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Aggregation Of Uncertainty And Multivariate Dependence: The Value Of Pooling Of Inventories Under Non-Normal Dependent Demand

  • Author(s): Corbett, Charles J.
  • Rajaram, Kumar
  • et al.
Abstract

In this paper we apply emerging theories in probability and statistics to examine the value of pooling of inventories under arbitrary non-normal dependent demand structures. Eppen (1979) showed that inventory costs in a centralized system increase with the correlation between multivariate normal product demands; using multivariate stochastic orders, we generalize this statement to arbitrary distributions. We then describe methods to construct models with arbitrary dependence structure, using the copula of a multivariate distribution to capture the dependence between the components of a random vector. For broad classes of distributions with arbitrary marginals, we confirm that pooling of inventories is more valuable when demands are less positively dependent.

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