John E. Boylan

On the bias of intermittent demand estimates

Forecasting and inventory control for intermittent demand items has been a major problem in the manufacturing and supply environment. Croston (Operational Research Quarterly 23 (1972) 289), proposed a method according to which intermittent demand estimates can be built from constituent events. Crostons method has been reported to be a robust method but has shown more modest benefits in forecasting accuracy than expected. In this research, one of the causes of this unexpected performance has been identified, as a first step towards improving Crostons method. Certain limitations are identified in Crostons approach and a correction in his derivation of the expected estimate of demand per time period is presented. In addition, a modification to his method that gives approximately unbiased demand per period estimates is introduced. All the conclusions are confirmed by means of an extended simulation experiment where Crostons and Revised Crostons methods are compared. The forecasting accuracy comparison corresponds to a situation of an inventory control system employing a re-order interval or product group review.

On the categorization of demand patterns

The categorization of alternative demand patterns facilitates the selection of a forecasting method and it is an essential element of many inventory control software packages. The common practice in the inventory control software industry is to arbitrarily categorize those demand patterns and then proceed to select an estimation procedure and optimize the forecast parameters. Alternatively, forecasting methods can be directly compared, based on some theoretically quantified error measure, for the purpose of establishing regions of superior performance and then define the demand patterns based on the results. It is this approach that is discussed in this paper and its application is demonstrated by considering EWMA, Crostons method and an alternative to Crostons estimator developed by the first two authors of this paper. Comparison results are based on a theoretical analysis of the mean square error due to its mathematically tractable nature. The categorization rules proposed are expressed in terms of the average inter-demand interval and the squared coefficient of variation of demand sizes. The validity of the results is tested on 3000 real-intermittent demand data series coming from the automotive industry.

Classification for forecasting and stock control : a case study

Different stock keeping units (SKUs) are associated with different underlying demand structures, which in turn require different methods for forecasting and stock control. Consequently, there is a need to categorize SKUs and apply the most appropriate methods in each category. The way this task is performed has significant implications in terms of stock and customer satisfaction. Therefore, categorization rules constitute a vital element of intelligent inventory management systems. Very little work has been conducted in this area and, from the limited research to date, it is not clear how managers should classify demand patterns for forecasting and inventory management. A previous research project was concerned with the development of a theoretically coherent demand categorization scheme for forecasting only. In this paper, the stock control implications of such an approach are assessed by experimentation on an inventory system developed by a UK-based software manufacturer. The experimental database consists of the individual demand histories of almost 16 000 SKUs. The empirical results from this study demonstrate considerable scope for improving real-world systems.

Forecasting for inventory planning: a 50-year review

Forecasting and planning for inventory management has received considerable attention from the Operational Research (OR) community over the last 50 years because of its implications for decision making, both at the strategic level of an organization and at the operational level. Many influential contributions have been made in this area, reflecting different perspectives that have evolved in divergent strands of the literature, namely: system dynamics, control theory and forecasting theory (both statistical and judgemental). Although this pluralism is healthy in terms of knowledge advancement, it also signifies the fragmentation of the OR discipline and the lack of cross-fertilization of ideas to develop more comprehensive approaches towards the resolution of the same issues. In this paper, the relevant literature is reviewed and synthesized to promote some convergence between these different approaches to inventory forecasting and planning. The review concludes with an inter-disciplinary agenda for further research.

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.

An aggregate-disaggregate intermittent demand approach (ADIDA) to forecasting: an empirical proposition and analysis

Intermittent demand patterns are characterised by infrequent demand arrivals coupled with variable demand sizes. Such patterns prevail in many industrial applications, including IT, automotive, aerospace and military. An intuitively appealing strategy to deal with such patterns from a forecasting perspective is to aggregate demand in lower-frequency ‘time buckets’ thereby reducing the presence of zero observations. However, such aggregation may result in losing useful information, as the frequency of observations is reduced. In this paper, we explore the effects of aggregation by investigating 5000 stock keeping units from the Royal Air Force (UK). We are also concerned with the empirical determination of an optimum aggregation level as well as the effects of aggregating demand in time buckets that equal the lead-time length (plus review period). This part of the analysis is of direct relevance to a (periodic) inventory management setting where such cumulative lead-time demand estimates are required. Our study allows insights to be gained into the value of aggregation in an intermittent demand context. The paper concludes with an agenda for further research.

Supply chain forecasting: Theory, practice, their gap and the future

Supply Chain Forecasting (SCF) goes beyond the operational task of extrapolating demand requirements at one echelon. It involves complex issues such as supply chain coordination and sharing of information between multiple stakeholders. Academic research in SCF has tended to neglect some issues that are important in practice. In areas of practical relevance, sound theoretical developments have rarely been translated into operational solutions or integrated in state-of-the-art decision support systems. Furthermore, many experience-driven heuristics are increasingly used in everyday business practices. These heuristics are not supported by substantive scientific evidence; however, they are sometimes very hard to outperform. This can be attributed to the robustness of these simple and practical solutions such as aggregation approaches for example (across time, customers and products). This paper provides a comprehensive review of the literature and aims at bridging the gap between theory and practice in the existing knowledge base in SCF. We highlight the most promising approaches and suggest their integration in forecasting support systems. We discuss the current challenges both from a research and practitioner perspective and provide a research and application agenda for further work in this area. Finally, we make a contribution in the methodology underlying the preparation of review articles by means of involving the forecasting community in the process of deciding both the content and structure of this paper.

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.

Forecasting for Inventory Management of Service Parts

Service parts are ubiquitous in modern societies. Their need arises whenever a component fails or requires replacement. In some sectors, such as the aerospace and automotive industries, a very wide range of service parts are held in stock, with significant implications for availability and inventory holding. Their management is therefore an important task.

Judgement and supply chain dynamics

Forecasting demand at the individual stock-keeping-unit (SKU) level often necessitates the use of statistical methods, such as exponential smoothing. In some organizations, however, statistical forecasts will be subject to judgemental adjustments by managers. Although a number of empirical and ‘laboratory’ studies have been performed in this area, no formal OR modelling has been conducted to offer insights into the impact such adjustments may have on supply chain performance and the potential development of mitigation mechanisms. This is because of the associated dynamic complexity and the situation-specific nature of the problem at hand. In conjunction with appropriate stock control rules, demand forecasts help decide how much to order. It is a common practice that replenishment orders may also be subject to judgemental intervention, adding further to the dynamic system complexity and interdependence. The system dynamics (SD) modelling method can help advance knowledge in this area, where mathematical modelling cannot accommodate the associated complexity. This study, which constitutes part of a UK government funded (EPSRC) project, uses SD models to evaluate the effects of forecasting and ordering adjustments for a wide set of scenarios involving: three different inventory policies; seven different (combinations of) points of intervention; and four different (combinations of) types of judgmental intervention (optimistic and pessimistic). The results enable insights to be gained into the performance of the entire supply chain. An agenda for further research concludes the paper.