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IMA Journal of Management Mathematics Advance Access originally published online on December 1, 2007
IMA Journal of Management Mathematics 2008 19(2):193-205; doi:10.1093/imaman/dpm032
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© The authors 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Hierarchical estimation as a basis for hierarchical forecasting

L. W. G. Strijbosch{dagger}, R. M. J. Heuts and J. J. A. Moors

Department of Econometrics & Operations Research, Tilburg University, Warandelaan 2, PO Box 90153, 5000 LE Tilburg, The Netherlands

{dagger} Email: l.w.g.strijbosch{at}uvt.nl

Received on 6 November 2006. Accepted on 29 October 2007.

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.

Keywords: hierarchical forecasting; aggregation; top-down approach


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