An algorithm to perform a complete parametric analysis relative to the constraint matrix for a 0–1-integer linear program

We designed and implemented an algorithm to solve the parametric 0–1-integer linear programming (ILP) problem relative to the constraint matrix; that is, to solve a family of 0–1-ILP problems in which the problems are related by having identical objective and right-hand-side vectors. Our algorithm works by choosing an appropriate finite sequence of non-parametric 0–1-mixed integer linear programming (MILP) problems in order to obtain a complete parametric analysis. The algorithm may be implemented by using any software capable of solving MILP problems.