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

Holger A. Stephan, Timo Gschwind, Stefan Minner

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.

Original languageEnglish
Pages (from-to)143-162
Number of pages20
JournalFlexible Services and Manufacturing Journal
Issue number3-4
StatePublished - Dec 2010
Externally publishedYes


  • Capacity planning
  • Markov demand model
  • Multi-stage stochastic programming


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