%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/LPnetlib/lp_dfl001
% name: LPnetlib/lp_dfl001
% [Netlib LP problem dfl001: minimize c'*x, where Ax=b, lo<=x<=hi]
% id: 619
% date: 1990
% author: M. Meketon
% ed: D. Gay
% fields: title name A b id aux kind date author ed notes
% aux: c lo hi z0
% kind: linear programming problem
%-------------------------------------------------------------------------------
% notes:
% A Netlib LP problem, in lp/data.  For more information                    
% send email to netlib@ornl.gov with the message:                           
%                                                                           
% 	 send index from lp                                                      
% 	 send readme from lp/data                                                
%                                                                           
% The following are relevant excerpts from lp/data/readme (by David M. Gay):
%                                                                           
% The column and nonzero counts in the PROBLEM SUMMARY TABLE below exclude  
% slack and surplus columns and the right-hand side vector, but include     
% the cost row.  We have omitted other free rows and all but the first      
% right-hand side vector, as noted below.  The byte count is for the        
% MPS compressed file; it includes a newline character at the end of each   
% line.  These files start with a blank initial line intended to prevent    
% mail programs from discarding any of the data.  The BR column indicates   
% whether a problem has bounds or ranges:  B stands for "has bounds", R     
% for "has ranges".  The BOUND-TYPE TABLE below shows the bound types       
% present in those problems that have bounds.                               
%                                                                           
%                        PROBLEM SUMMARY TABLE                              
%                                                                           
% Name       Rows   Cols   Nonzeros    Bytes  BR      Optimal Value         
% DFL001     6072  12230    41873     353192  B     1.12664E+07 **          
%                                                                           
%         BOUND-TYPE TABLE                                                  
% DFL001     UP                                                             
%                                                                           
% Submitted by Marc Meketon.                                                
%                                                                           
% DFL001, says Marc Meketon, "is a 'real-world' airline schedule planning   
% (fleet assignment) problem.  This LP was preprocessed by a modified       
% version of the KORBX(r) System preprocessor.  The problem reduced in      
% size (rows, columns, non-zeros) significantly.  The row and columns were  
% randomly sorted and renamed, and a fixed adjustment to the objective      
% function was eliminated.  The name of the problem is derived from the     
% initials of the person who created it."                                   
%                                                                           
% Bob Bixby reports that the CPLEX solver (running on a Sparc station)      
% finds slightly different optimal values for some of the problems.         
% On a MIPS processor, MINOS version 5.3 (with crash and scaling of         
% December 1989) also finds different optimal values for some of the        
% problems.  The following table shows the values that differ from those    
% shown above.  (Whether CPLEX finds different values on the recently       
% added problems remains to be seen.)                                       
%                                                                           
% Problem        CPLEX(Sparc)          MINOS(MIPS)                          
% DFL001       1.1266396047E+07            **                               
%                                                                           
% David Gay reports:                                                        
% ** On an IEEE-arithmetic machine (an SGI 4D/380S), I (dmg) succeeded in   
% getting MINOS 5.3 to report optimal objective values, 1.1261702419E+07    
% and 1.1249281428E+07, for DFL001 only by starting with LOAD files         
% derived from the solution obtained on the same machine by Bob             
% Vanderbei's ALPO (an interior-point code); starting from one of the       
% resulting "optimal" bases, MINOS ran 23914 iterations on a VAX before     
% reporting an optimal value of 1.1253287141E+07.  When started from the    
% same LOAD file used on the SGI machine, MINOS on the VAX reported an      
% optimal value of 1.1255107696E+07.  Changing the FEASIBILITY TOLERANCE    
% to 1.E-10 (from its default of 1.E-6) led MINOS on the SGI machine to     
% report "optimal" values of 1.1266408461E+07 and 1.1266402835E+07.  This   
% clearly is a problem where the FEASIBILITY TOLERANCE, initial basis, and  
% floating-point arithmetic strongly affect the "optimal" solution that     
% MINOS reports.  On the SGI machine, ALPO with SPLIT 3 found               
%  primal:  obj value =  1.126639607e+07      FEASIBLE   ( 2.79e-09 )       
%  dual:    obj value =  1.126639604e+07      FEASIBLE   ( 1.39e-16 )       
%                                                                           
% Bob Bixby reports the following about his experience solving DFL001       
% with CPLEX:                                                               
%   First, the value for the objective function that I get running          
%   defaults is 1.1266396047e+07, with the following residuals:             
%                                                                           
%   Max. unscaled (scaled) bound        infeas.: 4.61853e-14 (2.30926e-14)  
%   Max. unscaled (scaled) reduced-cost infeas.: 6.40748e-08 (6.40748e-08)  
%   Max. unscaled (scaled) Ax-b          resid.: 4.28546e-14 (4.28546e-14)  
%   Max. unscaled (scaled) c_B-B'pi      resid.: 8.00937e-08 (8.00937e-08)  
%                                                                           
%   The L_infinity condition number of the (scaled) optimal basis is        
%   213737.  I got exactly the same objective value solving the problem in  
%   several different ways.  I played a bit trying to get a better          
%   reduced-cost infeasibility, but that seems hopeless (if not pointless)  
%   given the c-Bpi residuals.                                              
%                                                                           
%   Just as an aside, this problem exhibits very interesting behavior when  
%   solved using a simplex method.  I ran reduced-cost pricing on it in     
%   phase I, with the result that it took 465810 iterations to get          
%   feasible.  Running the default CPLEX pricing scheme, the entire         
%   problem solved in 94337 iterations (33059 in phase I) on a              
%   Sparcstation.  Steepest-edge pricing (and a different scaling) took     
%   25803 iterations.  This is a nasty problem.                             
%                                                                           
%                                                                           
% Added to Netlib on  11 Oct. 1990                                          
% 9 Jan. 1991: Bixby's remarks about DFL001 added to lp/data/readme.        
%                                                                           
%-------------------------------------------------------------------------------
