The following table summarizes the solutions for the problems found here.  Each problem id links to a page where you can download individual files associated with that problem.  Follow this link to download all compressed folders each containing a set partitioning problem presented in several forms.  The folder also contains the cplex log file associated with the .lp form of the problem.  Column n is the number of original variables whose value is between 1 and max_coef, while m is the number of rows and also the number of appended variables to guarantee feasibility (their objective coefficient is 2*max_coef).  Therefore, the total number of variables in the set partitioning problem is n + m. 

As noted, the Penalty is 100 for all problems, however, if you want to change this penalty or create your own problems to solve and send the results to me, here is a link to my set partitioning problem generator.  Although you can run it by clicking on the link, you should probably save it to your computer (it should not crash, or destroy anything).  After saving it, simply double-click, answer the questions, and the files will be stored in the directory where you saved the generator. 

Problem id n m n+m col
density
max
coef
random seed Penalty CPLEX value CPLEX time to given value
(sec)
MIP Gap %
1 500 100 600 10% 10 0 100 511 4 70%
2 500 100 600 50% 10 0 100 768 33 optimal
3 500 100 600 90% 10 0 100 61 10 optimal
4 500 250 750 10% 10 0 100 2905 5 84%
5 500 250 750 50% 10 0 100 1968 218 optimal
6 500 250 750 90% 10 0 100 224 60 optimal
7 500 500 1000 10% 10 0 100 7073 64000 74%
8 500 500 1000 50% 10 0 100 4344 784 optimal
9 500 500 1000 90% 10 0 100 628 225 optimal