Forecasting Intermittent Demand by Markov Chain Model

International Journal of Forecasting, 2012

Organizations with large-scale inventory systems typically have a large proportion of items for which demand is intermittent and low volume. We examine various different approaches to demand forecasting for such products, paying particular attention to the need for inventory planning over a multi-period lead-time when the underlying process may be non-stationary. This emphasis leads to the consideration of prediction distributions for processes with time-dependent parameters. A wide range of possible distributions could be considered, but we focus upon the Poisson (as a widely used benchmark), the negative binomial (as a popular extension of the Poisson), and a hurdle shifted Poisson (which retains Croston's notion of a Bernoulli process for the occurrence of active demand periods). We also develop performance measures which are related to the entire prediction distribution, rather than focusing exclusively upon point predictions. The three models are compared using data on the monthly demand for 1046 automobile parts, provided by a US automobile manufacturer. We conclude that inventory planning should be based upon dynamic models using distributions that are more flexible than the traditional Poisson scheme.

This paper is concerned with identifying an effective method for forecasting the lead time demand of slow-moving inventories. Particular emphasis is placed on prediction distributions instead of point predictions alone. It is also placed on methods which work with small samples as well as large samples in recognition of the fact that the typical range of items has a mix of vintages due to different commissioning and decommissioning dates over time. Various forecasting methods are compared using monthly demand data for more than one thousand car parts. It is found that a multi-series version of exponential smoothing coupled with a Pólya (negative binomial) distribution works better than the other twenty-four methods considered, including the Croston method.

2009

Demand forecasting is one of the most crucial aspects of inventory management. For intermittent demand, i.e. demand peaks follow several periods of zero or low demands, forecasting is difficult. Furthermore, the choice of the forecasting method can have an impact on the inventory management policy that is best used. A simulation model is used to study a single-product inventory system facing demand of the intermittent type. In this paper, a decision support system is presented to choose between several forecasting methods and inventory management policies for intermittent demand.

Intermittent demand items account collectively for considerable proportions of the total stock value of any organization. Forecasting the relevant inventory requirements constitutes a very difficult task and most work in this area is based on Croston's estimator that relies upon exponentially smoothed demand sizes and inter-demand intervals. This method has been shown to be biased and a number of variants have been introduced in the literature, including the recently proposed TSB method that updates the demand probability instead of the demand interval and in doing so reacts faster to decreasing demand. The TSB has been shown theoretically to be unbiased (for all points in time), but its empirical performance has not been investigated yet and this constitutes one of the objectives of our work. More generally, we explore the empirical performance of forecasting methods used in an intermittent demand context, paying particular attention to the effects and implications of the smoothing constant values employed for updating purposes. We do so by means of experimentation on large empirical datasets from the military sector and automotive industry. The results enable insights to be gained into the sensitivity of the various methods' forecasting and stock control performance to the smoothing constant values used. The paper concludes with an agenda for further research.

The Journal of Engineering Research, 2021

Spare parts are among the most important and challenging fields for the intermittent demand forecast. Improving the accuracy of the forecasted results can improve the efficiency of the inventory control system as well as the adoption of beneficial strategic decisions in the face of the uncertainty inherent in the demand. The effectiveness of hybrid forecast models in predicting the stable and accurate results has made them a useful tool in counteracting the uncertainty and complexities of the time series structure. In the present study, a hybrid model will be introduced for forecasting the intermittent demand that can impressively overcome the limitations of individual models while simultaneously using the unique advantages of these models in dealing with the complexities in the intermittent demand. The accuracy in the forecasting ability is also increased by suitable examination of the structures and patterns in the intermittent data. The research modeling was done based the Crosto...

