Improved Linear Integer Programming Formulations of Nonlinear Integer Problems*

A variety of combinatorial problems (e.g., in capital budgeting, scheduling, allocation) can be expressed as a linear integer programming problem. However, the standard devices for doing this often produce an inordinate number of variables and constraints, putting the problem beyond the practical reach of available integer programming methods. This paper presents new formulation techniques for capturing the essential nonlinearities of the problem of interest, while producing a significantly smaller problem size than the standard techniques.