Practical Inventory Replenishment Policies for a Linear Trend in Demand Followed by a Period of Steady Demand

Inventory policies are considered for the situation of a deterministic linear trend in demand followed by a period of constant demand: an idealised form of a common situation in spares provisioning. An analytic optimal solution is derived and its practical shortcomings discussed. The performance of practical inventory policies for this situation are compared and a policy based on the well known economic batch quantity, suitably modified for linear trend, is shown to give small cost penalties when compared to the analytic solution. The good performance of the policy based on the economic batch quantity is maintained, even when used on examples which simulate situations where the parameters of demand are not known exactly. Indeed the method is then superior to all others tried, including the "optimal" analytic method.     

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.     

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.     

The impact of data collection on fill rate performance in the (R,s, Q) inventory model

In this paper we consider the determination of the reorder point s in an (R, s, Q) inventory model subject to a fill rate service level constraint. We assume that the underlying demand process is a compound renewal process. We then derive an approximation method to compute the reorder level such that a target service level is achieved. Restrictions on the input parameters are given, within which this method is applicable. Moreover, we will investigate the effects on the fill rate performance in case the underlying demand process is indeed a compound renewal process, while the demand process is modelled as a discrete-time demand process. That is, the time axis is divided in time units (for example, days) and demands per time unit are independent and identically distributed random variables. It will be shown that smooth and erratic behaviour of the inter-arrival times have different impacts on the performance of the fill rate when demand is modelled as a discrete-time process and in case the underlying demand process is a compound renewal process.     

Analysis and evaluation of an Assemble-to-Order system with batch ordering policy and compound Poisson demand

We consider a multi-product and multi-component Assemble-to-Order (ATO) system where the external demand follows compound Poisson processes and component inventories are controlled by continuous-time batch ordering policies. The replenishment lead-times of components are stochastic, sequential and exogenous. Each element of the bill of material (BOM) matrix can be any non-negative integer. Components are committed to demand on a first-come-first-serve basis. We derive exact expressions for key performance metrics under either the assumption that each demand must be satisfied in full (non-split orders), or the assumption that each unit of demand can be satisfied separately (split orders). We also develop an efficient sampling method to estimate these metrics, e.g., the expected delivery lead-times and the order-based fill-rates. Based on the analysis and a numerical study of an example motivated by a real world application, we characterize the impact of the component interaction on system performance, demonstrate the efficiency of the numerical method and quantify the impact of order splitting.     

On the (R,s, Q) inventory model when demand is modelled as a compound Bernoulli process

In this paper we present an approximation method to compute the reorder point s in an (R, s, Q) inventory model with a service level restriction. Demand is modelled as a compound Bernoulli process, i.e., with a fixed probability there is positive demand during a time unit; otherwise demand is zero. The demand size and the replenishment leadtime are random variables. It is shown that this kind of modelling is especially suitable for intermittent demand. In this paper we will adapt a method presented by Dunsmuir and Snyder such that the undershoot is not neglected. The reason for this is that for compound demand processes the undershoot has a considerable impact on the performance levels, especially when the probability that demand is zero during the leadtime is high, which is the case when demand is lumpy. Furthermore, the adapted method is used to derive an expression for the expected average physical stock. The quality of both the reorder point and the expected average physical stock, calculated with the method presented in this paper, rum out to be excellent, as has been verified by simulation.     

A Note on Determining Order Quantities with a Linear Trend in Demand

The economic order quantity concept has received much attention. However, the model is severely restricted by the assumption of constant demand. This paper presents a procedure for adjusting the economic order quantity model for the cases of increasing or decreasing linear trend demand patterns. The primary advantage of the proposed method is its simplicity in comparison with existing procedures and, as illustrated in two examples, its near-optimal performance     

联合订货下基于ø-散度的多产品库存鲁棒优化模型

针对多产品联合库存决策问题,在市场需求不确定条件下,建立了考虑联合订货成本的多产品库存鲁棒优化模型。针对不确定市场需求,采用一系列未知概率的离散情景进行描述,给出了基于最小最大准则的鲁棒对应模型,并证明了(s,S)库存策略的最优性。进一步,在仅知多产品市场需求历史数据基础上,采用基于ø-散度的数据驱动方法构建了满足一定置信度要求的关于未知需求概率分布的不确定集。在此基础上,为获得(s,S)库存策略的相关参数,运用拉格朗日对偶方法将所建模型等价转化为易于求解的数学规划问题。最后,通过数值计算分析了Kullback-Leibler散度和Cressie-Read散度以及不同的置信水平下的多产品库存绩效,并将其与真实分布下应用鲁棒库存策略得到的库存绩效进行对比。结果表明,需求分布信息的缺失虽然会导致一定的库存绩效损失,但损失值很小,表明基于文中方法得到的库存策略能够有效抑制需求不确定性扰动,具有良好的鲁棒性。     

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.     

