Hierarchical estimation as a basis for hierarchical forecasting

In inventory management, hierarchical forecasting (HF) is a hot issue: families of items are formed for which total demand is forecasted; total forecast then is broken up to produce forecasts for the individual items. Since HF is a complicated procedure, analytical results are hard to obtain; consequently, most literature is based on simulations and case studies. This paper succeeds in following a more theoretical approach by simplifying the problem: we consider estimation instead of forecasting. So, from a random sample we estimate both the total demand and the fraction of this total that individual items take; multiplying these two quantities gives a new estimate of the individual demand. Then, our research question is: Can aggregation of items, followed by fractioning, lead to more accurate estimates of individual demand? We consider two simple situations that can be analysed fully theoretically. Thirdly, a more practical situation is investigated by means of simulation.