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Vanishing Discount Approach Versus Stationary Distribution Approach

  • Dirk Beyer
  • Feng Cheng
  • Suresh P. Sethi
  • Michael Taksar
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 108)

Abstract

In Part III, we derived the structure of the optimal policy to minimize the long-run average cost by using the vanishing discount method. In the classical inventory literature, a stationary distribution approach is often used to minimize the long-run average cost. In this approach, the stationary distribution of the inventory levels is obtained for a specific class of policies, the best policy in this class is found, and then it is proven that this policy is average optimal. In this chapter, we review the stationary distribution approach in solving the simpler problem of an inventory model with i.i.d demands, and then show how the results of this analysis relate to those obtained by the vanishing discount approach.

Keywords

Inventory Model Markov Decision Process Average Cost Demand Distribution Renewal Function 
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Copyright information

© Springer-Verlag US 2010

Authors and Affiliations

  • Dirk Beyer
    • 1
  • Feng Cheng
    • 2
  • Suresh P. Sethi
    • 3
  • Michael Taksar
    • 4
  1. 1.M-FactorSan MateoUSA
  2. 2.Federal Aviation AdministrationOffice of Performance Analysis and StrategyWashingtonUSA
  3. 3.School of Management, M/S SM30The University of Texas at DallasRichardsonUSA
  4. 4.Department of MathematicsUniversity of MissouriColumbiaUSA

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