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.     

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, Croston's method and an alternative to Croston's 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.     

Experimental study of a Bayesian method for daily electricity load forecasting

The method of Bayesian model discrimination is investigated for the possible contributions it may provide in the area of automatically forecasting the daily electricity demand cycle. A set of differing demand models have probabilities attached to them in such a way that these would be continuously updated with the available data and the actual forecasts obtained as expectations across all the models. Simulation experiments indicate significantly improved forecasting performance over a commonly used rescaling type of approach. Some practical issues in implementation are discussed.     

γ-Robust facility relocation problem

In this paper, we consider relocating facilities, where we have demand changes in the network. Relocations are performed by closing some of the existing facilities from low demand areas and opening new ones in newly emerging areas. However, the actual changes of demand are not known in advance. Therefore, different scenarios with known probabilities are used to capture such demand changes. We develop a mixed integer programming model for facility relocation that minimizes the expected weighted distance while making sure that relative regret for each scenario is no greater than γ. We analyzed the problem structure and developed a Lagrangian Decomposition Algorithm (LDA) to expedite the solution process. Numerical experiments are carried out to show the performance of LDA against the exact solution method.     

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.     

Stochastic models for air cargo terminal manpower supply planning in long‐term operations

In this research, based on two deterministic‐demand planning models, we established two long‐term stochastic‐demand planning models by incorporating the stochastic disturbances of manpower demands that occur in actual operations. The models are formulated as mixed integer linear programs that are solved using a mathematical programming solver. To compare the performance of the two stochastic‐demand and two deterministic‐demand planning models under the stochastic demands that occur in actual operations, we further develop a simulation‐based evaluation method. Finally, we perform numerical tests using real operating data from a Taiwan air cargo terminal. The preliminary results show that the stochastic models could be useful for planning air cargo terminal manpower supply. Copyright © 2008 John Wiley & Sons, Ltd.     

New Alternating Direction Method for a Class of Nonlinear Variational Inequality Problems

The alternating direction method is an attractive method for a class of variational inequality problems if the subproblems can be solved efficiently. However, solving the subproblems exactly is expensive even when the subproblem is strongly monotone or linear. To overcome this disadvantage, this paper develops a new alternating direction method for cocoercive nonlinear variational inequality problems. To illustrate the performance of this approach, we implement it for traffic assignment problems with fixed demand and for large-scale spatial price equilibrium problems.     

A comparison of methods for lot-sizing in a rolling horizon environment

We argue that the superior performance of a recent method for lot-sizing in a rolling horizon scheme is to a large extent due to the assumption that quite accurate future demand estimates are available. We show that other methods, including a straightforward one, can use this information just as effectively.     

企业三重绩效评价模型—空间几何模型

按照可持续发展战略的要求,从经济、生态、社会三个方面构建了企业的三重绩效评价指标体系.运用空间几何方法建立了一套企业三重绩效评价模型,该模型包括静态绩效评价、静态平衡度评价、动态协调度评价以及综合评价.最后,对评价模型进行了初步应用.     

预测组合权重更新的过程控制及分析

源于与决策分析的相关性,预测组合已经逐渐形成了一个重要的研究领域。为此,本文引进EWMA技术对预测组合权重更新的过程进行控制,从而提出一种能够应用于实际且简单有效的EWMA赋权方法。这种赋权方法能够确定预测组合权重应该何时更新,而不是机械地更新预测组合权重。本文额外针对各种赋权方法在旅游预测组合模型中的预测性能(全面预测性能和总均方根误差)和预测效率(权重更新频率)进行了经验评估。结果显示:EWMA赋权方法的预测性能优于传统的赋权方法,并与CUSUM赋权方法相似,同时该赋权方法获得了最小的权重更新频率。综合考虑预测性能和预测效率,EWMA赋权方法相比于其他赋权方法在旅游实际应用过程中更具优势。