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升级   54.75% TA的每日心情 | 开心 2015-6-12 19:46 |
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签到天数: 6 天 [LV.2]偶尔看看I
群组: 数学建模 群组: 数学趣味、游戏、IQ等 群组: 学术交流A |
优化问题可以用LinGo软件求解,以下是我做的结果1 {; p. K+ e' i7 \& ^) N
# O, E0 M6 T( r$ m有2个产地和6个销地的运输问题,其产量、销量及距离如上表所示,试求总路程最小的运输方案,以及总路程。
) Z, n' t, E A3 ~; k以下是LinGo中的代码(数学表达式),LinGo中可以输入数学表达式或程序:5 u. Y4 y" i4 T5 x. ?: f
min=3.758324*x11+3.758324*x12+5.857687*x13+4.069705*x14+5.85235*x15+7.115125*x16+5.798808*x21+9.199185*x22+2.704163*x23+4.25*x24+1.118034*x25+5.303301*x26;
5 u( _! X6 P1 l% ^5 g! Kx11+x12+x13+x14+x15+x16<=20;
2 T# j' A* b8 ^4 {5 B+ D, ?x21+x22+x23+x24+x25+x26<=20;
) m0 N' f' s7 t5 O5 \: g. a& kx11+x21=3;
; k0 _3 C. `2 m! `6 yx12+x22=5;' q! U) w. Y; {& q2 y
x13+x23=4;
5 D/ t& B; Q& H2 px14+x24=7;
: ^; ]8 O7 K" Tx15+x25=6;
: o' E% u. Z) A% O3 t3 Ex16+x26=11;
, c k! y' v/ f( F. _+ k7 i) s@gin(x11);
! q! ?1 C7 i: ]@gin(x12); s! |$ N: b# ]/ s5 p% o" z7 @
@gin(x13);
: ^1 c; K9 j# x; k@gin(x14);
+ K, O: {& ]- X. Z@gin(x15);1 U6 c# x6 y! b8 u3 }
@gin(x16);
4 u% p9 j6 X- H: ?@gin(x21);
. i, v/ j; e; z |$ A7 d@gin(x22);( l- I5 a0 L% G, v1 B D7 W
@gin(x23);
, V3 U9 h I: s$ C" @@gin(x24);
, C' N. c5 q+ l: L@gin(x25);7 e7 w- ?# `- c ^8 S
@gin(x26);
& y9 ~% [3 T* n6 ^/ a0 W下面是运行结果:0 z4 F# r* ?) M2 l
Global optimal solution found.' b7 c9 F1 T; B F
Objective value: 136.2275
5 v6 P5 S' F: B/ B Objective bound: 136.2275$ ~+ S4 r2 M X/ {
Infeasibilities: 0.000000& }9 e5 u; o' i# l
Extended solver steps: 0
: b/ [/ q+ h/ z8 S Total solver iterations: 0+ ]* x) t2 I K& i
% B n& \( y, L" R/ X Variable Value Reduced Cost
+ C+ J# H) K6 ]% O6 ?, v, W X11 3.000000 3.7583244 c( ]; y# A2 ]8 x/ [) T6 X
X12 5.000000 3.7583242 v4 U: L" y2 i# A9 a4 x/ P
X13 0.000000 5.8576871 ]. {% }3 D) x( @/ Y% e6 P7 [
X14 7.000000 4.069705
5 E1 W5 m4 P& }/ K5 j/ M X15 0.000000 5.852350
4 n7 G( e( i8 l3 I0 @ X16 1.000000 7.115125, O4 e" L' o' J, o' z# A' H
X21 0.000000 5.7988084 @$ ?. T# E/ P: s2 ?
X22 0.000000 9.1991854 P/ y- c& ^& }8 b3 K0 e$ O: F
X23 4.000000 2.704163! c3 F. X7 B& ~ z+ f, m, v) r
X24 0.000000 4.250000" ]4 \. z) ~4 }
X25 6.000000 1.118034
& C( i- I T. k, t X26 10.00000 5.303301
9 H* o1 ?, {3 s: } Row Slack or Surplus Dual Price+ ^1 z8 \/ P9 X7 b8 R" [
1 136.2275 -1.0000001 g. w2 u- D2 F8 R# ` J
2 4.000000 0.000000
( {& s$ N( S: E, `7 h 3 0.000000 0.000000) N7 U9 z( u5 X+ D# C* L5 ?, N
4 0.000000 0.000000
4 K* e/ Y/ e" T \8 K 5 0.000000 0.000000
9 U8 u( @9 K/ R i 6 0.000000 0.000000
7 {' {: o# Y8 `2 |* l& q4 m7 a1 Q 7 0.000000 0.000000
6 C$ @! ?% V: G( N0 O- j# [& n 8 0.000000 0.000000
. f. G5 R. E* D& R1 L 9 0.000000 0.000000
5 [' X& H; l$ ^. Y: N- e" e由此得出,产地B1运往A1,A2,A3,A4,A5,A6的运量为3,5,0,7,0,1个单位,余4个单位;产地B2运往A1,A2,A3,A4,A5,A6的运量为0,0,4,0,6,10个单位,余量为0个单位;总路程136.2275个单位。: n K! z. a6 {) {/ H2 E- l) C
第二问:
