A mixed-integer programming formulation for the general capacitated lot-sizing problem

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A new mixed-integer programming (MIP) formulation is presented for the production planning of single-stage multi-product processes. The problem is formulated as a multi-item capacitated lot-sizing problem in which (a) multiple items can be produced in each planning period, (b) sequence-independent set-ups can carry over from previous periods, (c) set-ups can cross over planning period boundaries, and (d) set-ups can be longer than one period. The formulation is extended to model time periods of non-uniform length, idle time, parallel units, families of products, backlogged demand, and lost sales.

Original languageEnglish (US)
Pages (from-to)244-259
Number of pages16
JournalComputers and Chemical Engineering
Issue number1-2
StatePublished - Jan 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Chemical Engineering
  • Computer Science Applications


  • Mixed-integer programming
  • Multi-item capacitated lot sizing
  • Production planning
  • Set-up carry over
  • Set-up cross over


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