Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Robust compound Poisson parameter estimation for inventory control
AU - Prak, D.
AU - Teunter, R.
AU - Babai, M.Z.
AU - Boylan, J.E.
AU - Syntetos, A.
PY - 2021/10/31
Y1 - 2021/10/31
N2 - Most companies store demand data periodically and make periodic demand forecasts, whereas many demand processes in inventory control need parameter estimates at the individual customer level. Guidance on estimating the parameters of a continuous-time demand process from period demand data is lacking, in particular for the popular and well-studied compound Poisson class of demand. Whereas the statistics literature typically focuses on asymptotic properties, parameters for inventory control have to be estimated based on a limited number of periodic historical demand observations. We show that the standard Method-of-Moments (MM) estimator – the default choice in applied inventory control research – is severely biased for finite samples. The Maximum Likelihood (ML) estimator – which needs to be obtained by a numerical search – performs better, but both estimators lack robustness to misspecification of the demand size distribution. We propose an intuitive, consistent, closed-form MM alternative that dominates standard MM and ML in terms of estimation accuracy and on-target inventory performance. Its closed form does not depend on the specific demand size distribution, making it robust and easily applicable in large-scale applications with many items. In a case study, we find that the accuracy loss due to storing demand periodically is four times as high under standard MM as under the proposed estimator.
AB - Most companies store demand data periodically and make periodic demand forecasts, whereas many demand processes in inventory control need parameter estimates at the individual customer level. Guidance on estimating the parameters of a continuous-time demand process from period demand data is lacking, in particular for the popular and well-studied compound Poisson class of demand. Whereas the statistics literature typically focuses on asymptotic properties, parameters for inventory control have to be estimated based on a limited number of periodic historical demand observations. We show that the standard Method-of-Moments (MM) estimator – the default choice in applied inventory control research – is severely biased for finite samples. The Maximum Likelihood (ML) estimator – which needs to be obtained by a numerical search – performs better, but both estimators lack robustness to misspecification of the demand size distribution. We propose an intuitive, consistent, closed-form MM alternative that dominates standard MM and ML in terms of estimation accuracy and on-target inventory performance. Its closed form does not depend on the specific demand size distribution, making it robust and easily applicable in large-scale applications with many items. In a case study, we find that the accuracy loss due to storing demand periodically is four times as high under standard MM as under the proposed estimator.
KW - Compound Poisson demand
KW - Forecasting
KW - Inventory control
KW - Probability
KW - article
KW - forecasting
KW - inventory control
KW - maximum likelihood method
KW - probability
U2 - 10.1016/j.omega.2021.102481
DO - 10.1016/j.omega.2021.102481
M3 - Journal article
VL - 104
JO - Omega
JF - Omega
SN - 0305-0483
M1 - 102481
ER -