Solving market split problems with heuristical lattice reduction.

The market sharing problem was proposed by M. Dawande and G. Cornuéjols (INFORMS J. Comput. 11, ) to compare the performance of linear integer programming algorithms. Haibo Wang (Manuscript No. 251, Annuals of Operations Research, ) examined some hard instances of these problems and reported the results he obtained with the commercially available program CPLEX. This paper first describes a model, which allows to embed integer programs with inequalities into a lattice and then reports the progress with Wang's instances, by using a lattice based algorithm which employs a new heuristical sieving procedure. These results are compared to recent CPLEX 12.0 benchmarks. [ABSTRACT FROM AUTHOR]