9 G  > )P

q_snⁱⁿcⁱⁿ_scn =

i∈I

q_isnc^out_icn+

s^∈S

q_ssnc^out_scn ∀s ∈ S, n ∈ N , c ∈ C (3.15) q_snc^out_scn = Z^cyc.q_sNc^out_scN |_n=1+q_s,n−1c^out_sc,n−1 |_n>1+q_snⁱⁿcⁱⁿ_scn− q_sn^outc^out_scn

∀s ∈ S, n ∈ N , c ∈ C (3.16)

3.6.5

^{+ , - . /}

(Logical Constraints)

y_†Q^L_†n ≤ f† ≤ y†Q^U_†n † ∈

ii^, is, ss^, si

(3.17)

Ì (3.17) a b ¬ d ) a < ) ? E S ^{) *}  = h — = © a Q^L_† 6  5  a

v a ! ) ) ? E K « S ^{) *} ) ? < Q^U_† B 7 5  a v a ! ) ) ? E  {

k @ =   <   @ A U 7 a ^ ‘ 1 0 − 1^{n @} (Binary variables)< y_†< I

 6  @ ! ) a v 7 ­ ^  <  ^  < B y_† = 1^{< Ï 6 <} y_† = 0^{= : ?}

I R { n 7 U 6 E 4 m <  @ Q R ! ) a v ^  0 < a v a E ! ) )

? v w  ) ?  Z { E h —  a P    ) ?  E { n 7 ( { n  

I t  E ; < { n P

Ì (3.18)Í (3.19)B 6  # O 7 1 i V ! Q 7 V ] ° © f E 1 i V

! Q D E # E E P

y_iin = 0 ∀i ∈ I^c, i^ ∈ I, n ∈ N (3.18) y_iin = 0 ∀i ∈ I^c, i^ ∈ I, n ∈ N (3.19)

54 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

3.7

7 ^{0 1}  

(Objective Function)

8 Q R Z [ \ @ p K = M ^  ^{! E > ? < š Ì (3.24) :  :}

3.7 = ^{J K} ² (Objective Function) 55

56 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

3.8

 ¨ ©  ^{4 5} ~ ⁶ Œ  ^

-

^ 5 6 ^{ 7  } 4 ^{‹ 7   }

3.8.1

^{: ! " }

3 4  F _ E l m < ˜ §  V Generalized Algebraic Modeling System(GAMS, Brooke et al., 1988)<  z { < 4  z { K L M l m E { m  (solver) F

< ² V E MINLP solverp BARONP

3.8.2

¨ ^{m $ %} § ^{& '} ¯ ^{( F}

^-

^{n G}

^3.1

* 3.4 1 i V ! Q ; < I 6

Unit [Q^min_i , Q^max_i ] C_ic,maxⁱⁿ C_ic,max^out t^st_in t^end_in M_ic^load (ton) (kg salt/ton water) (h) (h) (kg)

A [0, 1000] 0 0.1 0 3 100

B [0, 280] 0.25 0.51 0 4 72.8

C [300, 400] 0.1 0.1 4 5.5 0

D [0, 280] 0.25 0.51 2 6 72.8

E [300, 400] 0.1 0.1 6 7.5 0

F [0, 500] 0 0.1 0 7.5 187.5

[0, 350] 0.1 0.25 0 7.5 187.5

[0, 200] 0.25 0.51 0 7.5 187.5

8 Q R + p 7 - ^L R  ^{7 1 i V ! Q (A-E)k } Majozi(2005)?  Q

R # O 7 1 i V ! Q (F) E ; < Á  - Ò 3.4 S } < ¼ „ Q G > E

Š ) ?  Z {  = 9 G > h S ^{) *} E K  G  < c   ^  ^{E ; < 0}

 < ¡ L M E ³ / ? ? P   + p   k 5  o 2 # O 7 1 i V !

Q < © ¬ ´ ^ \ V W G > h S ^{) *} E K  G  < G 4 ® 5 !  E

57

58 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

59

60 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

61

200 100 166.7 25083.3 200

62 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

63

64 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

65

66 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

) 3.22 Q 5 ; < Z  ^{" ! ? n M  > h G  -(C}fc,maxⁱⁿ = 0.25), (C_fc,max^out = 0.51)

0 2 4 6 Time (h)

3 5.5 7.5

100 300 500 700 900

0.1 0.3 0 (kg_salt/kg_water) 1100

Storage

(kg) Level

Conc.

575

Q A9 B9 D ^.  V $ ! < Q C9 E  V  ´ Q A ^ . 

