Reduction of State Space in Dynamic Programming with Integrated Forecasting

  • Dieter Bartmann


In many decision problems such as inventory control, cash management or production smoothing the uncertainty of demand is a central feature. The standard assumption is that demand in different periods is independently and identically distributed. But this assumption is rarely valid in practice, in particular when forecasts of demands are being made. If planning covers more than one period then all calculations are influenced by expectations regarding future data. This in turn requires an anticipation of future movements of the underlying demand process. Commercial suppliers of software handle this problem in a three stage approach: lotsize (or cash shipment or production rate), security reserves and forecast. By this separation into three parts, the solution obtained is only suboptimal.




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bartmann, D.: Dynamische Optimierung mit Prognose. Habilitationsschrift, TU München, 1983.Google Scholar
  2. Beckmann, M. J. : Production Smoothing and Invevtory Control. Operations Research 9 (1961) pp 453–467.CrossRefGoogle Scholar
  3. Bellman, R.: Dynamic Programming. Princeton University Press, Princeton N.J., 1957.Google Scholar
  4. Edgeworth, F.Y.: The Mathematical Theory of Banking. Journal of the Royal Statistic Society 51 (1888), pp. 120 ff.Google Scholar
  5. Johnson, G.D. & Thompson, H.E.: Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes. Management Science 21 (1975), pp. 1303–1307.CrossRefGoogle Scholar
  6. Lenz, H.-J.: Zeitreihenanalyse und Prognoseverfahren zur Optimierung der Kassenhaltung bei autokorrelierten Zahlungsprozessen. Berlin Verlag, Berlin, 1974.Google Scholar
  7. Schneider, H.: Servicegrad in Lagerhaltungsmodellen. Marchal und Matzenbacher, Berlin, 1979.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Dieter Bartmann
    • 1
  1. 1.Technische Universität MünchenMünchenGermany

Personalised recommendations