Forecasting the Intermittent Demand for Slow-Moving Items

Organizations with large-scale inventory systems typically have a large proportion of items for which demand is intermittent and low volume. We examine different approaches to forecasting for such products, paying particular attention to the need for inventory planning over a multi-period lead-time when the underlying process may be non-stationary. We develop a forecasting framework based upon the zero-inflated Poisson distribution (ZIP), which enables the explicit evaluation of the multi-period lead-time demand distribution in special cases and an effective simulation scheme more generally. We also develop performance measures related to the entire predictive distribution, rather than focusing exclusively upon point predictions. The ZIP model is compared to a number of existing methods using data on the monthly demand for 1,046 automobile parts, provided by a US automobile manufacturer. We conclude that the ZIP scheme compares favorably to other approaches, including variations of Croston's method as well as providing a straightforward basis for inventory planning.Croston's method; Exponential smoothing; Intermittent demand; Inventory control; Prediction likelihood; State space models; Zero-inflated Poisson distribution

Sequential Empirical Bayes method for filtering dynamic spatiotemporal processes

We consider online prediction of a latent dynamic spatiotemporal process and estimation of the associated model parameters based on noisy data. The problem is motivated by the analysis of spatial data arriving in real-time and the current parameter estimates and predictions are updated using the new data at a fixed computational cost. Estimation and prediction is performed within an empirical Bayes framework with the aid of Markov chain Monte Carlo samples. Samples for the latent spatial field are generated using a sampling importance resampling algorithm with a skewed-normal proposal and for the temporal parameters using Gibbs sampling with their full conditionals written in terms of sufficient quantities which are updated online. The spatial range parameter is estimated by a novel online implementation of an empirical Bayes method, called herein sequential empirical Bayes method. A simulation study shows that our method gives similar results as an offline Bayesian method. We also find that the skewed-normal proposal improves over the traditional Gaussian proposal. The application of our method is demonstrated for online monitoring of radiation after the Fukushima nuclear accident

A Comparison of Methods for Forecasting Demand for Slow Moving Car Parts

This paper has a focus on non-stationary time series formed from small non-negative integer values which may contain many zeros and may be over-dispersed. It describes a study undertaken to compare various suitable adaptations of the simple exponential smoothing method of forecasting on a database of demand series for slow moving car parts. The methods considered include simple exponential smoothing with Poisson measurements, a finite sample version of simple exponential smoothing with negative binomial measurements, and the Croston method of forecasting. In the case of the Croston method, a maximum likelihood approach to estimating key quantities, such as the smoothing parameter, is proposed for the first time. The results from the study indicate that the Croston method does not forecast, on average, as well as the other two methods. It is also confirmed that a common fixed smoothing constant across all the car parts works better than maximum likelihood approaches.Count time series; forecasting; exponential smoothing; Poisson distribution; negative binomial distribution; Croston method.

Statistical uncertainty of eddy flux–based estimates of gross ecosystem carbon exchange at Howland Forest, Maine

We present an uncertainty analysis of gross ecosystem carbon exchange (GEE) estimates derived from 7 years of continuous eddy covariance measurements of forest-atmosphere CO2fluxes at Howland Forest, Maine, USA. These data, which have high temporal resolution, can be used to validate process modeling analyses, remote sensing assessments, and field surveys. However, separation of tower-based net ecosystem exchange (NEE) into its components (respiration losses and photosynthetic uptake) requires at least one application of a model, which is usually a regression model fitted to nighttime data and extrapolated for all daytime intervals. In addition, the existence of a significant amount of missing data in eddy flux time series requires a model for daytime NEE as well. Statistical approaches for analytically specifying prediction intervals associated with a regression require, among other things, constant variance of the data, normally distributed residuals, and linearizable regression models. Because the NEE data do not conform to these criteria, we used a Monte Carlo approach (bootstrapping) to quantify the statistical uncertainty of GEE estimates and present this uncertainty in the form of 90% prediction limits. We explore two examples of regression models for modeling respiration and daytime NEE: (1) a simple, physiologically based model from the literature and (2) a nonlinear regression model based on an artificial neural network. We find that uncertainty at the half-hourly timescale is generally on the order of the observations themselves (i.e., ∼100%) but is much less at annual timescales (∼10%). On the other hand, this small absolute uncertainty is commensurate with the interannual variability in estimated GEE. The largest uncertainty is associated with choice of model type, which raises basic questions about the relative roles of models and data