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.     

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.     

A combined forecast—inventory control procedure for spare parts

This paper examines the performance of two different (s, Q) inventory models, namely a simple and an advanced model, for spare parts in a production plant of a confectionery producer in the Netherlands. The simple approach is more or less standard: the undershoot of the reorder level is not taken into account and the normal distribution is used as the distribution of demand during lead-time. The advanced model takes undershoots into account, differentiates between zero and nonzero demands during lead-time, and utilises the gamma distribution for the demand distribution. Both models are fed with parameters estimated by a procedure that forecasts demand sizes and time between demand occurrences separately (intermittent demand). The results show that the advanced approach yields a service level close to the desired one under many circumstances, while the simple approach is not consistent, in that it leads to much larger inventories in meeting the desired service level for all spare parts.     

A two-step method for forecasting spare parts demand using information on component repairs

Forecasting spare parts demand is notoriously difficult, as demand is typically intermittent and lumpy. Specialized methods such as that by Croston are available, but these are not based on the repair operations that cause the intermittency and lumpiness of demand. In this paper, we do propose a method that, in addition to the demand for spare parts, considers the type of component repaired. This two-step forecasting method separately updates the average number of parts needed per repair and the number of repairs for each type of component. The method is tested in an empirical, comparative study for a service provider in the aviation industry. Our results show that the two-step method is one of the most accurate methods, and that it performs considerably better than Croston’s method. Moreover, contrary to other methods, the two-step method can use information on planned maintenance and repair operations to reduce forecasts errors by up to 20%. We derive further analytical and simulation results that help explain the empirical findings.     

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.     

A mega-trend-diffusion grey forecasting model for short-term manufacturing demand

Accurate short-term demand forecasting is critical for developing effective production plans; however, a short forecasting period indicates that the product demands are unstable, rendering tracking of product development trends difficult. Determining the actual developing data patterns by using forecasting models generated using historical observations is difficult, and the forecasting performance of such models is unfavourable, whereas using the latest limited data for forecasting can improve management efficiency and maintain the competitive advantages of an enterprise. To solve forecasting problems related to a small data set, this study applied an adaptive grey model for forecasting short-term manufacturing demand. Experiments involving the monthly demand data for thin film transistor liquid crystal display panels and wafer-level chip-scale packaging process data showed that the proposed grey model produced favourable forecasting results, indicating its appropriateness as a short-term forecasting tool for small data sets.     

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.     

A hybrid spares demand forecasting method dedicated to mining industry

The paper addresses the problem of lumpy demand forecasting which is typical for spare parts. Several prediction methods are presented in the paper - traditional techniques based on time series and advanced methods which use artificial neural networks. The paper presents a new hybrid spares demand forecasting method dedicated to mining companies. The method combines information criteria, regression modeling and artificial neural networks. The paper also discusses simulation research related to efficiency assessment of the chosen variable selection methods and its application in the newly developed forecasting method. The assessment of this method is conducted by a comparison with traditional methods and is based on selected forecast errors.     

基于对故障规律统计分析的汽车备件需求预测

汽车备件的需求与汽车故障紧密相关,文章介绍了一种在对汽车故障进行统计分析并确定其分布规律的基础上预测备件需求的方法,预测中需要结合整车保有量的历史数据以及故障与备件的对应表。用统计的方法对某型客车的故障信息进行分析,认为故障的规律可用四种典型的分布进行描述。实例验证了这种方法的准确性高于传统方法,并且在计算机的辅助下可以方便操作。     

Decision support for spare parts acquisition in post product life cycle

A major task in service management is the timely and cost efficient provision of spare parts for durable products. This especially holds good, when the regular production of the product, its components and parts has been discontinued, but customer service still has to be guaranteed for quite a long time. In such post product life cycle period, three options are available to organize the spare parts acquisition, namely (i) setting up a single large order within the final lot of regular production, (ii) performing extra production runs until the end of service and (iii) using remanufacturing to gain spare parts from used products. These three options are characterized by different cost and flexibility properties. Due to the time-variability and uncertainty of demands for spare parts and also that of the returns of used products, it is a challenging task to find out the optimal combination of these three options. In this paper we show how this problem can be modeled and solved by Decision Tree and stochastic Dynamic Programming procedure. Based on the Dynamic Programming approach a heuristic method is proposed, which can be employed to come up with a simple solution procedure for real-world spare parts acquisition problems during the post product life cycle. A numerical example is presented to demonstrate the application of the solution methods described in the paper.     

