Local cuts and two-period convex hull closures for big-bucket lot-sizing problems

Akartunali, Kerem and Fragkos, Ioannis and Miller, Andrew J. and Wu, Tao (2016) Local cuts and two-period convex hull closures for big-bucket lot-sizing problems. INFORMS Journal on Computing, 28 (4). pp. 766-780. ISSN 1526-5528 (https://doi.org/10.1287/ijoc.2016.0712)

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Despite the significant attention they have drawn, big bucket lot-sizing problems remain notoriously difficult to solve. Previous work of Akartunali and Miller (2012) presented results (computational and theoretical) indicating that what makes these problems difficult are the embedded single-machine, single-level, multi-period submodels. We therefore consider the simplest such submodel, a multi-item, two-period capacitated relaxation. We propose a methodology that can approximate the convex hulls of all such possible relaxations by generating violated valid inequalities. To generate such inequalities, we separate two-period projections of fractional LP solutions from the convex hulls of the two-period closure we study. The convex hull representation of the two-period closure is generated dynamically using column generation. Contrary to regular column generation, our method is an outer approximation, and therefore can be used efficiently in a regular branch-and-bound procedure. We present computational results that illustrate how these two-period models could be effective in solving complicated problems.