OR Spectrum

, Volume 31, Issue 2, pp 385–404 | Cite as

A heuristic for the dynamic multi-level capacitated lotsizing problem with linked lotsizes for general product structures

Regular Article


In this paper, a new model formulation for the dynamic multi-level capacitated lotsizing problem with linked lotsizes is introduced. Linked lotsizes means that the model formulation correctly accounts for setup carryovers between adjacent periods if production of a product is continued in the next period. This model formulation is a good compromise between the big-bucket and small-bucket model formulation in that it inherits the stability of a big-bucket model and at least partially includes the precise description of setup operations provided by a small-bucket model. A Lagrangean heuristic is developed and tested in a numerical experiment with a set of invented data and a data set taken from industry. The solutions found show a good quality.


Lotsizing Multi-level Setup carry-over 


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  1. Billington PJ, McClain JO and Thomas LJ (1983). Mathematical programming approaches to capacity-constrained mrp systems: review, formulation and problem reduction. Manage Sci 29(10): 1126–1141 CrossRefGoogle Scholar
  2. Billington PJ, McClain JO and Thomas LJ (1986). Heuristics for multilevel lot-sizing with a bottleneck. Manage Sci 32(8): 989–1006 CrossRefGoogle Scholar
  3. Briskorn D (2006). A note on capacitated lot sizing with setup carry over. IIE Trans 38: 1045–1047 CrossRefGoogle Scholar
  4. Derstroff MC (1995). Mehrstufige Losgrößenplanung mit Kapazitätsbeschränkungen. Produktion und Logistik. Physica-Verlag, Heidelberg Google Scholar
  5. Drexl A and Kimms A (1997). Lot sizing and scheduling - survey and extensions. Eur J Oper Res 99(2): 221–235 CrossRefGoogle Scholar
  6. Haase K (1994). Lotsizing and scheduling for production planning. Springer, Berlin Google Scholar
  7. Haase K (1998) Capacitated lot-sizing with linked production quantities of adjacent periods. In: Drexl A, Kimms A (eds.) Beyond manufacturing resource planning (MRP II) – advanced models and methods for production planning. Springer, Berlin pp 127–146Google Scholar
  8. Jans R, Degraeve Z (2004) Meta-heuristics for dynamic lot sizing: a review and comparison of solution approaches. ERIM Report Series Research in Management pp 1–38Google Scholar
  9. Karimi B, Ghomi SMTF and Wilson JM (2003). The capacitated lot sizing problem: a review of models and algorithms. Omega 31: 365–378 CrossRefGoogle Scholar
  10. Meyr H (1999). Simultane Losgrößen- und Reihenfolgeplanung für kontinuierliche Produktionslnien. Gabler Edition Wissenschaft: Produktion und Logistik. Gabler, Wiesbaden Google Scholar
  11. Salomon M (1991). Deterministic lotsizing for production planning, Band 355 of lecture notes in economics and mathematical systems. Springer, Berlin Google Scholar
  12. Sox CR and Gao Y (1999). The capacitated lot sizing problem with setup carry-over. IIE Trans 31: 173–181 Google Scholar
  13. Sürie C (2005). Time continuity in discrete time models. Springer, Berlin Google Scholar
  14. Staggemeier AT, Clark AR (2001) A survey of lot-sizing and scheduling models. In: 23rd annual symposium of the brazilian operational research society (SOBRAPO). Campos do Jordao SP, Brazil, pp 938–947Google Scholar
  15. Tempelmeier H and Derstroff M (1996). A lagrangean-based heuristic for dynamic multilevel multi-item constrained lotsizing with setup times. Manag Sci 42(5): 739–757 CrossRefGoogle Scholar
  16. Wagner HM and Whitin TM (1958). Dynamic version of the economic lot size model. Manag Sci 5(1): 89–96 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Seminar für Supply Chain Management und ProduktionUniversität zu KölnCologneGermany

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