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Example 4.2: Altering Arc Data

This example examines the effect of changing some of the arc costs. The back-order penalty costs are increased by 20 percent. The sales profit of 25-inch TVs sent to the shops in May is increased by 30 units. The backorder penalty costs of 25-inch TVs manufactured in May for April consumption is decreased by 30 units. The production cost of 19-inch and 25-inch TVs made in May are decreased by 5 units and 20 units, respectively. How does the optimal solution of the network after these arc cost alterations compare with the optimum of the original network?

These SAS statements produce the new NODEDATA= and ARCDATA= data sets:

   title2 'Minimum Cost Flow problem- Altered Arc Data';
   data arc2;
      set arc1;
         oldcost=_cost_;
         oldfc=_fcost_;
         oldflow=_flow_;
         if key_id='backorder'
            then _cost_=_cost_*1.2;
            else if _tail_='f2_may_2' then _cost_=_cost_-30;
         if key_id='production' & mth_made='May' then
            if diagonal=19 then _cost_=_cost_-5;
                           else _cost_=_cost_-20;
   proc intpoint
      bytes=100000
      printlevel2=2
      nodedata=node0
      arcdata=arc2
      conout=arc3;
   run;
   
   proc print data=arc3;
      var _tail_ _head_ _capac_ _lo_ _supply_ _demand_ _name_ 
          _cost_ _flow_ _fcost_ oldcost oldflow oldfc 
          diagonal factory key_id mth_made;
          /* to get this variable order */
              sum oldfc _fcost_;
   run;

   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: The following messages relate to the equivalent 
         Linear Program solved by the Interior Point algorithm.
   NOTE: Number of <= constraints= 0 .
   NOTE: Number of == constraints= 21 .
   NOTE: Number of >= constraints= 0 .
   NOTE: Number of constraint coefficients= 136 .
   NOTE: Number of variables= 68 .
   NOTE: 0 columns, 0 rows and 0 coefficients were added to the 
         problem to handle unrestricted variables, variables that are 
         split, and constraint slack or surplus variables.
   NOTE: There are 54 nonzero elements in A * A transpose.
   NOTE: Of the 21 rows and columns, 14 are sparse.
   NOTE: There are 59 nonzero superdiagonal elements in the sparse rows of 
         the factored A * A transpose. This includes fill-in.
   NOTE: There are 80 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   167898972     0.834344       52835        26238       35092
   1    35575010    17420416     0.911474 1664.001693   826.349461           0
   2     1969763      739523     0.369979           0 1.267542E-12           0
   3      373828      189905     0.127240           0            0           0
   4      117843       45042     0.032721           0            0           0
   5       26090       15668     0.011493           0            0           0
   6 8608.105391 2994.589912     0.002212           0            0           0
   7 1477.385197  411.268625     0.000304           0            0           0
   8  103.724839   24.733676  0.000018304           0            0           0
   9    2.140932    0.002805 2.0758339E-9           0            0           0
   NOTE: Primal-Dual Predictor-Corrector Interior point algorithm performed 9 iterations.
   NOTE: Objective = -1285086.45.
   NOTE: The data set WORK.ARC3 has 64 observations and 21 variables.
   NOTE: There were 64 observations read from the data set WORK.ARC2.
   NOTE: There were 8 observations read from the data set WORK.NODE0.
   NOTE: The data set WORK.ARC3 has 64 observations and 21 variables.

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