International Journal on Information and Communication Technology (IJoICT), 2020

The imbalance between demand and supply is frequently occurred in a market. This is due to the availability of goods that cannot match with the demand or the growth rate of customer. This is not preferable since the profit is not on the track. In contrast, the goods are probably over supplied so that company has to expense additional cost for extra storage. Both situations can be anticipated if the demand is precisely estimated. Therefore, in this study we will estimate demand in market situation by implementing multivariate Markov chain model. Multivariate Markov chain model is popular model for forecasting by observing current state in various applications. This model is compatible with 5 data sequences (product types) defined as product A, product B, product C, product D and product E, with 6 conditions (no sales volume, very slow-moving, slow-moving, standard, fast moving, and very fast moving). As the result, the highest transition probability value for the sales demand in a co...

The South African Journal of Industrial Engineering, 2012

It is commonly assumed that intermittent demand appears randomly, with many periods without demand; but that when it does appear, it tends to be higher than unit size. Basic and well-known forecasting techniques and stock policies perform very poorly with intermittent demand, making new approaches necessary. To select the appropriate inventory management policy, it is important to understand the demand pattern for the items, especially when demand is intermittent. The use of a forecasting method designed for an intermittent demand pattern, such as Croston's method, is required instead of a simpler and more common approach such as exponential smoothing. The starting point is to establish taxonomic rules to select efficiently the most appropriate forecasting and stock control policy to cope with thousands of items found in real environments. This paper contributes to the state of the art in: (i) categorisation of the demand pattern; (ii) methods to forecast intermittent demand; and (iii) stock control methods for items with intermittent demand patterns. The paper first presents a structured literature review to introduce managers to the theoretical research about how to deal with intermittent demand items in both forecasting and stock control methods, and then it points out some research gaps for future development for the three topics.

Journal of Applied Mathematics and Physics

At any given time, a product stock manager is expected to carry out activities to check his or her holdings in general and to monitor the condition of the stock in particular. He should monitor the level or quantity available of a given product, of any item. On the basis of the observation made in relation to the movements of previous periods, he may decide to order or not a certain quantity of products. This paper discusses the applicability of discrete-time Markov chains in making relevant decisions for the management of a stock of COTRA-Honey products. A Markov chain model based on the transition matrix and equilibrium probabilities was developed to help managers predict the likely state of the stock in order to anticipate procurement decisions in the short, medium or long term. The objective of any manager is to ensure efficient management by limiting overstocking, minimising the risk of stock-outs as much as possible and maximising profits. The determined Markov chain model allows the manager to predict whether or not to order for the period following the current period, and if so, how much.

IntechOpen, 2023

A Markov model describes a randomly varying system that satisfies the Markov property. This means that future and past states at any time are independent of the current state. The two most commonly used types of Markov models are Markov chains and higher-order Markov chains. Therefore, three types of Markov models are proposed in this chapter of the book: (i) supply chain management, (ii) Markov queue waiting time monitoring, and (iii) Markov fuzzy time series forecasting. The introduction introduces Markov chain (MC) and summarizes the most important aspects of Markov chain analysis. The first model explores a Markov queue model coupled to a storage system using the classical (0, Q) policy. The second model focuses on the M/ M/1/N service mode and develops a control chart for an M s /M s /1/N type simulated queue to monitor customer waiting times. The third is a higher-order Markov model (HOMM), which uses fuzzy sets to predict future states based on given hypothetical time series data. Numerical calculations are designed to find optimal order quantities, monitor customer wait times, and predict future HOMM conditions.

International Journal on Information and Communication Technology (IJoICT), 2022

Estimation of the number of demands for a product must be done correctly, so that the company can get maximum profit. Therefore, this study discusses how to estimate the amount of sales demand in a company correctly. The model that will be used to estimate sales demand is the Multivariate Markov Chain Model. This model can estimate the future state by observing the present state. The model requires parameter estimation values ​​first, namely the transition probability matrix and the weighted Markov chain, where in previous studies an estimation of the transition probability matrix has been carried out, so that in this study we will continue to estimate the weighted Markov chain parameters. This model is compatible with 5 data sequences (product types) defined as product 1, product 2, product 3, product 4, and product 5, with 6 conditions (no sales volume, very slow-moving, slow-moving, standard, fast moving, and very fast moving). As the result, the state probability for product 1, ...