F. R. Johnston

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.

Forecasting for intermittent demand : the estimation of an unbiased average

The majority of the range of items held by many stockists exhibit intermittent demand. Accurate forecasting of the issue rate for such items is important and several methods have been developed, but all produce biased forecasts to a greater or lesser degree. This paper derives the bias expected when the order arrivals follows a Poisson process, which leads to a correction factor for application in practice. Extensions to some other arrival processes are briefly considered.

Optimality and robustness of combinations of moving averages

A combination of moving averages has been shown previously to be more accurate than simple moving averages, under certain conditions, and to be more robust to non-optimal parameter specification. However, the use of the method depends on specification of three parameters: length of greater moving average, length of shorter moving average, and the weighting given to the former. In this paper, expressions are derived for the optimal values of the three parameters, under the conditions of a steady state model. These expressions reduce a three-parameter search to a single-parameter search. An expression is given for the variance of the sampling error of the optimal combination of moving averages and this is shown to be marginally greater than that for exponentially weighted moving averages (EWMA). Similar expressions for optimal parameters and the resultant variance are derived for equally weighted combinations. The sampling variance of the mean of such combinations is shown to be almost identical to the optimal general combination, thus simplifying the use of combinations further. It is demonstrated that equal weight combinations are more robust than EWMA to noise to signal ratios lower than expected, but less robust to noise to signal ratios higher than expected.

Viewpoint and Respons

Good research results should be reproducible, and in one sense, it is gratifying our earlier ®ndings have been so carefully veri®ed. However, the paper by Snyder et al contains some errors which could mislead the unwary, for example the function in (10) is not the same as in (1) but its square and the equation between (4b) and (5) is not a covariance but a correlation coef®cient, and further requires correction to

Breadth of range and depth of stock: forecasting and inventory management at Euro Car Parts Ltd.

This paper investigates inventory management issues in a distribution network. The study is motivated by examining the operation of a wholesaling car parts company. Customer service requirements are of paramount importance in this market sector. The nature of the demand facing the company is characterised. The breadth of range of stock keeping units (SKUs) held at a stocking location and the quantity of each SKU held are normally treated in isolation but in this case, the rule developed to select the range of SKU was extended to determine the level of stock to hold. It is intuitively obvious that these two factors should be linked, yet the authors have not found any other literature developing the connection in a practical context. Forecasting issues are explored as the rule on stock range depends on a forecast of the number of orders received for each SKU at each stocking unit. Some implementation issues and extensions are indicated.