## LPnetlib/lp_lotfi

Netlib LP problem lotfi: minimize c'*x, where Ax=b, lo<=x<=hi
Name lp_lotfi LPnetlib 641 153 366 1,136 1,136 Linear Programming Problem No 1989 V. Lofti D. Gay
Structural Rank 153 true 9 1 0 0% 0% no no real
SVD Statistics
Matrix Norm 1.275023e+03
Minimum Singular Value 1.920182e-03
Condition Number 6.640116e+05
Rank 153
sprank(A)-rank(A) 0
Null Space Dimension 0
Full Numerical Rank? yes
Download ```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 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```