Matrix: LPnetlib/lp_lotfi

Description: Netlib LP problem lotfi: minimize c'*x, where Ax=b, lo<=x<=hi

LPnetlib/lp_lotfi graph
(bipartite graph drawing)

LPnetlib/lp_lotfi dmperm of LPnetlib/lp_lotfi

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  • download as a MATLAB mat-file, file size: 5 KB. Use UFget(641) or UFget('LPnetlib/lp_lotfi') in MATLAB.
  • download in Matrix Market format, file size: 6 KB.
  • download in Rutherford/Boeing format, file size: 5 KB.

    Matrix properties
    number of rows153
    number of columns366
    structural full rank?yes
    structural rank153
    # of blocks from dmperm9
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorV. Lofti
    editorD. Gay
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 153-by-1
    cfull 366-by-1
    lofull 366-by-1
    hifull 366-by-1
    z0full 1-by-1


    A Netlib LP problem, in lp/data.  For more information                    
    send email to 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 optimal value is from MINOS version 5.3 (of Sept. 1988)               
    running on a VAX with default options.                                    
                           PROBLEM SUMMARY TABLE                              
    Name       Rows   Cols   Nonzeros    Bytes  BR      Optimal Value         
    LOTFI       154    308     1086       6718       -2.5264706062E+01        
    From Vahid Lotfi.                                                         
    When included in Netlib: cost coefficients negated.                       
    LOTFI, says Vahid Lotfi, "involves audit staff scheduling.  This problem  
    is semi real world and we have used it in a study, the results of which   
    are to appear in Decision Sciences (Fall 1990).  The detailed             
    description of the problem is also in the paper.  The problem is          
    actually an MOLP with seven objectives, the first is maximization and     
    the other six are minimization.  The version that I am sending has the    
    aggregated objective (i.e., z1-z2-z3-z4-z5-z6-z7)."                       
    Added to Netlib on 27 June 1989                                           

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD9,210
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD1,900

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    LPnetlib/lp_lotfi svd

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.