Non-stationary demand forecasting by cross-sectional aggregation

In this paper the relative effectiveness of top-down (TD) versus bottom-up (BU) approaches is compared for cross-sectionally forecasting aggregate and sub-aggregate demand. We assume that the sub-aggregate demand follows a non-stationary Integrated Moving Average (IMA) process of order one and a Single Exponential Smoothing (SES) procedure is used to extrapolate future requirements. Such demand processes are often encountered in practice and SES is one of the standard estimators used in industry (in addition to being the optimal estimator for an IMA process). Theoretical variances of forecast error are derived for the BU and TD approach in order to contrast the relevant forecasting performances. The theoretical analysis is supported by an extensive numerical investigation at both the aggregate and sub-aggregate level, in addition to empirically validating our findings on a real dataset from a European superstore. The results demonstrate the increased benefit resulting from cross-sectional forecasting in a non-stationary environment than in a stationary one. Valuable insights are offered to demand planners and the paper closes with an agenda for further research in this area. © 2015 Elsevier B.V. All rights reserved

Stock keeping unit fill rate specification

The fill rate is the most widely applied service level measure in industry and yet there is minimal advice available on how it should be differentiated on an individual Stock Keeping Unit (SKU) basis given that there is an overall system target service level. The typical approach utilized in practice, and suggested in academic textbooks, is to set the individual service levels equal to the targeted performance required across an entire stock base or a certain class of SKUs (e.g., in ABC classification). In this paper it is argued that this approach is far from optimal and a simple methodology is proposed that is shown (on real life datasets) to be associated with reductions in stock investments. In addition, the new approach is intuitive, very easy to implement and thus highly likely to be positively received by practitioners and software manufacturer

Reduction of the value of information sharing as demand becomes strongly auto-correlated

Information sharing has been identified, in the academic literature, as one of the most important levers to mitigate the bullwhip effect in supply chains. A highly-cited article on the bullwhip effect has claimed that the percentage inventory reduction resulting from information sharing in a two level supply chain, when the downstream demand is autoregressive of order one, is an increasing function of the autoregressive parameter of the demand. In this paper we show that this is true only for a certain range of the autoregressive parameter and there is a maximum value beyond which the bullwhip ratio at the upstream stage is reduced and the percentage inventory reduction resulting from information sharing decreases towards zero. We also show that this maximum value of the autoregressive parameter can be as high as 0.7 which represents a common value that may be encountered in many practical contexts. This means that large benefits of information sharing cannot be assumed for those Stock Keeping Units (SKUs) with highly positively auto-correlated demand. Instead, equally careful analysis is needed for these items as for those SKUs with less strongly auto-correlated demand

Determining order-up-to levels under periodic review for compound binomial (intermittent) demand

We propose a new method for determining order-up-to levels for intermittent demand items in a periodic review system. Contrary to existing methods, we exploit the intermittent character of demand by modelling lead time demand as a compound binomial process. In an extensive numerical study using Royal Air Force (RAF) data, we show that the proposed method is much better than existing methods at approximating target service levels and also improves inventory-service efficiency. Furthermore, the proposed method can be applied for both cost and service oriented systems, and is easy to implement

Intermittent demand : linking forecasting to inventory obsolescence

The standard method to forecast intermittent demand is that by Croston. This method is available in ERP type solutions such as SAP and specialised forecasting software packages (e.g. Forecast Pro), and often applied in practice. It uses exponential smoothing to separately update the estimated demand size and demand interval whenever a positive demand occurs, and their ratio provides the forecast of demand per period. The Croston method has two important disadvantages. First and foremost, not updating after (many) periods with zero demand renders the method unsuitable for dealing with obsolescence issues. Second, the method is positively biased and this is true for all points in time (i.e. considering the forecasts made at an arbitrary time period) and issue points only (i.e. considering the forecasts following a positive demand occurrence only). The second issue has been addressed in the literature by the proposal of an estimator (Syntetos–Boylan Approximation, SBA) that is approximately unbiased. In this paper, we propose a new method that overcomes both these shortcomings while not adding complexity. Different from the Croston method, the new method is unbiased (for all points in time) and it updates the demand probability instead of the demand interval, doing so in every period. The comparative merits of the new estimator are assessed by means of an extensive simulation experiment. The results indicate its superior performance and enable insights to be gained into the linkage between demand forecasting and obsolescence

Analysis of order-up-to-level inventory systems with compound Poisson demand

We analyse a single echelon single item inventory system where the demand and the lead time are stochastic. Demand is modelled as a compound Poisson process and the stock is controlled according to a continuous time order-up-to (OUT) level policy. We propose a method for determining the optimal OUT level for cost oriented inventory systems where unfilled demands are backordered. We first establish an analytical characterization of the optimal OUT level. The actual calculation is based on a numerical procedure the accuracy of which can be set as highly as desired. By means of a numerical investigation, we show that the method is very efficient in calculating the optimal OUT level. We compare our results with those obtained using an approximation proposed in the literature and we show that there is a significant difference in accuracy for slow moving items. Our work allows insights to be gained on stock control related issues for both fast and slow moving Stock Keeping Units (SKUs).Stock control Compound Poisson Queuing system Order-up-to-level Slow moving items

Determining order-up-to levels under periodic review for compound binomial (intermittent) demand

We propose a new method for determining order-up-to levels for intermittent demand items in a periodic review system. Contrary to existing methods, we exploit the intermittent character of demand by modelling lead time demand as a compound binomial process. In an extensive numerical study using Royal Air Force (RAF) data, we show that the proposed method is much better than existing methods at approximating target service levels and also improves inventory-service efficiency. Furthermore, the proposed method can be applied for both cost and service oriented systems, and is easy to implement.Compound binomial (intermittent) demand Periodic stock control Service levels Empirical investigation

Demand forecasting in supply chains:a review of aggregation and hierarchical approaches

Demand forecasts are the basis of most decisions in supply chain management. The granularity of these decisions lead to different forecast requirements. For example, inventory replenishment decisions require forecasts at the individual SKU level over lead time, whereas forecasts at higher levels, over longer horizons, are required for supply chain strategic decisions. The most accurate forecasts are not always obtained from data at the 'natural' level of aggregation. In some cases, forecast accuracy may be improved by aggregating data or forecasts at lower levels, or disaggregating data or forecasts at higher levels, or by combining forecasts at multiple levels of aggregation. Temporal and cross-sectional aggregation approaches are well established in the literature. More recently, it has been argued that these two approaches do not make the fullest use of data available at the different hierarchical levels of the supply chain. Therefore, consideration of forecasting hierarchies (over time and other dimensions), and combinations of forecasts across hierarchical levels, have been recommended. This paper provides a comprehensive review of research dealing with aggregation and hierarchical forecasting in supply chains, based on a systematic search. The review enables the identification of major research gaps and the presentation of an agenda for further research

Forecasting and stock control: A study in a wholesaling context

Wholesalers add value to the products they deal with by essentially bringing them closer to the end consumers. In that respect, the effective control of stock levels becomes an important measure of operational performance especially in the context of achieving high customer service levels. In this paper, we address issues pertinent to forecasting and inventory management in a wholesaling environment and discuss the recommendations proposed in such a context in a case study organization. Our findings demonstrate the considerable scope that exists for improving current practices and offers insights into possible managerial issues.Forecasting Inventory Demand categorisation Wholesaling