A study of the lot-sizing polytope

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.