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The INTPOINT Procedure

Example 5.4: Using Constraints and More Alteration to Arc Data

Suppose the 25-inch screen TVs produced at factory 1 in May can be sold at either shop with an increased profit of 40 dollars each. What is the new optimal solution? 

   title2 'Using Constraints and Altering arc data';
   data new_arc4;
      set arc4;
         oldcost=_cost_;
         oldflow=_flow_;
         oldfc=_fcost_;
         if _tail_='f1_may_2' 
            & (_head_='shop1_2' | _head_='shop2_2')
            then _cost_=_cost_-40;
   
   proc intpoint
      bytes=1000000 
      printlevel2=2
      arcdata=new_arc4 nodedata=node0
      condata=con3 sparsecondata rhsobs='CHIP/BO LIMIT'
      conout=arc5;
   run;
   proc print data=arc5 (drop = _status_ _rcost_);
      var _tail_ _head_ _cost_ _capac_ _lo_ 
          _supply_ _demand_ _name_ 
          _flow_ _fcost_ oldflow oldfc;
             /* to get this variable order */
      sum oldfc _fcost_;
   run;

The following messages appear on the SAS log: 

   NOTE: Number of nodes= 20 .
   NOTE: Number of supply nodes= 4 .
   NOTE: Number of demand nodes= 4 .
   NOTE: Total supply= 4350 , total demand= 4150 .
   NOTE: Number of arcs= 64 .
   NOTE: Number of <= side constraints= 5 .
   NOTE: Number of == side constraints= 0 .
   NOTE: Number of >= side constraints= 0 .
   NOTE: Number of side constraint coefficients= 16 .
   NOTE: The following messages relate to the equivalent 
         Linear Program solved by the Interior Point algorithm.
   NOTE: Number of <= constraints= 5 .
   NOTE: Number of == constraints= 21 .
   NOTE: Number of >= constraints= 0 .
   NOTE: Number of constraint coefficients= 152 .
   NOTE: Number of variables= 68 .
   NOTE: 5 columns, 0 rows and 5 coefficients were added to the problem to 
         handle unrestricted variables, variables that are 
         split, and constraint slack or surplus variables.
   NOTE: There are 82 nonzero elements in A * A transpose.
   NOTE: Of the 26 rows and columns, 14 are sparse.
   NOTE: There are 80 nonzero superdiagonal elements in the sparse rows of the 
         factored A * A transpose. This includes fill-in.
   NOTE: There are 68 operations of the form u[i,j]=u[i,j]-u[q,j]*u[q,i]/u[q,q] 
         to factorize the sparse rows of A * A transpose.
Iter Complem_aff Complem-ity  Duality_gap Tot_infeasb  Tot_infeasc Tot_infeasd
   0   -1.000000   176072547     0.833846       52835        40217       46430
   1    49323199    21763015     0.910646 2971.887954  2262.182150 2506.228441
   2     4256602     1419262     0.526045           0 6.291145E-11   51.536868
   3      371793      247491     0.159553           0            0    8.939364
   4      119362       60394     0.043112           0            0    1.565229
   5       27925       21537     0.015622           0            0    0.576834
   6       10494 6617.424035     0.004839           0            0    0.124639
   7 3367.128699 1357.529806     0.000996           0            0    0.001406
   8  498.362201  156.077166     0.000115           0            0    0.000163
   9   28.159576    1.000647  0.000000735           0            0           0
  10    0.000549 0.000050153 -8.10256E-11           0            0           0
   NOTE: Primal-Dual Predictor-Corrector Interior point algorithm performed 10 iterations.
   NOTE: Objective = -1295661.8.
   NOTE: The data set WORK.ARC5 has 64 observations and 17 variables.
   NOTE: There were 64 observations read from the data set WORK.NEW_ARC4.
   NOTE: There were 8 observations read from the data set WORK.NODE0.
   NOTE: There were 21 observations read from the data set WORK.CON3.
   NOTE: The data set WORK.ARC5 has 64 observations and 17 variables.

