Multiple machine continuous setup lotsizing with sequence-dependent setups

Bernardo Almada-Lobo*, Diego Klabjan, Maria Antónia Carravilla, José F. Oliveira

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


We address the short-term production planning and scheduling problem coming from the glass container industry. A furnace melts the glass that is distributed to a set of parallel molding machines. Both furnace and machine idleness are not allowed. The resulting multi-machine multi-item continuous setup lotsizing problem with a common resource has sequence-dependent setup times and costs. Production losses are penalized in the objective function since we deal with a capital intensive industry. We present two mixed integer programming formulations for this problem, which are reduced to a network flow type problem. The two formulations are improved by adding valid inequalities that lead to good lower bounds. We rely on a Lagrangian decomposition based heuristic for generating good feasible solutions. We report computational experiments for randomly generated instances and for real-life data on the aforementioned problem, as well as on a discrete lotsizing and scheduling version.

Original languageEnglish (US)
Pages (from-to)529-552
Number of pages24
JournalComputational Optimization and Applications
Issue number3
StatePublished - Nov 2010


  • Continuous setup lotsizing
  • Heuristics
  • Integer programming
  • Lagrangian decomposition
  • Sequence-dependent setup

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics


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