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【1】求解:
! j j! C7 r1 @: ~设水库A、B、C分别向甲、乙、丙、丁四个小区供水量为x11、x12、x13、x14、x21、x22、x23、x24、x31、x32、x33、x34,则有:
8 W* f( @* O# e. |max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
* N, ^! ^+ ?, a; @, rst
: X' ]: t; o, l4 |' g$ Rx34=0; y' e' @4 v( f, d' e) l
x11+x12+x13+x14<=50;9 K1 P+ g1 X. A. v& [
x21+x22+x23+x24<=60;
- D, Z6 p# X1 Q. G: ?x31+x32+x33+x34<=50;
- Y4 I5 e9 k8 Q& X& {* U, ex11+x21+x31>=30;! c0 k9 m" @) ]( k& L, t' @; v
x11+x21+x31<=80;1 N. x& @1 g1 Y
x12+x22+x32>=70;
& X6 F8 _7 ^ Qx12+x22+x32<=140;. ~1 U/ @3 S8 c9 \$ e# H) D
x13+x23+x33>=10;
7 u8 u7 Z! q/ u$ v# d; M3 _7 Xx13+x23+x33<=30;2 y) m' H+ R' A
x14+x24+x34>=10;
& ?! h. C6 l& F4 Z9 t* ax14+x24+x34<=50;
, T7 x1 o( a1 c" `end
2 u- h6 C, \8 Z3 z4 L& JLINGO程序:
9 H$ s' r* i1 Cmax=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;9 `6 {* T* B- T' I9 Z0 x0 X9 U! C
x11+x12+x13+x14<=50;
2 ~* J% N, r3 G* S6 A7 Y4 Tx21+x22+x23+x24<=60;
8 A& G" ]. \# H4 cx31+x32+x33+x34<=50; T U# o' G4 ]+ h* m; O
x11+x21+x31>=30;
. G( B( P0 T' p2 G1 hx11+x21+x31<=80;
+ [' b( O2 P) X6 Gx12+x22+x32>=70;
( x) m% U' `) E# a6 `" ax12+x22+x32<=140;: ~6 m+ |4 C5 E& }# w0 O" |4 t& ~
x13+x23+x33>=10; B( j4 h9 L' k( I8 {
x13+x23+x33<=30;( [! }7 T/ V3 N4 O0 F; `
x14+x24+x34>=10;0 A: n, r/ r( s4 m
x14+x24+x34<=50;/ ~7 l$ q$ ^- [+ M. M) B; ]
end
3 t) c( z( p4 @$ j运行结果:: e8 @ M# b1 N+ g2 ^8 i8 `9 k
Global optimal solution found.8 S+ [5 C0 D3 }" @
Objective value: 47600.007 E8 w' O5 l, L9 K4 q' d& ?
Total solver iterations: 7
) K* a0 \1 \6 W( B% Y3 [% G# K8 @' t' S# D: m- }/ b0 f
0 q; ]! N$ Y7 ^3 CVariable Value Reduced Cost. I9 W: _/ E& b0 @
X11 0.000000 30.00000
# M) c+ d- D/ Z$ VX12 50.00000 0.000000
! h! P) K/ h6 A3 GX13 0.000000 50.00000
! `9 y8 `5 X8 E' }% B8 HX14 0.000000 20.00000# s/ l; _: l' Y( z
X21 0.000000 10.00000+ ]) i8 Z0 U: }3 I
X22 50.00000 0.000000
9 W6 k7 K. {( ?3 A1 v' o: B8 G. aX23 0.000000 20.000001 b8 j$ ^& E0 c. R. y
X24 10.00000 0.000000
0 d$ r: f" i1 k! F# VX31 40.00000 0.000000
6 p! y5 ?& b N3 g0 ^$ w WX32 0.000000 10.00000
2 C$ G7 H7 D1 J9 GX33 10.00000 0.0000000 r, }4 G6 d4 p7 `) Z& e) \
X34 0.000000 240.00004 ^* b/ {- S" L
6 ]4 k& K5 G) M. `( w( a9 K
Row Slack or Surplus Dual Price
/ {% x9 K' L' X) g! d1 47600.00 1.000000
2 k* Z5 b" |# u! [/ e& v2 0.000000 320.0000
6 o! p4 x+ G, G) E3 0.000000 320.0000# w5 w0 z# B0 a9 N) z
4 0.000000 260.0000
1 y- `8 U$ X! K0 B9 L9 v5 10.00000 0.000000( @+ ?$ j$ C# t
6 40.00000 0.000000
9 ^7 O! F( F8 R! r8 d6 }# B7 30.00000 0.000000
5 X' K5 _+ \( ^( {& Z8 40.00000 0.000000# q. b( G3 Y) [2 o& O% A
9 0.000000 -40.000008 A1 u: c3 J8 ~
10 20.00000 0.000000( x* U! c0 _3 \5 \8 \7 f( @
11 0.000000 -20.00000
5 s9 t2 ?, G9 ~9 u12 40.00000 0.000000
" [% l! ]. J0 q- p3 @7 r! C8 U
8 V( r+ m, f( [! Y【2】求解:
0 t( t1 f) f& A& H8 u, D模型:( J: K: o' J. n
max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
) Y1 W* B Q' N, q7 _9 Q2 lst
. S: E: |, T$ J7 G3 Gx34=0;2 e+ a7 C) h4 V% ^9 p* F6 t! Q
x11+x12+x13+x14<=100; G: x! S; K% N3 g6 S
x21+x22+x23+x24<=120;/ T# E- H7 x! P9 W6 [
x31+x32+x33+x34<=100;- n/ L, F! N3 `3 t7 b, q/ O1 K
x11+x21+x31>=30;
# j7 G9 D ^: X7 J6 R' q% wx11+x21+x31<=80;( y) y2 O7 ~8 g2 k
x12+x22+x32>=70;
& r. `5 z. L6 M B: o& e* Y6 \x12+x22+x32<=140;
! O2 l' Y* [- J3 D$ Bx13+x23+x33>=10;& f" h; K) Q; O! l" n6 ]! O% ?
