Flexible Services and Manufacturing Journal

, Volume 22, Issue 3–4, pp 143–162 | Cite as

Manufacturing capacity planning and the value of multi-stage stochastic programming under Markovian demand



Capacity planning is a crucial part of global manufacturing strategies in the automotive industry, especially in the presence of volatile markets with high demand uncertainty. Capacity adjustments in machining intensive areas, e.g. body shop, paint shop, or aggregate machining face lead times exceeding a year, making an elaborated decision support indispensable. In this regard, two-stage stochastic programming is a frequently used framework to support capacity and flexibility decisions under uncertainty. However, it does not anticipate future capacity adjustment opportunities in response to market demand developments. Motivated by empirical findings from the automotive industry, we develop a multi-stage stochastic dynamic programming approach where the evolution of demand is represented by a Markov demand model. An efficient multi-stage solution algorithm is proposed and the benefits compared to a rolling horizon application of a two-stage approach are illustrated for different generic manufacturing networks. Especially network structures with limited flexibility might significantly benefit from applying a multi-stage framework.


Capacity planning Multi-stage stochastic programming Markov demand model 



The authors gratefully acknowledge the comments of two anonymous referees that helped to improve the manuscript.


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Holger A. Stephan
    • 1
  • Timo Gschwind
    • 2
  • Stefan Minner
    • 3
  1. 1.Daimler AG, Production Network Planning TrucksStuttgartGermany
  2. 2.Chair of Logistics ManagementJohannes Gutenberg University MainzMainzGermany
  3. 3.Department of Business AdministrationUniversity of ViennaViennaAustria

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