智能电表最优更换及备件库存联合决策

智能电表是智能电网运行的关键部件,提高其可靠性和可用度对保证电力的持续不间断供应和准确电能测量至关重要。充足的智能电表库存是其换装与维修的基本保障。本文基于智能电表的故障特性和换装需求分析,建立了智能电表的最优更换与备件库存联合决策模型,并给出了优化方法,以求得可以使系统长期平均运营成本最小的最优更换与备件库存策略。     

Renewal theory forecasting for stock control

A method is described for forecasting spares demand from data on model sales. The method uses concepts borrowed from renewal theory. The scheme is particularly useful for producing a forecast of all-time future demand for a spare so that a decision may be made about the timing of the final production run.     

Spare parts logistics and installed base information

Many of the challenges in spare parts logistics emerge due to the combination of large service networks, and sporadic/slow-moving demand. Customer heterogeneity and stringent service deadlines entail further challenges. Meanwhile, high revenue rates in service operations motivate companies to invest and optimize the service logistics function. An important aspect of the spare parts logistics function is its ability to support customer-specific requirements with respect to service deadlines. To support customer specific operations, many companies are actively maintaining and utilizing installed base data during forecasting, planning and execution stages. In this paper, we highlight the potential economic value of installed base data for spare parts logistics. We also discuss various data quality issues that are associated with the use of installed base data and show that planning performance depends on the quality dimensions.     

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 sales of slow and fast moving inventories

Traditional computerised inventory control systems usually rely on exponential smoothing to forecast the demand for fast moving inventories. Practices in relation to slow moving inventories are more varied, but the Croston method is often used. It is an adaptation of exponential smoothing that (1) incorporates a Bernoulli process to capture the sporadic nature of demand and (2) allows the average variability to change over time. The Croston approach is critically appraised in this paper. Corrections are made to underlying theory and modifications are proposed to overcome certain implementation difficulties. A parametric bootstrap approach is outlined that integrates demand forecasting with inventory control. The approach is illustrated on real demand data for car parts.     

Evaluation of inventory policies with unidirectional substitutions

We propose evaluation approaches to multi-item base-stock inventory policies where unidirectional substitutions are allowed. The problems in the paper are in the context of spare parts management and we identify two substitution cases: substitution upon demand arrivals and substitution upon order deliveries. This leads us to three unidirectional substitution policies, for each of which we develop Markovian models. As the number of part types increases, computational effort required to solve the Markovian models increases rapidly. To reduce computation burden, an approximation approach based on the decomposition of multi-dimensional state transition is used for systems with two or more spare part types. Numerical studies show unidirectional substitution improves various system performance measures such as the average inventory level, the average backlogged demand, and the fill rate. The proposed decomposition approach reduces the computation required to compute the performance measures and the approximation errors seems to be quite small.     

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.     

Optimal lateral transshipment policies for a two location inventory problem with multiple demand classes

We consider an inventory model for spare parts with two stockpoints, providing repairable parts for a critical component of advanced technical systems. As downtime costs for these systems are expensive, ready–for–use spare parts are kept in stock to be able to quickly respond to a breakdown of a system. We allow for lateral transshipments of parts between the stockpoints upon a demand arrival. Each stockpoint faces demands from multiple demand classes. We are interested in the optimal lateral transshipment policy. There are three ways in which a demand can by satisfied: from own stock, via a lateral transshipment, or via an emergency procedure. Using stochastic dynamic programming, we characterize and prove the structure of the optimal policy, that is, the policy for satisfying the demands which minimizes the average operating costs of the system. This optimal policy is a threshold type policy, with state-dependent thresholds at each stockpoint for every demand class. We show a partial ordering in these thresholds in the demand classes. In addition, we derive conditions under which the so-called hold back and complete pooling policies are optimal, two policies that are often assumed in the literature. Furthermore, we study several model extensions which fit in the same modeling framework.     

A stochastic model for joint spare parts inventory and planned maintenance optimisation

Spare parts demands are usually generated by the need of maintenance either preventively or at failures. These demands are difficult to predict based on historical data of past spare parts usages, and therefore, the optimal inventory control policy may be also difficult to obtain. However, it is well known that maintenance costs are related to the availability of spare parts and the penalty cost of unavailable spare parts consists of usually the cost of, for example, extended downtime for waiting the spare parts and the emergency expedition cost for acquiring the spare parts. On the other hand, proper planned maintenance intervention can reduce the number of failures and associated costs but its performance also depends on the availability of spare parts. This paper presents the joint optimisation for both the inventory control of the spare parts and the Preventive Maintenance (PM) inspection interval. The decision variables are the order interval, PM interval and order quantity. Because of the random nature of plant failures, stochastic cost models for spare parts inventory and maintenance are derived and an enumeration algorithm with stochastic dynamic programming is employed for finding the joint optimal solutions over a finite time horizon. The delay-time concept developed for inspection modelling is used to construct the probabilities of the number of failures and the number of the defective items identified at a PM epoch, which has not been used in this type of problems before. The inventory model follows a periodic review policy but with the demand governed by the need for spare parts due to maintenance. We demonstrate the developed model using a numerical example.