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 defense 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.

Forecasting: theory and practice

“…It is also possible to adapt Croston's method so that sizes and intervals are updated based on a simple moving average (SMA) procedure instead of SES. Boylan and Syntetos (2003), Shale et al (2006), andSyntetos et al (2015a) presented correction factors to overcome the bias associated with Croston's approach under a Poisson demand arrival process and/or estimation of demand sizes and intervals using an SMA.…”

Determining the Optimal Order Quantity with Compound Erlang Demand under (T,Q) Policy

“…With demand arrivals following the Erlang distribution, in conjunction with a Gamma distribution for demand size, Saidane et al [25,26] propose an algorithm to determine the optimal base stock level under a costoriented continuous review inventory system and conduct numerical investigations to compare the performance of this model in cost reduction with that of the compound Poisson distribution and the classic Newsvendor model, respectively. Syntetos et al [27] not only demonstrate the superiority of deviating from the memoryless demand model, but also take the degree of intermittence into consideration and explore its connection with forecast accuracy through a numerical investigation. In sum, the above literature under a compound Erlang process all assume that the lead time is constant.…”