钢管切割问题

qlb061

  x

KoWuDa

1. MODEL:
   
2. ! Uses Lingo's programming capability to do
   
3.   on-the-fly column generation for a
   
4.   cutting-stock problem;
   
5. SETS:
   
6.   PATTERN: COST, X;
   
7.   FG: WIDTH, DEM, PRICE, Y, YIELD;
   
8.   FXP( FG, PATTERN): NBR;
   
9. ENDSETS
   
10. 
    
11. DATA:
    
12.   PATTERN = 1..10; ! Allow up to 20 patterns;
    
13.   RMWIDTH = 6000;    ! Raw material width;
    
14.   FG =  F4  F6  F8 F9 F10;!Finished goods...;
    
15.   WIDTH= 1816 916 616 439 602;!their widths...;
    
16.   DEM = 1000 600 200 250 500;!and demands;
    
17.   BIGM = 999;
    
18. ENDDATA
    
19. 
    
20. SUBMODEL MASTER_PROB:
    
21.   [MSTROBJ] MIN= @SUM( PATTERN( J)| J #LE# NPATS:
    
22.    COST( J)*X( J));
    
23.   @FOR( FG( I):
    
24.    [R_DEM]
    
25.     @SUM( PATTERN( J)| J #LE# NPATS:
    
26.      NBR( I, J) * X( J)) >= DEM( I);
    
27.   );
    
28. ENDSUBMODEL
    
29. 
    
30. SUBMODEL INTEGER_REQ:
    
31.   @FOR( PATTERN: @GIN( X));
    
32. ENDSUBMODEL
    
33. 
    
34. SUBMODEL PATTERN_GEN:
    
35.   [SUBOBJ] MAX = @SUM( FG( I): PRICE( I)* Y( I));
    
36.   @SUM( FG( I): WIDTH( I)*Y( I)) <= RMWIDTH;
    
37.   @FOR( FG( I): @GIN(Y( I)));
    
38. ENDSUBMODEL
    
39. 
    
40. CALC:
    
41. 
    
42.   ! Set parameters;
    
43.   @SET( 'DEFAULT');
    
44.   @SET( 'TERSEO', 2); ! Turn off default output;
    
45. 
    
46.   ! Max number of patterns we'll allow;
    
47.   MXPATS = @SIZE( PATTERN);
    
48.   ! Make first pattern an expensive super pattern;
    
49.   COST( 1) = BIGM;
    
50.   @FOR( FG( I): NBR( I, 1) = 1);
    
51. 
    
52.   ! Loop as long as the reduced cost is
    
53.     attractive and there is space;
    
54.   NPATS = 1;
    
55.   RC = -1;   ! Clearly attractive initially;
    
56.   @WHILE( RC #LT# 0 #AND# NPATS #LT# MXPATS:
    
57.     ! Solve for best patterns to run among ones
    
58.        generated so far;
    
59.     @SOLVE( MASTER_PROB);
    
60.     ! Copy dual prices to PATTERN_GEN submodel;
    
61.     @FOR( FG( I): PRICE( I) = -@DUAL( R_DEM( I)));
    
62.     ! Generate the current most attractive pattern;
    
63.     @SOLVE( PATTERN_GEN);
    
64.     ! Marginal value of current best pattern;
    
65.     RC = 1 - SUBOBJ;
    
66.     ! Add the pattern to the Master if it is attractive;
    
67.     @IFC( RC #LT# 0:
    
68.        NPATS = NPATS + 1;
    
69.        @FOR( FG( I): NBR( I, NPATS) = Y( I));
    
70.        COST( NPATS) = 1;
    
71.         );
    
72.   );
    
73. 
    
74.   ! Finally solve Master as an IP;
    
75.   @SOLVE( MASTER_PROB, INTEGER_REQ);
    
76. 
    
77. ENDCALC
    
78. 
    
79. ! This following calc section displays the
    
80.   solution in a tabular format;
    
81. CALC:
    
82.   ! Compute yield of each FG;
    
83.   @FOR( FG( F): YIELD( F) =
    
84.    @SUM( PATTERN( J)| J #LE# NPATS:
    
85.     NBR( F, J) * X(J))
    
86.   );
    
87.   ! Compute some stats;
    
88.   TOTAL_FT_USED = @SUM( PATTERN( I) | I #LE# NPATS: X( I)) * RMWIDTH;
    
89.   TOTAL_FT_YIELD = @SUM( FG( I) | I #LE# NPATS: YIELD( I) * WIDTH( I));
    
90.   PERC_WASTE =  100 * ( 1 - ( TOTAL_FT_YIELD / TOTAL_FT_USED)) ;
    
91. ! Display the table of patterns and their usage;
    
92.   FW = 6;
    
93.   @WRITE( @NEWLINE( 1));
    
94.   @WRITE( ' Total raws used:    ', @SUM(PATTERN( I) | I #LE# NPATS: X( I)) , @NEWLINE( 2),
    
95.           ' Total feet yield:   ', TOTAL_FT_YIELD , @NEWLINE( 1),
    
96.           ' Total feet used:    ', TOTAL_FT_USED , @NEWLINE( 2),
    
97.           ' Percent waste:    ', @FORMAT( PERC_WASTE, '#5.2G'), '%', @NEWLINE( 1));
    
98.   @WRITE( @NEWLINE( 1), 24*' ', 'Pattern:', @NEWLINE( 1));
    
99.   @WRITE( '   FG  Demand Yield');
    
100.   @FOR( PATTERN( I) | I #LE# NPATS: @WRITE( @FORMAT( I, '6.6G')));
     
101.   @WRITE( @NEWLINE( 1));
     
102.   @WRITE( ' ',FW*( NPATS+3)*'=', @NEWLINE( 1));
     
103.   @FOR( FG( F):
     
104.     @WRITE((FW - @STRLEN( FG( F)))*' ', FG( F), ' ',
     
105.       @FORMAT( DEM( F), '6.6G'), @FORMAT( YIELD( F), '6.6G'));
     
106.     @FOR( FXP( F, P) | P #LE# NPATS:
     
107.       @WRITE( @IF( NBR( F, P) #GT# 0,
     
108.       @FORMAT( NBR( F, P), "6.6G"), '     .')));
     
109.     @WRITE( @NEWLINE( 1))
     
110.   );
     
111.   @WRITE( ' ',FW*( NPATS+3)*'=', @NEWLINE( 1));
     
112.   @WRITE( 2*FW*' ', ' Usage:');
     
113.   @WRITEFOR( PATTERN( P) | P#LE# NPATS: @FORMAT( X( P), '6.6G'));
     
114.   @WRITE( @NEWLINE( 1));
     
115. ENDCALC
     
116. END

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请问如果有十种长度,可以切六种规格,那个六在哪改呢