The feasibility version of the market split problem

Here, it is possible to experiment with the market split problem. For a definition of the market split problem see [1].

First, we generate an instance of the problem.

• Please, select a value of m.

• Then a m x 10(m-1) matrix M and a vector b of length m is randomly generated.

• The entries of M are integers between 0 and 99. The i-th entry of b is the sum of the corresponding row of M, divided by 2 and rounded to next integer value.

• Now, the market split problem is: Does a 0/1-vector x exist such that
  M * x = b ?

Literature:
[1] G. Cornuejols and Milind Dawande: A class of hard small 0-1 programs.
In R.~E. Bixby, E.A. Boyd, and R.Z. Rios-Mercado, editors, Integer Programming and Combinatorial Optimization. 6th International IPCO Conference, Houston, Texas, June 1998. Springer Lecture Notes in Computer Science 1412, Heidelberg, 1998.