Periodic control of intermittent demand items: theory and empirical analysis

In this paper we propose a modification to the standard forecasting, periodic order-up-to-level inventory control approach to dealing with intermittent demand items, when the lead-time length is shorter than the average inter-demand interval. In particular, we develop an approach that relies upon the employment of separate estimates of the inter-demand intervals and demand sizes, when demand occurs, directly for stock control purposes rather than first estimating mean demand and then feeding the results in the stock control procedure. The empirical performance of our approach is assessed by means of analysis on a large demand data set from the Royal Air Force (RAF, UK). Our work allows insights to be gained on the interactions between forecasting and stock control as well as on demand categorization-related issues for forecasting and inventory management purposes.     

Spare parts management: Linking distributional assumptions to demand classification

Spare parts are known to be associated with intermittent demand patterns and such patterns cause considerable problems with regards to forecasting and stock control due to their compound nature that renders the normality assumption invalid. Compound distributions have been used to model intermittent demand patterns; there is however a lack of theoretical analysis and little relevant empirical evidence in support of these distributions. In this paper, we conduct a detailed empirical investigation on the goodness of fit of various compound Poisson distributions and we develop a distribution-based demand classification scheme the validity of which is also assessed in empirical terms. Our empirical investigation provides evidence in support of certain demand distributions and the work described in this paper should facilitate the task of selecting such distributions in a real world spare parts inventory context. An extensive discussion on parameter estimation related difficulties in this area is also provided.     

Forecasting for Items with Intermittent Demand

In a service environment, a stockist usually has many slow moving items whose infrequency of demand can give rise to forecasting problems. Moreover, when a demand occurs, the request is sometimes for more than a single unit, which results in so-called lumpy demand. In this paper, the standard method for dealing with such intermittent demand is reassessed. Some general results are presented that enable variance estimates to be made, and these are particularly straightforward when the demand occasions can be represented as a Poisson process. Some experimental evidence is advanced to support this model in the specific situation under study. Since EWMA forecasts are central to many commercial systems, a simulation analysis was conducted to determine under what conditions intermittent demand requires its own model, rather than an unadjusted EWMA. Superior performance is demonstrated for items that have an average inter-order interval greater than 1.25 forecast review periods, and the magnitude of the improvement increases as the average interval lengthens.     

A new approach of forecasting intermittent demand for spare parts inventories in the process industries

Accurate demand forecasting is of vital importance in inventory management of spare parts in process industries, while the intermittent nature makes demand forecasting for spare parts especially difficult. With the wide application of information technology in enterprise management, more information and data are now available to improve forecasting accuracy. In this paper, we develop a new approach for forecasting the intermittent demand of spare parts. The described approach provides a mechanism to integrate the demand autocorrelated process and the relationship between explanatory variables and the nonzero demand of spare parts during forecasting occurrences of nonzero demands over lead times. Two types of performance measures for assessing forecast methods are also described. Using data sets of 40 kinds of spare parts from a petrochemical enterprise in China, we show that our method produces more accurate forecasts of lead time demands than do exponential smoothing, Croston's method and Markov bootstrapping method.     

Selecting the best periodic inventory control and demand forecasting methods for low demand items

The (s,S) form of the periodic review inventory control system has been claimed theoretically to be the best for the management of items of low and intermittent demand. Various heuristic procedures have been put forward, usually justified on the basis of generated data with known properties. Some stock controllers also have other simple rules which they employ and which are rarely seen in the literature. Determining how to forecast future demands is also a major problem in the area. The research described in this paper compares various periodic inventory policies as well as some forecasting methods and attempts to determine which are best for low and intermittent demand items. It evaluates the alternative methods on some long series of daily demands for low demand items for a typical spare parts depot.     

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.     

Forecast combinations for intermittent demand

Intermittent demand is characterised by infrequent demand arrivals, where many periods have zero demand, coupled with varied demand sizes. The dual source of variation renders forecasting for intermittent demand a very challenging task. Many researchers have focused on the development of specialised methods for intermittent demand. However, apart from a case study on hierarchical forecasting, the effects of combining, which is a standard practice for regular demand, have not been investigated. This paper empirically explores the efficiency of forecast combinations in the intermittent demand context. We examine both method and temporal combinations of forecasts. The first are based on combinations of different methods on the same time series, while the latter use combinations of forecasts produced on different views of the time series, based on temporal aggregation. Temporal combinations of single or multiple methods are investigated, leading to a new time-series classification, which leads to model selection and combination. Results suggest that appropriate combinations lead to improved forecasting performance over single methods, as well as simplifying the forecasting process by limiting the need for manual selection of methods or hyper-parameters of good performing benchmarks. This has direct implications for intermittent demand forecasting in practice.     

Forecasting for the ordering and stock-holding of spare parts

A modern military organization like the UK's Royal Air Force is dependent on readily available spare parts for in-service aircraft in order to maximize operational capability. A large proportion of spare parts are known to have an intermittent or slow-moving demand pattern, presenting particular problems as far as forecasting and inventory control are concerned. In this paper, we use extensive demand and replenishment lead-time data to assess the practical value of forecasting models put forward in the literature for addressing these problems. We use an analytical method for classifying the consumable inventory into smooth, irregular, slow-moving and intermittent demand patterns. Recent forecasting developments are compared against more commonly used methods across the identified demand patterns. One recently developed method, a modification to Croston's method referred to as the approximation method, is observed to provide significant reductions in the value of the stock-holdings required to attain a specified service level for all demand patterns.     

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.     

