The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts

Zbigniew Michna , Stephen Disney , Peter Nielsen


We quantify the bullwhip effect (which measures how the variance of replenishment orders is ampli- fied as the orders move up the supply chain) when both random demands and random lead times are estimated using the industrially popular moving average forecasting method. We assume that the lead times constitute a sequence of independent identically distributed random variables and the correlated demands are described by a first-order autoregressive process. We obtain an expression that reveals the impact of demand and lead time forecasting on the bullwhip effect. We draw a number of conclusions on the bullwhip behaviour with respect to the demand auto-correlation and the number of past lead times and demands used in the forecasts. We find maxima and minima in the bullwhip measure as a function of the demand auto-correlation.
Author Zbigniew Michna (BM / DoL)
Zbigniew Michna,,
- Department of Logistics
, Stephen Disney - Cardiff Business School [Cardiff University]
Stephen Disney,,
, Peter Nielsen - Aalborg University
Peter Nielsen,,
Journal seriesOmega-International Journal of Management Science, [Omega], ISSN 0305-0483, (N/A 140 pkt)
Issue year2020
Publication size in sheets0.5
ASJC Classification1408 Strategy and Management; 1802 Information Systems and Management; 1803 Management Science and Operations Research
Languageen angielski
Michna_Z_Disney_S_M_Nielsen_P_the_impact_of_stochastic_2020.pdf 1,29 MB
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Michna_Z_The_impact_of_stochastic_Inpress.docx 15,05 KB
Score (nominal)140
Score sourcejournalList
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2017 = 2.805; WoS Impact Factor: 2018 = 5.341 (2) - 2018=6.318 (5)
Citation count*7 (2020-11-25)
Additional fields
UwagaThe first author acknowledges support by the National Science Centre grant 2012/07/B/HS4/00702
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.