The application of valid inequalities to the multi-stage lot-sizing problem

A capacitated multi-stage lot-sizing problem for general production structures with setup and lead times is considered. The problem is formulated as a mixed integer linear program and valid inequalities that are high dimension faces of the problem’s convex hull are identified. A fast separation algorithm is developed to iteratively select those inequalities that cut off the solution of the linear programming relaxation. The resulting much improved lower bounds are used in a Branch-and-Bound algorithm. Computational test results are presented.