Forecasting of compound Erlang demand

Abstract

Intermittent demand items dominate service and repair inventories in many industries and they are known to be the source of dramatic inefficiencies in the defence sector. However, research in forecasting such items has been limited. Previous work in this area has been developed upon the assumption of a Bernoulli or a Poisson demand arrival process. Nevertheless, intermittent demand patterns may often deviate from the memory-less assumption. In this work we extend analytically previous important results to model intermittent demand based on a compound Erlang process, and we provide a comprehensive categorisation scheme to be used for forecasting purposes. In a numerical investigation we assess the benefit of departing from the memory-less assumption and we provide insights into how the degree of determinism inherent in the process affects forecast accuracy. Operationalised suggestions are offered to managers and software manufacturers dealing with intermittent demand items.

Keywords:

• demand forecasting
• demand categorisation
• Erlang process
• service logistics

Electronic supplementary material

The online version of this article (doi:10.1057/jors.2015.27) contains supplementary material, which is available to authorized users.

Supplementary information accompanies this article on the Journal of the Operational Research Society website (www.palgrave-journals.com/jors)

Electronic supplementary material

The online version of this article (doi:10.1057/jors.2015.27) contains supplementary material, which is available to authorized users.

Supplementary information accompanies this article on the Journal of the Operational Research Society website (www.palgrave-journals.com/jors)

Acknowledgements

We would like to thank the three anonymous referees for their comments that greatly helped to improve the content of our paper and its presentation.

Notes

1 DOD defines secondary inventory items to include reparable components, subsystems, and assemblies other than major end items (eg, ships & aircrafts), consumable repair parts, bulk items, subsistence, and expendable end items.

2 A practical inventory management application in the defence sector is described by Scala et al (2013). Relevant studies demonstrate the tremendous scope for improving the control of defence inventories.

3 In continuous review inventory control it is only necessary to consider making replenishment decisions just after a demand has occurred. This is true for Bernoulli and Poisson processes, where the time between demands is geometrically and exponentially distributed, respectively, and hence the demand process is associated with the memory-less property from which the above fact follows. However, for renewal demand processes, including the Erlang arrival processes studied in this paper, this is no longer true, in general. Rather, for these processes the passage of time itself may carry information about the demand process. Thus, it may be optimal that a certain time span should trigger a replenishment order, even if a demand has not occurred. Therefore, an order may not only be triggered by a change in the inventory position (defined in the usual way). Heuristically, and for practical purposes, replenishment orders may, of course, be allowed only at the time instances just after a demand has occurred (or at predetermined time intervals, as in a periodic review system). This issue has important implications for the kind of information that is useful for inventory control purposes but is not further pursued in this study.

4 SKU classification for forecasting purposes typically works in the opposite way. That is, ad hoc classification rules are being used to separate SKUs into categories, followed by the specification of a forecasting method for each of the categories. But if the purpose of classification is the selection of forecasting methods, then it makes more sense to compare directly possible estimators and then categorize demand based on regions of superior forecast performance.

5 The calculation of θ_r for high values of r results in complex numbers. As the imaginary part of these numbers is negligible, only the real part is considered in the numerical calculations conducted in this paper.