Advances in Business and Management Forecasting

Kenneth D. Lawrence, Ronald K. Klimberg, Kenneth D. Lawrence, Ronald K. Klimberg

• Publisher: Emerald Publishing Limited
• Year: 2017
• Print ISBN: 9781787430709
• eBook ISBN: 9781787432567
• Topic: Business
• Subtopic: Business General
• Index: Business

Volume 12, Advances in Business and Management Forecasting, is a blind refereed serial publication. It presents state-of-the-art studies in the application of forecasting methodologies to such areas as supply chain, health care, prospecting for donations from university alumni, and the use of clustering and regression in forecasting. The orientation of this volume is for business applications for both the researcher and the practitioner of forecasting. 

Volume 12 is divided into three sections: Forecasting Applications, Predictive Analytics and Time Series. An interdisciplinary group of experts explore wide-ranging topics including multi-criteria scoring models, detecting rare events, the assessment of control charts for intermittent data, and fuzzy time series models.

SECTION C
TIME SERIES, INTERMITTENT DATA AND SUPPLY CHAIN APPLICATIONS

ASSESSING THE DESIGN OF CONTROL CHARTS FOR INTERMITTENT DATA

Matthew Lindsey and Robert Pavur

ABSTRACT

Control charts are designed to be effective in detecting a shift in the distribution of a process. Typically, these charts assume that the data for these processes follow an approximately normal distribution or some known distribution. However, if a data-generating process has a large proportion of zeros, that is, the data is intermittent, then traditional control charts may not adequately monitor these processes. The purpose of this study is to examine proposed control chart methods designed for monitoring a process with intermittent data to determine if they have a sufficiently small percentage of false out-of-control signals. Forecasting techniques for slow-moving/intermittent product demand have been extensively explored as intermittent data is common to operational management applications (Syntetos & Boylan, 2001, 2005, 2011; Willemain, Smart, & Schwarz, 2004). Extensions and modifications of traditional forecasting models have been proposed to model intermittent or slow-moving demand, including the associated trends, correlated demand, seasonality and other characteristics (Altay, Litteral, & Rudisill, 2012). Croston’s (1972) method and its adaptations have been among the principal procedures used in these applications. This paper proposes adapting Croston’s methodology to design control charts, similar to Exponentially Weighted Moving Average (EWMA) control charts, to be effective in monitoring processes with intermittent data. A simulation study is conducted to assess the performance of these proposed control charts by evaluating their Average Run Lengths (ARLs), or equivalently, their percent of false positive signals.

Keywords: Croston’s method; forecasting; slow-moving inventory; control chart

INTRODUCTION

Control charts were designed to signal when a shift in a process has occurred while having a designated ARL when the process is in-control. They are an important quality management improvement technique. Control charts are used to monitor the stability of a process and typically do not assume that non-zero values occur only intermittently. Since items with intermittent demand often account for large portions of a company’s inventory and even its revenue, modeling processes with intermittent data has received considerable attention in the forecasting literature. Modifications of forecasting methods, including Bayesian approaches, have received attention in the literature to manage inventory in supply chain applications in which intermittent demand is common (Lindsey & Pavur, 2014; Syntetos & Boylan, 2001, 2005, 2011; Willemain, Smart, & Schwarz, 2004). Control charts have not been investigated for these processes as the number of zero demand values complicates the distribution of the data.

Control charts indicate when a process is stable and only has random variation present. Control charts were developed in the 1920s as a means of identifying common variation and variation due to a special cause. Identifying special cause variation signals the need to adjust the given process. Complex systems are discussed in the literature that utilize control charts to recognize changes and choose the optimal forecasting techniques (Kadri, Harrou, Chaabane, Sun, & Tahon, 2016; Wang, Liu, & Ji, 2016; Tan, Lee, & Lam, 2015). A wide variety of industries and a wide variety of processes can be monitored with control charts. One such process that utilizes control charts with intermittent data is described by Albers (2011) who applies control charts to monitoring rare failures in health care monitoring, which has many similarities to the properties of slow-moving inventory.

Extensions of forecasting methods based on Croston’s procedure have been applied to estimating future demand of non-stationary time series that involve demand trends, correlated demand, seasonality components, and other characteristics (Altay, Litteral, & Rudisill, 2012; Lindsey & Pavur, 2013, 2016a). Additional research has examined the effect of the selection of smoothing constant (Lindsey & Pavur, 2016b). Croston’s (1972) method has proven itself overtime and is now one of the principal procedures for forecasting items with slow or intermittent demand. Estimating future demand with underlying shifts in demand rates is another challenging area of research involving Croston’s method.

Categorizing the patterns according to labels such as “erratic” or “lumpy” may allow the practitioner to better identity appropriate forecasting methods for the purposes of inventory management (Boylan & Syntetos, 2007; Syntetos, Boylan, & Croston, 2005). Willemain et al. (2004) used nine industrial datasets to assess the performance of Croston’s method, exponential smoothing, and bootstrapping. They report that the bootstrapping approach performed well especially for short lead times. An issue with intermittent data is the problem of non-stationary. Data may indeed be highly “erratic.” Croston’s method generally assumes stationarity as it uses an estimate of the Mean Time Between Demands (MTBDs) and the estimate of the demand to compute an overall long run average demand per time period. The true population value of this average demand per time period may be varying overtime. Exponential smoothing methods can be responsive since different weighting or smoothing constants can be selected appropriately. In general, Croston’s method has remained widely recommended for intermittent data despite shortcomings.

One of the improvements of Croston’s method is known as the Syntetos–Boylan Approximation (SBA) Croston method and has been recommended as a bias correction method in using Croston’s method with intermittent data. Croston’s method was recognized as providing a biased estimator for the average demand per period. Syntetos and Boylan (2005) illustrate an easy way to improve Croston method that corrects for bias. In our proposed control charts for intermittent data, the SBA method is adapted to the control chart design. This method is seen to have benefits under certain conditions when implemented in the control chart design.

LITERATURE REVIEW

Process control remains an important aspect of quality management. Whether the application is a pharmaceutical process, a service operation, or an inventory management system, control charts must be designed to assess the variation in the process accordingly using statistical characteristics of the data. Spare parts for aircraft engines requires an inventory control system in which many of the items represent a very low demand level. Health care requires statistical process control to understand if target values are being met. The changes in health often occur on an intermittent basis (Albers, 2011). The number of infections is another application in which control charts may be useful, however, the presence of low values or zero values may occur in certain time periods. In many applications, accurate estimates of the average value per time period is not as important as knowing if the process is getting worse and if a change in the process has occurred.

High demand values in supply chain applications are readily addressed in forecasting using standard forecasting methods such as exponential smoothing. Croston-type of forecasting methods can provide more accurate results when high demand values are mixed with a significant number of zeros. Croston’s (1972) technique for intermittent data has evolved into one of the most popular practices to forecast demand for intermittent and slow-moving items and has various adaptations (Ramaekers & Janssens, 2014; Teunter, Syntetos, & Babai, 2010; Xu, Wang, & Shi, 2012). Multiple benefits of Croston’s method have been documented by Willemain, Smart, Shockor, and DeSautels (1994) and Johnston and Boylan (1996). Croston’s procedure creates one forecast for the demand amount and another forecast for the time between demands and then computes a ratio to provide a single forecast. Syntetos and Boylan...

Table of contents

• Cover
• Title Page
• Section A Forecasting Applications
• Section B Predictive Analytics, Regression Analysis and Clustering in Forecasting
• Section C Time Series, Intermittent Data and Supply Chain Applications