Lagrangean decomposition for integer programming : theory and applications

Abstract

Given a mixed-integer programming problem whose constraint set is the intersection of several specially structured constraint sets, it is possible to induce decomposition in the Lagrangean relaxation problems artificially by introducing copies of the original variables for a subset of constraints and dualizing the equivalence conditions between the original variables and the copies. Duality is studied for Lagrangean decomposition and compared with conventional Lagrangean duality. The implications of Lagrangean decomposition can be quite profound for integer programming problems containing special classes of constraints such as subtour elimination constraints or matching inequalities. Several application problems exemplify the use of Lagrangean decomposition