Progressive selection method for the coupled lot-sizing and cutting-stock problem

Tao Wu, Kerem Akartunali, Raf Jans, Zhe Liang

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)
61 Downloads (Pure)


The coupled lot-sizing and cutting-stock problem has been a challenging and significant problem for industry, and has therefore received sustained research attention. The quality of the solution is a major determinant of cost performance in related production and inventory management systems, and therefore there is intense pressure to develop effective practical solutions. In the literature, a number of heuristics have been proposed for solving the problem. However, the heuristics are limited in obtaining high solution qualities. This paper proposes a new progressive selection algorithm that hybridizes heuristic search and extended reformulation into a single framework. The method has the advantage of generating a strong bound using the extended reformulation, which can provide good guidelines on partitioning and sampling in the heuristic search procedure so as to ensure an efficient solution process. We also analyze per-item and per-period Dantzig-Wolfe decompositions of the problem and present theoretical comparisons. The master problem of the per-period Dantzig-Wolfe decomposition is often degenerate, which results in a tailing-off effect for column generation. We apply a hybridization of Lagrangian relaxation and stabilization techniques to improve the convergence. The discussion is followed by extensive computational tests, where we also perform detailed statistical analyses on various parameters. Comparisons with other methods indicate that our approach is computationally tractable and is able to obtain improved results.
Original languageEnglish
Pages (from-to)523-543
Number of pages11
JournalINFORMS Journal on Computing
Issue number3
Early online date11 Jul 2017
Publication statusPublished - 30 Jul 2017


  • operational research
  • lot sizing
  • integer programming
  • cutting stock
  • heuristics
  • column generation


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