Deriving Inventory-Control Policies for Periodic Review with Genetic Programming

  • Peer Kleinau
  • Ulrich W. Thonemann
Part of the Operations Research Proceedings book series (ORP, volume 2003)


In Germany alone, inventories are estimated to be worth of more than 500 billion €. To manage these inventories, numerous inventory-control policies have been developed in the last decades. These inventory-control policies are typically derived analytically, which is often complicated and time consuming. For many relevant settings, such as complex multi-echelon models, there exist no closed-form formulae to describe the optimal solution. Optimal solutions for those problems are determined by complex algorithms that require several iteration steps. In this paper, we present an alternative approach to derive optimal or near-optimal inventory-control policies that are based on Genetic Programming (GP). GP is an algorithm related to Genetic Algorithms. It applies the principles of natural evolution to solve optimization problems. In this paper, we show how closed-form heuristics for a common inventory-control setting with periodic review can be found with GP. The advantage of GP is that inventory-control policies can be derived empirically without solving complex mathematical models.


Inventory Genetic Programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arrow, K.A., Harris, T.E., Marschak, T. 1951. Optimal inventory Policy. Econometrica 19, 250–272.CrossRefGoogle Scholar
  2. 2.
    Hadley, G., Whitin, T. 1963. Analysis of Inventory Systems. Englewood Cliffs, NY, Prentice-Hall.Google Scholar
  3. 3.
    Harris, F. W. 1915. Operations and Costs. Factory Management Series, Chicago.Google Scholar
  4. 4.
    Koza, J. R. 1992. Genetic Programming — On the programming of computers by means of natural selection. MIT Press, Cambridge.Google Scholar
  5. 5.
    Koza, J. R., Bennett, F. H., Andre, D., Keane, M. A. 1999. Genetic Programming III — Darwinian Invention and Problem Solving. Kaufmann, San Francisco.Google Scholar
  6. 6.
    Rao, U. S. 2003. Properties of the Periodic Review (R,T) Inventory Control Policy for Stationary. Stochastic Demand, Manufacturing & Service Operations Management 5(1), 37–53.CrossRefGoogle Scholar
  7. 7.
    Tempelmeier, H. 2003. Material-Logistik: Modelle für die Produktionsplanung und-Steuerung und das Supply Chain Management. Springer, Berlin.Google Scholar
  8. 8.
    Zipkin, P. H. 2000. Foundations of inventory management. McGraw-Hill, Boston.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Peer Kleinau
    • 1
  • Ulrich W. Thonemann
    • 1
  1. 1.Münster UniversityGermany

Personalised recommendations