On the decomposition property for a dynamic inventory rationing problem with multiple demand classes and backorder

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Original languageEnglish
Pages (from-to)99-106
Journal / PublicationEuropean Journal of Operational Research
Issue number1
Online published8 Jul 2017
Publication statusPublished - 16 Feb 2018


In this paper, we study a dynamic inventory rationing problem of a single item with multiple demand classes and backorder. Demand classes are differentiated by their unit backlogging costs. The corresponding dynamic programming problem is multidimensional and computationally challenging. With a novel state transformation, we find that the optimal policy can be described by a nested base stock policy. In particular, we can decompose the value function as the sum of single-variable convex functions. This property breaks the curse of dimensionality and significantly reduces computational effort in computing optimal policies. Our approach allows us to extend the results to systems with ordering, exogenous supply, priority upgrading.

Research Area(s)

  • (T) Inventory, Decomposability, Multiple demand classes, Rationing

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