OR Spectrum

, Volume 32, Issue 2, pp 231–261 | Cite as

Dynamic capacitated lot-sizing problems: a classification and review of solution approaches

  • Lisbeth Buschkühl
  • Florian Sahling
  • Stefan Helber
  • Horst Tempelmeier
Regular Article


This paper presents a review of four decades of research on dynamic lot-sizing with capacity constraints. We discuss both different modeling approaches to the optimization problems and different algorithmic solution approaches. The focus is on research that separates the lot-sizing problem from the detailed sequencing and scheduling problem. Our conceptional point of reference is the multi-level capacitated lot-sizing problem (MLCLSP). We show how different streams of research emerged over time. One result is that many practically important problems are still far from being solved in the sense that they could routinely be solved close to optimality in industrial practice. Our review also shows that currently mathematical programing and the use of metaheuristics are particularly popular among researchers in a vivid and flourishing field of research.


Dynamic capacitated lot-sizing MLCLSP CLSP CLSPL Mathematical programing Lagrangian relaxation Decomposition Metaheuristics Greedy heuristics 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Lisbeth Buschkühl
    • 1
  • Florian Sahling
    • 2
  • Stefan Helber
    • 2
  • Horst Tempelmeier
    • 1
  1. 1.Seminar für Supply Chain Management und ProduktionUniversität zu KölnCologneGermany
  2. 2.Institut für ProduktionswirtschaftLeibniz Universität HannoverHannoverGermany

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