The impact of temporal aggregation on supply chains with ARMA(1,1) demand processes

Bahman Rostami-Tabar, M.Z. Babai, Mohammad Ali, John Boylan

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
85 Downloads (Pure)


Various approaches have been considered in the literature to improve demand forecasting in supply chains. Among these approaches, non-overlapping temporal aggregation has been shown to be an effective approach that can improve forecast accuracy. However, the benefit of this approach has been shown only under single exponential smoothing (when it is a non-optimal method) and no theoretical analysis has been conducted to look at the impact of this approach under optimal forecasting. This paper aims to bridge this gap by analysing the impact of temporal aggregation on supply chain demand and orders when optimal forecasting is used. To do so, we consider a two-stage supply chain (e.g. a retailer and a manufacturer) where the retailer faces an autoregressive moving average demand process of order (1,1) -ARMA(1,1)- that is forecasted by using the optimal Minimum Mean Squared Error (MMSE) forecasting method. We derive the analytical expressions of the mean squared forecast error (MSE) at the retailer and the manufacturer levels as well as the bullwhip ratio when the aggregation approach is used. We numerically show that, although the aggregation approach leads to an accuracy loss at the retailer's level, it may result in a reduction of the MSE at the manufacturer level up to 90% and a reduction of the bullwhip effect in the supply chain that can reach up to 84% for high lead-times.
Original languageEnglish
Pages (from-to)920-932
Number of pages13
JournalEuropean Journal of Operational Research
Issue number3
Early online date11 Sep 2018
Publication statusPublished - 16 Mar 2019

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in[European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, [273], [3], (2017)] DOI: 10.1016/j.ejor.2018.09.010

© 2017, Elsevier. Licensed under the Creative Commons AttributionNonCommercial-NoDerivatives 4.0 International


  • Forecasting
  • Temporal aggregation
  • Forecast accuracy
  • Bullwhip effect
  • MMSE forecasting method


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