On inventory problems with arbitrary cost pattern, demand pattern and demand distribution

Abstract

A detailed analysis of inventory models without setup costs, arbitrary demand distribution and arbitrary demand and cost pattern is given. First it is shown that the corresponding one-period model without ordering costs may be reduced to another simpler one with appropriately modified demand distribution. Several representations are given for the modified demand distribution. As one of the main results this reduction turns out to be robust in most cases. In a final chapter the results are applied to the determination of an optimal policy for a class of N-period inventory models with convex holding-and shortage costs and without setup costs.