A study of the lot-sizing polytope

Authors:
Alper Atamtürk;Juan Carlos Muñoz
Affiliations:
University of California, Department of Industrial Engineering and Operations Research, USA;University of California, Department of Civil and Environmental Engineering, USA Currently in Pontificia Universidad Católica de Chile.
Venue:
Mathematical Programming: Series A and B
Year:
2004

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Abstract

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 computational experiments on solving the lot–sizing problem with varying cost and capacity characteristics.