: l3 w( L$ E# rmin=(@sqrt((a1-1.25)^2+(b1-1.25)^2))*x11+(@sqrt((a1-8.75)^2+(b1-0.75)^2))*x12+(@sqrt((a1-0.5)^2+(b1-4.75)^2))*x13+(@sqrt((a1-5.25)^2+(b1-5)^2))*x14+(@sqrt((a1-3)^2+(b1-6.5)^2))*x15+(@sqrt((a1-7.25)^2+(b1-7.75)^2))*x16+(@sqrt((a2-1.25)^2+(b2-1.25)^2))*x21+(@sqrt((a2-8.75)^2+(b2-0.75)^2))*x22+(@sqrt((a2-0.5)^2+(b2-4.75)^2))*x23+(@sqrt((a2-5.25)^2+(b2-5)^2))*x24+(@sqrt((a2-3)^2+(b2-6.5)^2))*x25+(@sqrt((a2-7.25)^2+(b2-7.75)^2))*x26;
z7 p8 R, Y6 c# I; c- @( ax11+x12+x13+x14+x15+x16<=20;0 S) {6 Q1 W! U8 G v9 b3 |3 y/ j
x21+x22+x23+x24+x25+x26<=20;
+ x% {: N( P! G! c# L4 |& {x11+x21=3;
' S4 L( y8 D4 N/ M% V: O! P R, Yx12+x22=5;
/ R' C/ _" Z8 r8 ~$ t; S' e% [* qx13+x23=4;
* o6 y. K6 A! J% gx14+x24=7;% Y; W3 `( x2 O
x15+x25=6;! [/ P, E3 j6 g( y0 q8 q! Y) N
x16+x26=11;
& e, O* Y& j, K% V$ g@gin(x11);
% m" f' v* t5 E+ M9 q1 J@gin(x12);
! I- o/ m2 j( A* Y@gin(x13);- t9 F/ m3 m6 x
@gin(x14);
' C" t8 K' w- u# Y6 s2 T( V5 b T@gin(x15);
+ u7 \9 A" i, |6 f, B j; P9 \@gin(x16);: e1 Q" @ C2 m4 F
@gin(x21);0 v) s- J3 a9 H1 T9 z
@gin(x22);
) k0 {, m4 j+ b* {@gin(x23);, a: D2 U# f/ ]" ~$ d
@gin(x24);% U& K7 e. v4 r" M
@gin(x25); m) G1 G, O% B$ F" E) n6 J+ r
@gin(x26);
! @2 p. v8 Y: j4 P& R结果:, e9 u4 ^2 U0 d; o3 ^
Local optimal solution found.% Y- s/ J2 \! H; U$ j* ?$ G
Objective value: 93.357915 h" d3 A3 t, g- s
Objective bound: 93.35791
- u3 N2 M+ o, S0 J5 O Infeasibilities: 0.000000
5 \0 l' s! M+ M9 \( U/ Z Extended solver steps: 0- Y1 ^8 p' X. @4 N0 { X3 |9 i& W& V
Total solver iterations: 443 ^& b: ]+ {8 X' j! T m8 N$ ^4 W
; ` o4 J; @" Y
Variable Value Reduced Cost
$ X0 d2 L7 b6 Q3 T4 U! m A1 3.137191 0.000000
" [) m* n5 }2 s3 B2 v6 H) F7 F( M/ T B1 6.211140 0.000000
( `. D# E- P* A$ l- |, Z2 n/ k1 x X11 0.000000 0.000000# v g4 m1 ?& c0 L) [
X12 0.000000 0.000000
! W3 O0 O& d h% A! U8 Y* k" O; W X13 4.000000 0.000000+ \. t3 b# l0 m( u' A$ x
X14 7.000000 0.000000
$ ]+ D% f7 N1 G i& K: Q5 ]- b X15 6.000000 0.0000001 r0 ^% M* k& c
X16 0.000000 0.000000
, _, s) I% b# H7 E2 O A2 7.250000 6.618652& o0 d) j2 _' D |7 v
B2 7.750000 -2.355740# e6 o( S: D+ }6 w* q0 x( c4 x
X21 3.000000 0.000000
' V, u, v9 u+ P3 j' Z. Y X22 5.000000 0.0000007 L @7 v. D C$ i) ~/ K: U5 ^
X23 0.000000 0.000000' ~+ |# p4 E7 v, E
X24 0.000000 0.000000
( s$ X5 }( {5 w9 P* o' ?/ n X25 0.000000 0.000000
' J/ g! R3 x$ Q" {& J; k X26 11.00000 0.000000
9 U# G# ~8 G0 p. I! ~* ]+ Z Row Slack or Surplus Dual Price6 X# y% t! l8 _7 O( C) Y ^
1 93.35791 -1.000000* _. ~8 Z4 e/ o6 ]4 G4 T( v
2 3.000000 0.000000# h+ ^4 N( {7 s( K3 M/ b5 A
3 1.000000 0.000000
, ?% n2 q6 @( k" W7 z 4 0.000000 0.000000
2 T2 t K; E( D V, w 5 0.000000 0.000000
: |1 C5 h/ Q! F$ u. } 6 0.000000 0.000000# r+ ?9 M! @3 g- m7 D+ {# r
7 0.000000 0.000000
9 L; S2 i$ x3 m4 _/ }4 ]/ F 8 0.000000 0.000000
e) s F% h% `4 C. v$ B1 Y 9 0.000000 0.000000
- _5 z7 _' z+ t3 [2 y* s2 e由此得出,两个产地的坐标分别为B1(3.137191,6.211140),! |0 i1 `, F/ \& K) Y" V V( z
B2(7.250000,7.750000)
3 ^& e: l( d- K& w
& n4 O) h* s# v8 ]0 E 1# lss_and_ymm |
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