An empirical analysis and stochastic modelling of aggregate demand behaviour in a spare parts inventory system
The focus of the work here was an empirical analysis of the aggregate independent demand behaviour for spare parts inventories, principally in the automotive industry. In particular, using the pioneering work of RG Brown (1959), who showed that inventory usage values are often log normally distributed, we set out and developed models that go some considerable way to explaining the underlying stochastic basis for this phenomena, why it occurs and some limiting conditions. The justification for this approach was on the grounds that by providing a more fundamental understanding of the underlying stochastic processes that explain the emergent aggregate demand behaviour, a sound starting point would be provided for developing more sophisticated analytical ways to view an inventory range, as a total entity, for planning and control purposes. The analysis was based on extensive data collected from the DAF Trucks (GB) Ltd. spare parts systems spanning the period 1975 to 1986, together with supporting studies from a number of other systems. The analysis showed that in the systems studied spare parts prices are lognormally distributed and this is most likely to be the result of a stochastic process known as the 'theory of breakage'. Analysis also showed that in the DAF Trucks case aggregated and volumes in very short time periods are distributed as a combined Log Series /Negative Binomial distribution (LSD/NBD). The combined LSD/NBD model of aggregate demand volumes is itself fully explained by a stochastic model known as the Afwedson model, which in turn is derived from more elementary conditions based on the Poisson process. We then demonstrated that if these short period aggregate demand distributions are cumulated period by period they converge to a log normal distribution as the stable long run model of aggregate demand volumes. As a result of the lognormality of prices and volumes the resultant inventory usage values are also log normal. Furthermore from insight into the underlying factors that explain the lognormality we have identified the factors and variables that govern the valueso f the parameterso f the particular log normal models of usage values. - The research protocol used in this work incorporated the law verifying process know as 'retroduction' after work and discussions of Uji Ijiri and Herbert Simon (1977); and to a lesser extent we utilised simulation for validation and verification of the derived models. From the proven log normality of demand volumes and usage values we have demonstrated that a number of related key inventory factors are also lognormal, in particular inventory- item turnover rates. Furthermore our conclusions show that some standard inventory performance measures, such as the inventory wide 'stock turnover rate' and the 'stock to sales' ratio, are poor measures to use in the case of highly skewed inventory variables. Finally we have suggested several potentially fruitful areas for developing improved methods of monitoring inventory performance in a variety of circumstances.