VRP问题的lingo程序（多旅行商问题）

王冰清

taowenbao

很好的喔~~~~~~~~~~

jiaqing

付钱了。

问安少年

muqian...................

一只想死的鱼

这个模型不是很清晰吧，你应该把模型写出来，可供参考的。表面上看很普通的程序，而多旅行商和VRP有区别的，你这里的约束也不够。。。太少了

yinfeng0814

看看楼主的程序，学习学习

yinfeng0814

5个体力点对新人来说太贵了啊

liyunan220

我下载了 去哪里找啊

liyunan220

MODEL:

! The Vehicle Routing Problem (VRP);
/ z! N% n. b8 f7 [- G0 V
( }2 M, T9 C3 l# r, r9 @!************************************;
! WARNING: Runtimes for this model   ;
- \" H3 r! E; [' {5 y! increase dramatically as the number;
! of cities increase. Formulations   ;
! with more than a dozen cities      ;
! WILL NOT SOLVE in a reasonable     ;
: Q, K+ J) _9 O1 E/ {) D! amount of time!                    ;
!************************************;

SETS:
  ! Q(I) is the amount required at city I,
1 h, Y+ P9 @4 m1 B2 j4 m    U(I) is the accumulated delivers at city I ;
   CITY/1..8/: Q, U;
- m2 Y+ y3 w' {& N
' l. J1 R$ m8 u3 ~  ! DIST(I,J) is the distance from city I to city J
/ |3 P9 w: `& h. r) n    X(I,J) is 0-1 variable: It is 1 if some vehicle
, h8 h. B5 X* I    travels from city I to J, 0 if none;
   CXC( CITY, CITY): DIST, X;
ENDSETS

# X& @4 {8 u  ^6 P/ o& C DATA:
- e9 |# {; C) }+ _3 C" n  ! city 1 represent the common depo;
( R+ `, A/ v1 I; D  ^/ _   Q  =  0    6    3    7    7   18    4    5;
' [# c3 O8 _# C" u( t8 u. P
- Q; U) Y6 C7 p/ s: y0 e+ w  ! distance from city I to city J is same from city
3 k: p" u/ G& x! X% S% u$ H    J to city I distance from city I to the depot is
    0, since the vehicle has to return to the depot;

; p) M1 Y+ h# w# Z$ o. b7 g. I8 i   DIST =  ! To City;
  ! Chi  Den Frsn Hous   KC   LA Oakl Anah   From;
      0  996 2162 1067  499 2054 2134 2050!Chicago;
      0    0 1167 1019  596 1059 1227 1055!Denver;
# D: ]' x1 v$ o8 n2 A      0 1167    0 1747 1723  214  168  250!Fresno;
      0 1019 1747    0  710 1538 1904 1528!Houston;
8 U) E: X' a- P! w2 H      0  596 1723  710    0 1589 1827 1579!K. City;
( \. N( o+ p3 |4 r9 Z4 }2 B      0 1059  214 1538 1589    0  371   36!L. A.;
+ f9 j  {. _7 F1 j      0 1227  168 1904 1827  371    0  407!Oakland;
% V' W4 l4 x. R0 `' T* m; a' h      0 1055  250 1528 1579   36  407    0;!Anaheim;
1 M7 B+ }" O- k9 q
  ! VCAP is the capacity of a vehicle ;
% x8 O4 ]( Z, w1 R   VCAP = 18;
ENDDATA
+ v* M7 s. V! `) U) w% S
( a: ]8 I: y) {  U  ! Minimize total travel distance;
   MIN = @SUM( CXC: DIST * X);

  ! For each city, except depot....;
   @FOR( CITY( K)| K #GT# 1:
( G- h  ?! e2 G/ W( y: R: c9 U' {
( G5 s! t' X( S5 N! Q  A+ Y" i  ! a vehicle does not travel inside itself,...;
     X( K, K) = 0;

  ! a vehicle must enter it,... ;
     @SUM( CITY( I)| I #NE# K #AND# ( I #EQ# 1 #OR#
9 w0 U: \2 R# Q- |$ Q. \, M      Q( I) + Q( K) #LE# VCAP): X( I, K)) = 1;
3 M% H0 {* n& b- }
. D9 {3 U6 {1 W) t) b0 g+ v/ E9 g" v2 e  ! a vehicle must leave it after service ;
     @SUM( CITY( J)| J #NE# K #AND# ( J #EQ# 1 #OR#
      Q( J) + Q( K) #LE# VCAP): X( K, J)) = 1;

  ! U( K) is at least amount needed at K but can't
    exceed capacity;
* n) j- `7 ^4 O1 Y* Z- D     @BND( Q( K), U( K), VCAP);

  ! If K follows I, then can bound U( K) - U( I);
8 v; g5 g* {. |; B0 a  N     @FOR( CITY( I)| I #NE# K #AND# I #NE# 1:
      U( K) >= U( I) + Q( K) - VCAP + VCAP *
, m( e1 y; a( }# X5 C       ( X( K, I) + X( I, K)) - ( Q( K) + Q( I))
        * X( K, I);
     );
4 Y4 A; n9 [  B) i" D  ?# d# t
# d$ X  G; ]0 K$ b  ! If K is 1st stop, then U( K) = Q( K);
) W  C. p/ i* A     U( K) <= VCAP - ( VCAP - Q( K)) * X( 1, K);
& g  v; Z6 E0 S- h6 M6 M$ ^
  ! If K is not 1st stop...;
     U( K)>= Q( K)+ @SUM( CITY( I)|
      I #GT# 1: Q( I) * X( I, K));
   );
6 a" v1 w& P2 }) C! [
' c: v! L' A. @& R9 T: i  ! Make the X's binary;
   @FOR( CXC: @BIN( X));

  ! Minimum no. vehicles required, fractional
: B' x* L1 R% `: N: t    and rounded;
   VEHCLF = @SUM( CITY( I)| I #GT# 1: Q( I))/ VCAP;
   VEHCLR = VEHCLF + 1.999 -
$ j/ N, {5 u9 t+ u9 j/ a    @WRAP( VEHCLF - .001, 1);
  z5 Y) W& D+ w* l7 d! s
  ! Must send enough vehicles out of depot;
   @SUM( CITY( J)| J #GT# 1: X( 1, J)) >= VEHCLR;
7 {$ a9 H' [' E' o9 i END
) x8 ]! J, u  y# _1 H, W 请问大家里面U(I)的公式如何理解啊 U(I)是城市I 的累积交付量么？谢谢