Uncapacitated Lot Sizing with Backlogging: The Convex Hull

Simge Kucukyavuz (simgesie.arizona.edu)
Yves Pochet (pochetcore.ucl.ac.be)

Abstract: An explicit description of the convex hull of solutions to the uncapacitated lot-sizing problem with backlogging, in its natural space of production, setup, inventory and backlogging variables, has been an open question for many years. In this paper, we identify facet-defining inequalities that subsume all previously known valid inequalities for this problem. We show that theses inequalities are enough to describe the convex hull of solutions. We give polynomial separation algorithms for some special cases. Finally, we report a summary of computational experiments with our inequalities that illustrates their effectiveness.

Keywords: Lot-sizing, backlogging, facets, separation algorithms, computation

Category 1: Applications -- OR and Management Sciences

Category 2: Integer Programming (Cutting Plane Approaches )

Category 3: Combinatorial Optimization (Polyhedra )

Citation: CORE Discussion Paper, 2007/6

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Entry Submitted: 06/09/2006
Entry Accepted: 06/12/2006
Entry Last Modified: 02/21/2007

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