Output 5.4.1: CONOUT=ARC5
 
Using Constraints and Altering arc data

Obs _tail_ _head_ _cost_ _capac_ _lo_ _SUPPLY_ _DEMAND_ _name_ _FLOW_ _FCOST_ oldflow oldfc
1 fact1_1 f1_apr_1 78.60 600 50 1000 . prod f1 19 apl 533.333 41920.00 533.333 41920.00
2 f1_mar_1 f1_apr_1 15.00 50 0 . .   0.000 0.00 0.000 0.00
3 f1_may_1 f1_apr_1 33.60 20 0 . . back f1 19 may 0.000 0.00 0.000 0.00
4 f2_apr_1 f1_apr_1 11.00 40 0 . .   0.000 0.00 0.000 0.00
5 fact1_2 f1_apr_2 174.50 550 50 1000 . prod f1 25 apl 250.000 43625.00 250.000 43625.00
6 f1_mar_2 f1_apr_2 20.00 40 0 . .   0.000 0.00 0.000 0.00
7 f1_may_2 f1_apr_2 49.20 15 0 . . back f1 25 may 0.000 0.00 0.000 0.00
8 f2_apr_2 f1_apr_2 21.00 25 0 . .   0.000 0.00 0.000 0.00
9 fact1_1 f1_mar_1 127.90 500 50 1000 . prod f1 19 mar 333.333 42633.33 333.333 42633.33
10 f1_apr_1 f1_mar_1 33.60 20 0 . . back f1 19 apl 20.000 672.00 20.000 672.00
11 f2_mar_1 f1_mar_1 10.00 40 0 . .   40.000 400.00 40.000 400.00
12 fact1_2 f1_mar_2 217.90 400 40 1000 . prod f1 25 mar 400.000 87160.00 400.000 87160.00
13 f1_apr_2 f1_mar_2 38.40 30 0 . . back f1 25 apl 30.000 1152.00 30.000 1152.00
14 f2_mar_2 f1_mar_2 20.00 25 0 . .   25.000 500.00 25.000 500.00
15 fact1_1 f1_may_1 90.10 400 50 1000 .   128.333 11562.83 128.333 11562.83
16 f1_apr_1 f1_may_1 12.00 50 0 . .   0.000 0.00 0.000 0.00
17 f2_may_1 f1_may_1 13.00 40 0 . .   0.000 0.00 0.000 0.00
18 fact1_2 f1_may_2 113.30 350 40 1000 .   350.000 39655.00 350.000 39655.00
19 f1_apr_2 f1_may_2 18.00 40 0 . .   0.000 0.00 0.000 0.00
20 f2_may_2 f1_may_2 13.00 25 0 . .   0.000 0.00 0.000 0.00
21 f1_apr_1 f2_apr_1 11.00 99999999 0 . .   13.333 146.67 13.333 146.67
22 fact2_1 f2_apr_1 62.40 480 35 850 . prod f2 19 apl 480.000 29952.00 480.000 29952.00
23 f2_mar_1 f2_apr_1 18.00 30 0 . .   0.000 0.00 0.000 0.00
24 f2_may_1 f2_apr_1 30.00 15 0 . . back f2 19 may 0.000 0.00 0.000 0.00
25 f1_apr_2 f2_apr_2 23.00 99999999 0 . .   0.000 0.00 0.000 0.00
26 fact2_2 f2_apr_2 196.70 680 35 1500 . prod f2 25 apl 550.000 108185.00 577.500 113594.25
27 f2_mar_2 f2_apr_2 28.00 50 0 . .   0.000 0.00 0.000 0.00
28 f2_may_2 f2_apr_2 64.80 15 0 . . back f2 25 may 0.000 0.00 0.000 0.00
29 f1_mar_1 f2_mar_1 11.00 99999999 0 . .   0.000 0.00 0.000 0.00
30 fact2_1 f2_mar_1 88.00 450 35 850 . prod f2 19 mar 290.000 25520.00 290.000 25520.00
31 f2_apr_1 f2_mar_1 20.40 15 0 . . back f2 19 apl 0.000 0.00 0.000 0.00
32 f1_mar_2 f2_mar_2 23.00 99999999 0 . .   0.000 0.00 0.000 0.00
