Parametric Integer Programming Analysis: A Contraction Approach

An algorithm is presented for solving families of integer linear programming problems in which the problems are “related” by having identical objective coefficients and constraint matrix coefficients. The righthand-side constants have the form b + θd where b and d are conformable vectors and θ varies from zero to one. The approach consists primarily of solving the most relaxed problem (θ=1) using cutting planes and then contracting the region of feasible integer solutions in such a manner that the current optimal integer solution is eliminated. The algorithm was applied to 1800 integer linear programming problems with reasonable success. Integer programming problems which have proved to be unsolvable using cutting planes have been solved by expanding the region of feasible integer solutions (θ=1) and then contracting to the original region