Performance of approximations for compound Poisson distributed demand in the newsboy problem

Abstract

This paper considers the classical single period inventory model. The number of customer orders during the period follows a known Poisson distribution and individual customer order sizes are independent random variables. Two costs are incurred: a cost per unit of unsatisfied demand and a cost per unit of stock purchased. The objective is to minimise the expected sum of these two costs. A customer order which cannot be met in full is met to the extent that available stock permits. Although the sizes of all customer orders are known at the time only regularly updated estimates of the first two moments of the customer order size distribution are maintained. Therefore, aggregate demand follows a compound Poisson distribution for which the moments are known but for which the exact distribution is unknown. The immediate objective of this research is to explore the effectiveness of a number of approaches for approximating a compound Poisson distribution in a single period setting. The longer-term objective is to find relatively simple but effective ways of handling a compound Poisson demand process in more general inventory settings.