© 1999 by Institute of Mathematics and its Applications
Bayesian decision-making in inventory modelling
School of Mathematical Sciences, University of Exeter Exeter EX4 4QE, UK
The objective of this paper is to advocate the use of Bayesian methods in tackling decision problems with limited past data. It is assumed that a Bayesian approach is least likely to be successful when there is no information on which to base a meaningful prior. Here we use a limiting, invariant, form of the conjugate prior distribution to represent this ignorance. The results of decisions based on Bayesian methods with this ‘non-informative’ prior are compared with those which result from deriving a point estimate for the unknown parameter. The particular context considered here is that of a single-period inventory model with compound Poisson demand made up of a known demand size distribution but an unknown demand rate. The demand rate is assumed to be high enough for a normal approximation to the compound Poisson distribution to be used, in which case it is possible to analyse the behaviour directly. An extension to the multi-period model with zero lead time is considered briefly. The results lend support to the use of Bayesian methods, with or without a meaningful prior, for which the analysis and computation are no more complex than those required by standard methods.
Keywords: Inventory; newsboy problem; compound Poisson demand; Bayesian decision-making