Inventory Control Under Parametric Uncertainty of Underlying Models

  • Nicholas A. Nechval
  • Konstantin N. Nechval
  • Maris Purgailis
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 229)

Abstract

A large number of problems in inventory control, production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty of underlying models. In the present paper we consider the case, where it is known that the underlying distribution belongs to a parametric family of distributions. The problem of determining an optimal decision rule in the absence of complete information about the underlying distribution, i.e., when we specify only the functional form of the distribution and leave some or all of its parameters unspecified, is seen to be a standard problem of statistical estimation. Unfortunately, the classical theory of statistical estimation has little to offer in general type of situation of loss function. In the paper, for improvement or optimization of statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a performance index is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rules, which have smaller risk than any of the well-known decision rules. A numerical example is given.

Keywords

Demand Distribution Inventory Model Optimization Risk Uncertainty 

Notes

Acknowledgments

This research was supported in part by Grant No. 06.1936, Grant No. 07.2036, Grant No. 09.1014, and Grant No. 09.1544 from the Latvian Council of Science and the National Institute of Mathematics and Informatics of Latvia.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Nicholas A. Nechval
    • 1
  • Konstantin N. Nechval
    • 2
  • Maris Purgailis
    • 3
  1. 1.Department of Statistics, EVF Research InstituteUniversity of LatviaRigaLatvia
  2. 2.Department of Applied MathematicsTransport and Telecommunication InstituteRigaLatvia
  3. 3.Department of CyberneticsUniversity of LatviaRigaLatvia

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