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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9 V! W% D; g% }* F
" x+ T5 |) U2 i3 Q X4 @/ ~
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。
9 @. g. J; h; ^& R+ }$ D# [; T7 u! a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:6 C2 J( A0 _& n1 S4 Z
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;$ m1 g# i5 n- K# ]8 r4 L- a2 c/ y* s
x11+x12+x13+x14+x15+x16<=20;
7 q% S/ T% S* ix21+x22+x23+x24+x25+x26<=20;
! p2 s/ B) K6 s& D( D- e0 `x11+x21=3;; Z& g8 F5 o3 {4 o7 S
x12+x22=5;& d1 h" V* H1 ~4 M2 Y. H J
x13+x23=4;; M3 @. Z' _1 Z: w9 c* E
x14+x24=7;
i; T9 b) |0 O* z( G" U, }$ Y9 T4 h; r9 Ox15+x25=6;- L* p& F" X6 J0 B) T {" P% n1 c
x16+x26=11;
6 V+ H# @! R( q* M@gin(x11);" o+ D7 m( e+ w1 s7 A. U' s
@gin(x12);5 V) E& {0 T a [$ O* }
@gin(x13);
. ]! L, {7 l! X@gin(x14);3 C0 M4 D$ |+ M" k
@gin(x15);
$ E% h/ o9 g( G! [- S; c+ E" G L@gin(x16); K4 w& W( \& g7 o' ]2 s/ ]# O
@gin(x21);7 z5 X/ d9 J- @# y! Y! A
@gin(x22);: t; ]" T- b1 Q7 R
@gin(x23);/ f0 n5 `9 I) C0 d" v3 r# U6 L
@gin(x24);
- r7 Y- f- V: F. V6 e8 {@gin(x25);
- B( u1 n5 p6 s0 b$ R2 d/ s) ^- X@gin(x26);
7 U; r0 u* J; z) D( [3 k3 k下面是运行结果:
$ ~( Y, _7 ~6 ^5 _3 |8 y" QGlobal optimal solution found.
. E+ F. f4 m1 G Objective value: 136.2275
& J) T" Z1 W% G- c {+ u. O Objective bound: 136.2275
( G0 W( `( _- ~, b Infeasibilities: 0.0000009 b9 D8 w3 b( Q( S& A6 W# h
Extended solver steps: 0
: z+ l: f% S. V @% |5 ^, A; _/ A Total solver iterations: 0$ O) C! @" N2 l8 k5 u
1 q% s1 Z5 C& {- N$ f4 D" {7 K Variable Value Reduced Cost" r! v) K4 a j! ?$ }4 ?, K
X11 3.000000 3.758324
% [1 q5 O9 b4 C X12 5.000000 3.758324: P6 F* J6 k% d% S9 S* B4 n
X13 0.000000 5.857687
3 |3 v$ W6 {: ` X14 7.000000 4.069705
- R+ F! b. x p2 A% S, ~( p X15 0.000000 5.852350. k7 j- O% N- N; Y0 A0 H
X16 1.000000 7.115125
5 S0 S% f2 m; K- ?* T; s( F( U X21 0.000000 5.798808) ~/ j' r: E% o. \0 d
X22 0.000000 9.199185
5 y" J) \+ T/ F( M o9 m- Y X23 4.000000 2.704163% M- C5 {# e* f
X24 0.000000 4.250000' U9 u0 \" r# D; ]* A( o+ g7 L3 Q
X25 6.000000 1.118034
( h: v% J, J* T( N9 g- { |9 H X26 10.00000 5.303301
+ X* ]$ w, O2 }! M& ^' p Row Slack or Surplus Dual Price, k, c) Y7 f! X7 [! k
1 136.2275 -1.000000
2 J% g5 a: o/ m6 l# g* Q _ 2 4.000000 0.000000
- D% E( _) B. v( g2 w2 a/ E 3 0.000000 0.000000
$ }/ f$ \7 g- o- T 4 0.000000 0.000000
0 V" D$ f( s6 W0 e" [* r 5 0.000000 0.000000
9 O$ D1 ^2 l4 E+ \& l# [5 X 6 0.000000 0.000000# e1 h8 a7 q1 T$ w" Z* m: s: O4 g3 B
7 0.000000 0.000000
, C# N: ?! I2 K5 h$ e3 G 8 0.000000 0.000000 D8 Y$ {/ w- f; X' R
9 0.000000 0.000000) ^& k+ w% D R- K
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。
