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Example 2.4: 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; 
       run; 
  
    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; 
       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 Programming problem 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: After preprocessing, number of <= constraints= 5. 
    NOTE: After preprocessing, number of == constraints= 20. 
    NOTE: After preprocessing, number of >= constraints= 0. 
    NOTE: The preprocessor eliminated 1 constraints from the 
          problem. 
    NOTE: The preprocessor eliminated 9 constraint coefficients 
          from the problem. 
    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 74 nonzero elements in A * A transpose. 
    NOTE: Of the 25 rows and columns, 14 are sparse. 
    NOTE: There are 74 nonzero superdiagonal elements in the 
          sparse rows of the factored A * A transpose. This 
          includes fill-in. 
    NOTE: There are 65 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   178045680     0.833846       52835        39643       49592 
    1    51679271    22114244     0.911781 2979.752508  2235.802470 2678.044487 
    2     4360227     1397064     0.521965           0 2.084022E-11   46.964760 
    3      337615      239843     0.155358           0            0    8.067907 
    4      119497       59613     0.042674           0            0    1.263035 
    5       30689       20758     0.015076           0            0    0.430638 
    6 9107.182114 7099.343072     0.005192           0            0    0.109413 
    7 3406.632390 1496.513249     0.001098           0            0    0.003935 
    8  616.222707  155.883444     0.000114           0            0    0.000480 
    9   23.880446    1.372116  0.000001007           0            0           0 
   10    0.000755 0.000068819 -4.28512E-10           0            0           0 
    NOTE: The 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.