Group-theoretic method of decomposition methods in integer linear programming (Q1802604)

A decomposition method for the solution of block linear integer programming problems with connecting constraints, which are of the form of equations on a finite Abelian group is suggested. In this method the solution of the input problem is reduced to solving some problems on subgroups having smaller orders. The above method is used for obtaining lower bounds in a branch and bound method for solving block linear integer programming problems. The determination of the lower bounds is based on constructing special auxiliary problems. These problems are block linear integer programming problems with connecting constraints of the above type. In the result a new decomposition method based on a group theoretic approach is obtained for solving block linear integer programs.