x13+x23+x33<=30;4 G# R+ x9 J: J! A8 @: O* b
x14+x24+x34>=10;+ y9 q; o" D, k7 p5 n' C: U) N; E
x14+x24+x34<=50;! y4 m/ M& | Q5 Q' p* I9 V
end9 F2 |& i! K2 ]9 D
LINGO程序:
* l5 H8 H2 X$ l4 e" lmax=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;. o" e4 U/ J2 |. [; \' b6 A
x11+x12+x13+x14<=100;- D. t7 S& d$ X. r; t0 o8 I
x21+x22+x23+x24<=120;" `0 R+ e1 ?4 P& O* G
x31+x32+x33+x34<=100;
1 D/ x3 A1 f( \$ M( s+ Y8 Ux11+x21+x31>=30;
1 M+ E, p" r+ Ex11+x21+x31<=80;2 E7 f, W$ J7 q, B) }) V
x12+x22+x32>=70;2 V6 _# ]2 F4 N8 B) `" i% h
x12+x22+x32<=140;8 e" Z' l/ `- u& r
x13+x23+x33>=10;
1 f+ z3 @/ }2 I" l D9 qx13+x23+x33<=30;
" I4 M, M& c$ }x14+x24+x34>=10;
- h4 F3 b6 U4 r7 C) x ?x14+x24+x34<=50;
# [. @) W' R! d- G5 v, ?9 ^1 jend$ @0 u+ n) ^/ t0 |1 ^* ^- `* Z# t. F
运行结果: - Q, D2 ]- t6 a8 a+ p4 W" D
Global optimal solution found.
8 b4 {" R* \! ?% Y- L Objective value: 88700.00
" A+ A' A) E0 S4 V7 @; a Total solver iterations: 7/ G( S7 Q' s) G9 Z
. C- A/ ~1 l- l
- T3 l; i6 D5 m9 u3 T9 [Variable Value Reduced Cost
' i5 `+ Z( V9 U( S+ r2 EX11 0.000000 20.00000
, W0 o8 k) o& a1 B7 S- ?' \- {X12 100.0000 0.000000
6 n+ i1 s" K& |$ A4 eX13 0.000000 40.00000( e% B# M8 g, d g7 r9 K/ n
X14 0.000000 20.00000* G4 V9 i8 L7 [9 w; a" J x
X21 30.00000 0.000000
/ q( x& A: [0 s+ AX22 40.00000 0.000000
$ K$ _5 z. u: g9 MX23 0.000000 10.000003 |5 P& v! w* W9 E# }. [
X24 50.00000 0.000000
; e( G* |) N) qX31 50.00000 0.000000
. p% s! D1 a: RX32 0.000000 20.000007 ^8 }; ^2 h4 z1 r' ~
X33 30.00000 0.000000
S' b* x4 N5 @! Q) @6 E% e T2 pX34 0.000000 250.0000
" V: [$ {' h5 {% B
1 X% I6 e+ }" W. d* q4 aRow Slack or Surplus Dual Price" `; o( f5 p+ U' Q( ?, E+ {
1 88700.00 1.000000* e% v4 ]8 A9 x+ L. }. O, q
2 0.000000 50.00000
: M3 j7 C6 s# G% j# E3 0.000000 50.00000
2 C) l& ~0 }; ~* J$ |4 20.00000 0.000000; v3 q# {+ z' R! F( d$ n8 A
5 50.00000 0.000000! g* `! ?0 O# W9 q( ^$ K f- I2 d
6 0.000000 260.0000
& S" | K; w( \+ Y7 70.00000 0.000000/ m$ `8 B2 Y: m& Q$ T4 H( m
8 0.000000 270.00005 q, K- j; ^& [/ R9 I0 E
9 20.00000 0.000000
) T$ n* l I8 D10 0.000000 220.00009 p# M8 X/ t' }* N) p( _
11 40.00000 0.000000+ u# F) g3 ], k* \# ]6 F* `' F
12 0.000000 250.0000 |
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