33 fact2_2 f2_mar_2 182.00 650 35 1500 . prod f2 25 mar 650.000 118300.00 650.000 118300.00
34 f2_apr_2 f2_mar_2 37.20 15 0 . . back f2 25 apl 0.000 0.00 0.000 0.00
35 f1_may_1 f2_may_1 16.00 99999999 0 . .   115.000 1840.00 115.000 1840.00
36 fact2_1 f2_may_1 128.80 250 35 850 .   35.000 4508.00 35.000 4508.00
37 f2_apr_1 f2_may_1 20.00 30 0 . .   0.000 0.00 0.000 0.00
38 f1_may_2 f2_may_2 26.00 99999999 0 . .   0.000 0.00 350.000 9100.00
39 fact2_2 f2_may_2 181.40 550 35 1500 .   150.000 27210.00 122.500 22221.50
40 f2_apr_2 f2_may_2 38.00 50 0 . .   0.000 0.00 0.000 0.00
41 f1_mar_1 shop1_1 -327.65 250 0 . 900   143.333 -46963.17 143.333 -46963.17
42 f1_apr_1 shop1_1 -300.00 250 0 . 900   250.000 -75000.00 250.000 -75000.00
43 f1_may_1 shop1_1 -285.00 250 0 . 900   13.333 -3800.00 13.333 -3800.00
44 f2_mar_1 shop1_1 -297.40 250 0 . 900   250.000 -74350.00 250.000 -74350.00
45 f2_apr_1 shop1_1 -290.00 250 0 . 900   243.333 -70566.67 243.333 -70566.67
46 f2_may_1 shop1_1 -292.00 250 0 . 900   0.000 0.00 0.000 0.00
47 f1_mar_2 shop1_2 -559.76 99999999 0 . 900   0.000 0.00 0.000 0.00
48 f1_apr_2 shop1_2 -524.28 99999999 0 . 900   0.000 0.00 0.000 0.00
49 f1_may_2 shop1_2 -515.02 99999999 0 . 900   350.000 -180257.00 0.000 0.00
50 f2_mar_2 shop1_2 -567.83 500 0 . 900   500.000 -283915.00 500.000 -283915.00
51 f2_apr_2 shop1_2 -542.19 500 0 . 900   50.000 -27109.50 400.000 -216876.00
52 f2_may_2 shop1_2 -491.56 500 0 . 900   0.000 0.00 0.000 0.00
53 f1_mar_1 shop2_1 -362.74 250 0 . 900   250.000 -90685.00 250.000 -90685.00
54 f1_apr_1 shop2_1 -300.00 250 0 . 900   250.000 -75000.00 250.000 -75000.00
55 f1_may_1 shop2_1 -245.00 250 0 . 900   0.000 0.00 0.000 0.00
56 f2_mar_1 shop2_1 -272.70 250 0 . 900   0.000 0.00 0.000 0.00
57 f2_apr_1 shop2_1 -312.00 250 0 . 900   250.000 -78000.00 250.000 -78000.00
58 f2_may_1 shop2_1 -299.00 250 0 . 900   150.000 -44850.00 150.000 -44850.00
59 f1_mar_2 shop2_2 -623.89 99999999 0 . 1450   455.000 -283869.95 455.000 -283869.95
60 f1_apr_2 shop2_2 -549.68 99999999 0 . 1450   220.000 -120929.60 220.000 -120929.60
61 f1_may_2 shop2_2 -500.00 99999999 0 . 1450   0.000 0.00 0.000 0.00
62 f2_mar_2 shop2_2 -542.83 500 0 . 1450   125.000 -67853.75 125.000 -67853.75
63 f2_apr_2 shop2_2 -559.19 500 0 . 1450   500.000 -279595.00 177.500 -99256.23
64 f2_may_2 shop2_2 -519.06 500 0 . 1450   150.000 -77859.00 472.500 -245255.85
                    -1295661.80   -1282708.63

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