Multi-item sales forecasting with total and split exponential smoothing

Efficient supply chain management relies on accurate demand forecasting. Typically, forecasts are required at frequent intervals for many items. Forecasting methods suitable for this application are those that can be relied upon to produce robust and accurate predictions when implemented within an automated procedure. Exponential smoothing methods are a common choice. In this empirical case study paper, we evaluate a recently proposed seasonal exponential smoothing method that has previously been considered only for forecasting daily supermarket sales. We term this method ‘total and split’ exponential smoothing, and apply it to monthly sales data from a publishing company. The resulting forecasts are compared against a variety of methods, including several available in the software currently used by the company. Our results show total and split exponential smoothing outperforming the other methods considered. The results were also impressive for a method that trims outliers and then applies simple exponential smoothing.     

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.     

Forecasting intermittent demand: a comparative study

Methods for forecasting intermittent demand are compared using a large data set from the UK Royal Air Force. Several important results are found. First, we show that the traditional per period forecast error measures are not appropriate for intermittent demand, even though they are consistently used in the literature. Second, by comparing the ability to approximate target service levels and stock holding implications, we show that Croston's method (and a variant) and Bootstrapping clearly outperform Moving Average and Single Exponential Smoothing. Third, we show that the performance of Croston and Bootstrapping can be significantly improved by taking into account that an order in a period is triggered by a demand in that period.     

Multi-item inventory control with full truckloads: A comparison of aggregate and individual order triggering

In this paper, we consider the stochastic joint replenishment problem in an environment where transportation costs are dominant and full truckloads or full container loads are required. One replenishment policy, taking into account capacity restrictions of the total order volume, is the so-called QS policy, where replenishment orders are placed to raise the individual inventory positions of all items to their order-up-to levels, whenever the aggregate inventory position drops below the reorder level. We first provide a method to compute the policy parameters of a QS policy such that item target service levels can be met, under the assumption that demand can be modeled as a compound renewal process. The approximation formulas are based on renewal theory and are tested in a simulation study which reveals good performance. Second, we compare the QS policy with a simple allocation policy where replenishment orders are triggered by the individual inventory positions of the items. At the moment when an individual inventory position drops below its item reorder level, a replenishment order is triggered and the total vehicle capacity is allocated to all items such that the expected elapsed time before the next replenishment order is maximized. In an extensive simulation study it is illustrated that the QS policy outperforms this allocation policy since it results in lower inventory levels for the same service level. Although both policies lead to similar performance if items are identical, it can differ substantially if the item characteristics vary.     

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.     

电力需求预测管理信息系统

本文根据电力需求预测模型的特点，提出了能给预测过程提供信息支持和辅助决策的管理信息系统，并对系统进行了详细的分析和设计。     

Using shared sell-through data to forecast wholesaler demand in multi-echelon supply chains

Operational forecasting in supply chain management supports a variety of short-term planning decisions, such as production scheduling and inventory management. In this respect, improving short-term forecast accuracy is a way to build a more agile supply chain for manufacturing companies. Demand forecasting often relies on well-established univariate forecasting methods to extrapolate historical demand. Collaboration across the supply chain, including information sharing, is suggested in the literature to improve upon the forecast accuracy of such traditional methods. In this paper, we review empirical studies considering the use of downstream information in demand forecasting and investigate different modeling approaches and forecasting methods to incorporate such data. Where empirical findings on information sharing mainly focus on point-of-sale data in two-level supply chains, this research empirically investigates the added value of using sell-through data originating from intermediaries, next to historical demand figures, in a multi-echelon supply chain. In a case study concerning a US drug manufacturer, we evaluate different methods to incorporate this data and consider both time series methods and machine learning techniques to produce multi-step ahead weekly forecasts. The results show that the manufacturer can effectively improve its short-term forecast accuracy by integrating sell-through data into the forecasting process and provide useful insights as to the different modeling approaches used. The conclusion holds for all forecast horizons considered, though it is most pronounced for one-step ahead forecasts. Therefore, our research provides a clear incentive for manufacturers to assess the forecast accuracy that can be achieved by using sell-through data.     

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.     

A note on the inventory models for deteriorating items with ramp type demand rate

In this research we study the inventory models for deteriorating items with ramp type demand rate. We first clearly point out some questionable results that appeared in (Mandal, B., Pal, A.K., 1998. Order level inventory system with ramp type demand rate for deteriorating items. Journal of Interdisciplinary Mathematics 1, 49–66 and Wu, K.S., Ouyang, L.Y., 2000. A replenishment policy for deteriorating items with ramp type demand rate (Short Communication). Proceedings of National Science Council ROC (A) 24, 279–286). And then resolve the similar problem by offering a rigorous and efficient method to derive the optimal solution. In addition, we also propose an extended inventory model with ramp type demand rate and its optimal feasible solution to amend the incompleteness in the previous work. Moreover, we also proposed a very good inventory replenishment policy for this kind of inventory model. We believe that our work will provide a solid foundation for the further study of this sort of important inventory models with ramp type demand rate.     

Effects of imperfect products on lot sizing with work in process inventory

The economic production quantity (EPQ) is one of the most widely known inventory control models that can be regarded as the generalized form of the Economic Order Quantity. However, the model is built on an unrealistic assumption that all the produced items need to be of perfect quality. Also, the introduction of work in process, WIP, as part of the inventory has been of lesser concern in developing inventory models. This paper attempts to develop the economic production quantity considering work in process inventory and manufacturing imperfect products that may be either reworkable or non-reworkable. The non-reworkable imperfect products are sold at a reduced price. This paper introduces a new model for this problem.