The lot-sizing polytope is a fundamental structure contained in many practical production planning problems. Here we study this polytope and identify facet-defining inequalities that cut off all fractional extreme points of its linear programming relaxation, as well as liftings from those facets. We give a polynomial-time combinatorial separation algorithm for the inequalities when capacities are constant. We also report on an extensive computational study on solving the lot-sizing problem for instances up to 365 time periods with varying cost and capacity characteristics.
Mathematical Programming 99, 443-465, 2004.