An examination of the size of orders from customers,their characterisation and the implications for inventory control of slow moving items

This paper examines half a million observations of the size of orders from customers at an electrical wholesaler. It notes: the distribution of the size of customer orders for a single item (stock keeping unit or SKU) is very skewed and resembles a geometric distribution; while the average size of an order is different for different items, for one SKU the mean order size is effectively the same at different branches even when the branches have very different demand rates; across a range of SKUs there is a strong relationship linking the mean and the variance of order size. The general results above are shown to apply to even the slowest movers. This extension is important because for items with intermittent demand the size of customer orders is required to produce an unbiased estimate of demand. Also a knowledge of the distribution of demand is important for setting maximum and minimum stock levels and the scheme employed is described.     

Discount Weighted Moving Averages

An estimator to replace exponentially weighted moving averages is described and examples of its use are given. It has similar limiting properties but includes the on-line estimation of the forecast error variance as an integral part. The procedures for starting off and intervention are given.     

New ideas in neutrino detection

What is new in the field of neutrino detection? In addition to new projects probing both the low and high ends of the neutrino energy scale, an inexpensive, effective technique is being developed to allow tagging of antineutrinos in water Cherenkov (WC) detectors via the addition to water of a solute with a large neutron cross-section and energetic γ daughters. Gadolinium is an excellent candidate since in recent years it has become very inexpensive, now less than $8 per kilogram in the form of commercially available gadolinium trichloride. This non-toxic, non-reactive substance is highly soluble in water. Neutron capture on gadolinium yields an 8.0 MeV gamma cascade easily seen in detectors like Super-Kamiokande. The uses of GdCl₃ as a possible upgrade for the Super-Kamiokande detector — with a view toward improving its performance as an antineutrino detector for supernova neutrinos and reactor neutrinos — are discussed, as are the ongoing R&;D efforts which aim to make this dream a reality within the next two years.     

The giant muon Knight shift in antimony: Evidence for a Kondo impurity

A detailed study has been undertaken of the muon Knight shift in high purity antimony single crystals. No periodic variations with magnetic field (de Haas–van Alphen oscillations) are observed. The temperature dependence below 175 K is close to that expected for a Kondo‐like impurity with an anisotropic muon–electron hyperfine interaction. At higher temperatures the paramagnetic state becomes unstable and a transition occurs to a second state. The longitudinal relaxation rate rises from an apparently non‐zero value at T=0 to a maximum at 50 K, followed by a slow decline. This leads to a Korringa product which is strongly temperature dependent. This revised version was published online in August 2006 with corrections to the Cover Date.     

In vivo proton magnetic resonance spectroscopy studies of human brain

In vivo localized proton magnetic resonance spectroscopy (MRS) studies of brain were performed on eighteen normal subjects using the stimulated echo (STE) sequence. The absolute concentrations and proton relaxation times of N-acetyl aspartate (NAA), total creatine (Cr) and choline (Cho) were estimated. The MRS data was quantitatively analyzed for repeatability and intersubject variability. Quantitative analysis indicates excellent spectral repeatability. Significant intersubject variations in [NAA] and [Cr] have been observed while the intersubject variability in [Cho] has been found to be fairly small. Significant intensity distortions have been observed for mixing times longer than 50 msec.     

The Variance of Lead-Time Demand

Many short-term forecasting systems are based on exponentially weighted moving averages. It is usual to forecast the cumulative demand over a lead time or production horizon, and to describe this forecast in terms of its mean and variance. When the forecast horizon is fixed, the variance is often taken as the product of the number of periods and the variance per period. This is a serious error and typically underestimates the variance by a factor of about two. This paper details the need for a proper awareness of the correction factors.