  ^E ! ^{! < Q F B — F G 0   V }  ^{! 9 F G  V }

 ^{E  ! P 4 Ä 3.22 p   " ! ? n M E 3 e < -  S } “}

^{   = p 575kgP}

3. Q R ^{  Q 2 c ; <}

 ‘ ^{  6  Q 2 c ; < E ^ } š Ä 3.23 < }  ^{!  V ? - p}

1000kg^{< Q ? & Q} A V ^  ^{! < © f E Q .  V Q A }

— ^{  E 2 c ! < - — Q A G ‘   E ! ? - « < J  p}

E  = '  Z - p 813kg ^Ä 3.24 P

K  < Ò 3.5 p 3 4 + p 3.1 E Š ^ <   S ? M  ^  ^{! E >}

? ' ^{  E  ‘ ? C V C <  2 c ; < E Á  Z  ] - « P 4  }

1 i V ! Q F — (C_maxⁱⁿ = 0.1)^< (C_max^out = 0.25) ^{0 < j  p  R  p º}

 ^{Q R  p 0 ¶ S x 5 - « }  ^{! E > ? < š }  1 i V ! Q F}

— (C_maxⁱⁿ = 0)^< (C_max^out = 0.1)^{0 < - —} F ? ]  V ^  ^{! < J  j  p}

67 121.95 61 61 91.46 30.5

91.46

68 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

* 3.5 + p 3.1 E Š ^

(Cmaxⁱⁿ )F Operation mode Single operation Cyclic operation

(Cmax^out)F Storage tank 0 1 2

0 Freshwater (kg) 3760.5 3017.8 2875

-0.1 Ratio (%) 100 80 76.5

-Tank size (kg) (base) 300 300 -0.1 Freshwater (kg) 2635.5 1513.6 1330 1150

0.25 Ratio (%) 100 61.3 48.9 43.6

Tank size (kg) (base) 1000 998 720,280 0.25 Freshwater (kg) 2253 1432.5 1000

-0.51 Ratio (%) 100 63.6 44.4

-Tank size (kg) (base) 575 813

-3.8.3

¨ ^{m $ %} § ^{& '} ¯ ^{( F}

^-

^{n G}

^3.2

8 > R + p B 7 k  Wang 1995E o R  ^{7 1 i V ! Q (Q 1-3)}

 Q R # O 7 1 i V ! Q (Q 4)< © ; < Á  ’ — Ò 3.6 6 a S }

“ Q G > E Š ) ?  Z {  = 9 G > h S ^{) *} E K  G  < c  

^  ^{E ; < 0  < ¡ L M E ³ / ? ? P   + p   5  E ! }

r % p o 2 < C ^{  9 Q R   Q Q 5 ; < 9 Q R   Q 2 c}

; < = ? Z p ^ }  ,  5  7

69

* 3.6 1 i V ! Q ; < I 6

Unit [Q^min_i , Q^max_i ] C_ic,maxⁱⁿ C_ic,max^out t^st_in t^end_in M_ic^load (ton) (kg salt/ton water) (h) (h) (kg)

1 [0, 100] 0.1 0.4 0.5 1.5 30

70 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

71

72 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

3.8.4

^{# $ %} § ^{& '} ¯ ^{( F}

^-

^{n G}

^3.3

 + p 3.3 a <   5  E 7 Q R   ^{E !  : R < k 9 ½ : =}

E  R + p  Q R I t y -  R ^{  E ¡ 5 = : < ?    = E }

 ^{! > ? < n - —  I E 2 c 0 7 7.5hr 4  II B 7 1.5hr< J}

  Q R 2 c "  II ; < 5 @ p ^L 5 < 4  R  " E 1 i V ! Q

; < Á  š Ò 3.7 P

* 3.7 1 i V ! Q ; < I 6

Plant Unit [Q^min_i , Q^max_i ] C_ic,maxⁱⁿ C_ic,max^out t^st_in t^end_in M_ic^load (ton) (kg salt/ton water) (h) (h) (kg)

I A [0, 1000] 0 0.1 0 3 100

B [0, 280] 0.25 0.51 0 4 72.8

C [300, 400] 0.1 0.1 4 5.5 0

D [0, 280] 0.25 0.51 2 6 72.8

E [300, 400] 0.1 0.1 6 7.5 0

F [0, 350] 0.1 0.25 0 7.5 187.5

II 1 [0, 100] 0.1 0.4 0.5 1.5 30

2 [0, 40] 0 0.2 0 0.5 8

3 [0, 25] 0.1 0.2 0.5 1 25

4 [0, 85] 0 0.1 0 1.5 25.5

- Ä 3.30 } “  Iy -   ^{E I t  < }  ^{! > ? - p 1000(ton)<}

 9 ½ E + p a B p 1330(ton)^{ Z 1 o} 25%^  ^{! ? < m I   S ? M}

 ? \ Q A  V ^  ^{! < 4 © f E Q  V E . p  p " E  !}

< - — Q C9 E V  E ! - — ¹ p  { ^{< J  0   x   V}

6 < 4  ^{p 1E  = B - Ä 3.31 } “ p 956(ton) P}

73

74 y z { | } ~ ^{œ †} † ^-‡ |  ˆ ‰ ° ^œ Œ  < =

4

N  ^{O & ' ( )}

4.1

^*

 Ÿ d   < - — ! “ o 1 R  R  ?  c £ ^{$ +} B h ^{, -  !} <

 ‘  V ! i ™ a 4 — ! \ Î  V E  m d ^. 9 6 * < 4  ^* E 2

² 4 — !  K L M E N O Ç \ ^* E   ® 5 P

1 2 3 4  " E 1 i V ! Q ? # O 7 K ?  ^{7 Q p %  2 3}

Y < = > ? @ A B C D E F 7 G H I J K L M E N O P ' 9   !

 : R " ¬ Q : \ S ] E a v # E < G 4 = > ` ^ _ <   ` ^ _

d e f g B h F i 7 P ¼ „ ) ?  =  > ?  = <  ? Ô _ 6 { n 7

< x  3 4 K = ^  ^{! E > ?  K =   E  =  R V W E Z}

[ < k  !  K L M E N O l m < # n o p Q R q r E s t I @ u

v w B C (MINLP)@ A l m < x y ^/  z { < K ~ S | } !  E K L

M N O P  Q K L M N O < ¼ „ !  : R E Ô _ ?  ¬ Q a v

75

76 ^S ¥ · ^{0 1} ¸ ²

# E E 3 e Z P

 < ( 2 ² < º ¹ < < (  !  E   F  ~ 3 4 V ! Q ¸

p  ^{7 N # O 7 Q = 4 1  2 B ® 5   " \}  ^{7  # O 7 Q}

E !  N O < I - U 7 ` ^ _ E  , < = > Q ^ 5 4  I E @ A U

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在文檔中 應用數學規劃法設計含批式與連續式製程之跨廠區用水網路 (頁 60-99)