TY - JOUR

T1 - Estimating the cumulative distribution function of lead-time demand using bootstrapping with and without replacement

AU - Boylan, John E.

AU - Babai, M. Zied

N1 - This is the author’s version of a work that was accepted for publication in International Journal of Production Economics. 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 International Journal of Production Economics, 252, 2022 DOI: 10.1016/j.ijpe.2022.108586

PY - 2022/10/31

Y1 - 2022/10/31

N2 - Forecasting of the cumulative distribution function (CDF) of demand over lead time is a standard requirement for effective inventory replenishment. In practice, while the demand for some items conforms to standard probability distributions, the demand for others does not, thus making it challenging to estimate the CDF of lead-time demand. Distribution-free methods have been proposed, including resampling of demand from previous individual periods of the demand history, often referred to as bootstrapping in the inventory forecasting literature. There has been a lack of theoretical research on this form of resampling. In this paper, we analyse the bias and variance of CDF estimates obtained by resampling, both with and without replacement. Counterintuitively, we find that the ‘with replacement’ approach does not always dominate ‘without replacement’ in terms of mean square error of CDF estimates. Closed-form expressions are given for the components of Mean Square Error, with and without replacement. For shorter lead times, of two or three periods, these may be used directly to identify series that may benefit from resampling without replacement. Inventory performance implications are evaluated on simulated and empirical data. It is found that marked differences may arise between ‘with replacement’ and ‘without replacement’ bootstrapping approaches. The latter method can be more beneficial for lower target Cycle Service Levels, longer lead times and shorter demand histories.

AB - Forecasting of the cumulative distribution function (CDF) of demand over lead time is a standard requirement for effective inventory replenishment. In practice, while the demand for some items conforms to standard probability distributions, the demand for others does not, thus making it challenging to estimate the CDF of lead-time demand. Distribution-free methods have been proposed, including resampling of demand from previous individual periods of the demand history, often referred to as bootstrapping in the inventory forecasting literature. There has been a lack of theoretical research on this form of resampling. In this paper, we analyse the bias and variance of CDF estimates obtained by resampling, both with and without replacement. Counterintuitively, we find that the ‘with replacement’ approach does not always dominate ‘without replacement’ in terms of mean square error of CDF estimates. Closed-form expressions are given for the components of Mean Square Error, with and without replacement. For shorter lead times, of two or three periods, these may be used directly to identify series that may benefit from resampling without replacement. Inventory performance implications are evaluated on simulated and empirical data. It is found that marked differences may arise between ‘with replacement’ and ‘without replacement’ bootstrapping approaches. The latter method can be more beneficial for lower target Cycle Service Levels, longer lead times and shorter demand histories.

U2 - 10.1016/j.ijpe.2022.108586

DO - 10.1016/j.ijpe.2022.108586

M3 - Journal article

VL - 252

JO - International Journal of Production Economics

JF - International Journal of Production Economics

SN - 0925-5273

M1 - 108586

ER -