Linear-programming extended formulations for the single-item lot-sizing problem with backlogging and constant capacity

Authors:
Mathieu Van Vyve
Affiliations:
Center of Operations Research and Econometrics (CORE), Université catholique de Louvain. 34, voie du Roman Pays, 1348, Louvain-la-Neuve, Belgium
Venue:
Mathematical Programming: Series A and B
Year:
2006

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Abstract

Recently, several authors [8, 10] have argued for the use of extended formulations to tighten production planning models. In this work we present two linear-programming extended formulations of the constant-capacity lot-sizing problem with backlogging. The first one applies to the problem with a general cost function and has O(n3) variables and constraints. This improves on the more straightforward O(n4) Florian and Klein [2] type formulation. The second one applies when the costs satisfy the Wagner-Whitin property but it has O(n2) variables and O(n3) constraints. As a by-product, we positively answer an open question of Miller and Wolsey [4] about the tightness of an extended formulation for the continuous mixing set.