2 C& Y. H* m; i* s7 \- z第二问:
3 R1 T0 p' t @5 gmin=(@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;' E) {( N/ M# D8 t
x11+x12+x13+x14+x15+x16<=20;
" m( f5 f( @; C* X* M- ox21+x22+x23+x24+x25+x26<=20;
& {% |/ a/ [% C4 {( Yx11+x21=3;5 a2 N: j+ z8 ~& V/ D
x12+x22=5;
' A2 f) [' J9 V# w$ L. i( C$ bx13+x23=4;* c' A3 C; |; |! o/ N! i8 Q
x14+x24=7;
3 y; K5 L8 q. {x15+x25=6;* @/ j0 g. s9 L/ C
x16+x26=11;
+ C* r; k [( z5 C0 E@gin(x11);
- g; R9 T! z: v6 a+ x@gin(x12);
# C' m! T5 \; R# x@gin(x13);
0 t' w' y h3 L$ H! i@gin(x14);
( K# H' ~2 E1 W7 A% T+ _7 A@gin(x15);: t# V1 h7 K: y& q- Z
@gin(x16);6 k6 _8 _) e" X# V
@gin(x21);8 S0 G* N) O. |
@gin(x22);
# b, u8 l/ e! W9 H@gin(x23);
_6 b) b1 Y5 n@gin(x24);) D, K& g& Z6 D$ u5 _7 D4 h. K" V
@gin(x25);
9 H& [3 l; I* A, J2 q+ o! A@gin(x26);9 E, ?0 Q) Q7 @$ K2 U
结果:1 d. x' V: a! B' Q& H
Local optimal solution found.
' G8 f0 W. m f+ c2 ?: a Objective value: 93.35791
I, R* K" j( x5 ]- n( D% [7 U J& z Objective bound: 93.35791
0 A/ {$ ~3 v* W# ~1 E Infeasibilities: 0.000000
- N; }# u1 \# S5 G6 c Extended solver steps: 0
* _" r+ m- O" k5 y2 _' W. L Total solver iterations: 44# j, c$ f7 P7 O& N$ b
! G7 {' e& R4 M5 S Variable Value Reduced Cost/ u3 j5 j) ^8 E2 @( G. }
A1 3.137191 0.0000008 i2 q: {! E5 p2 B" f
B1 6.211140 0.000000
2 \. c& w: D* r% Y4 [, A2 d X11 0.000000 0.000000
F0 Q [( t1 F X12 0.000000 0.0000003 v" v' j9 X7 n0 A. u
X13 4.000000 0.000000/ a$ l! @; ~" x
X14 7.000000 0.000000
3 c5 a2 b- \0 U X15 6.000000 0.000000+ N, C9 d* l1 ?! N6 Y
X16 0.000000 0.000000
& R8 `: ^6 z; ^& i; E I) ~ A2 7.250000 6.618652
4 C$ Q" r, l6 G9 d/ w# _ B2 7.750000 -2.3557409 |* p, f2 W# }" h, t, m8 W
X21 3.000000 0.000000$ x& ~3 z. O+ y& c) p& C; g
X22 5.000000 0.000000+ C, i' q; J& x) C
X23 0.000000 0.000000
: ?0 S5 Y, B' j H, A X24 0.000000 0.000000
2 T' J& F8 p" H2 k X25 0.000000 0.000000
& l/ [. t; y3 ?& r/ A" I2 A X26 11.00000 0.000000
5 C6 T* R1 t; r" |5 Z9 f Row Slack or Surplus Dual Price& l7 v% r, y: W# | V+ e
1 93.35791 -1.000000$ H4 K" _1 a3 R- _8 H$ `- H
2 3.000000 0.0000003 c' S( A* Z0 A. N2 {/ x2 _' M5 W
3 1.000000 0.000000
/ X. J: D }* v8 S3 _! E% f 4 0.000000 0.000000
9 |5 g7 C I5 y" d+ L4 h5 u 5 0.000000 0.000000
4 |# F& i- C$ \- s7 [4 z5 } 6 0.000000 0.000000
9 ^( D o& m3 \! m) X9 O5 m4 c 7 0.000000 0.000000
7 x2 F5 x$ p0 ~) T3 I 8 0.000000 0.000000) K& r: g9 ]/ _% Z9 r( z
9 0.000000 0.000000
" ?7 H* g2 ~( c( m# {0 i" V由此得出,两个产地的坐标分别为B1(3.137191,6.211140),
$ O* I6 W0 j; ?' g, O8 i2 VB2(7.250000,7.750000)7 m- s4 N# B+ ]! @0 T' q* y
) T. Z3 Z3 g+ {$ n! D5 ^/ N0 n: K 1# lss_and_ymm |
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