A hybrid Benders approach for coordinated capacitated lot-sizing of multiple product families with set-up times

Bayley T., SÜRAL H., Bookbinder J. H.

INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH, vol.56, no.3, pp.1326-1344, 2018 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1080/00207543.2017.1338778
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1326-1344
  • Keywords: Benders decomposition, evolutionary algorithm, Lagrangian relaxation, mixed integer program, production planning, FORMULATIONS, HEURISTICS, ALGORITHM, MODEL


We examine a coordinated capacitated lot-sizing problem for multiple product families, where demand is deterministic and time-varying. The problem considers set-up and holding costs, where capacity constraints limit the number of individual item and family set-up times and the amount of production in each period. Using a strong reformulation and relaxing the demand constraints, we improve both the upper and lower bounds using a combination of Benders decomposition and an evolutionary algorithm, followed by subgradient optimisation. Through computational experiments, we show that our method consistently achieves better bounds, reducing the duality gap compared to other single-family methods studied in the literature.