On modeling multiple choice requirements for simple mixed integer programming solvers

This note introduces the Special Ordered Inequalities (SOI) as a new technique for integer programming modeling of multiple choice requirements and piecewise linear functions. The standard modeling technique based on the use of Special Ordered Set (SOS) structure requries a branch and bound solver to be armed with the special tools for SOS processing. Otherwise, the standard branching rule applied on individual SOS variables may lead to enormously long computation process thus making impossible to solve quite small problems in a reasonable time. The proposed SOI modeling technique allows us to eliminate the necessity of the special branching rule for handling SOS structure. The standard branching on individual variables of SOI is equivalent to the special SOS branching. Thus the proposed modeling technique seems to be very attractive for users of simple mixed integer programming solvers as well as for those who want to build solver independent mathematical programming models.