TY - JOUR

T1 - The impact of temporal aggregation on supply chains with ARMA(1,1) demand processes

AU - Rostami-Tabar, Bahman

AU - Babai, M. Zied

AU - Ali, Mohammad

AU - Boylan, John E.

N1 - 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, 2018 DOI: 10.1016/j.ejor.2018.09.010

PY - 2019/3/16

Y1 - 2019/3/16

N2 - 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.

AB - 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.

KW - Forecasting

KW - Temporal aggregation

KW - Forecast accuracy

KW - Mean Square Error

KW - Bullwhip effect

KW - MMSE forecasting method

U2 - 10.1016/j.ejor.2018.09.010

DO - 10.1016/j.ejor.2018.09.010

M3 - Journal article

VL - 273

SP - 920

EP - 932

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 3

ER -