Nezih Altay - Service Parts Management: Demand Forecasting and Inventory Control

Service Parts Management: Demand Forecasting and Inventory Control — read online for free the complete book (whole text) full work

Below is the text of the book, divided by pages. System saving the place of the last page read, allows you to conveniently read the book "Service Parts Management: Demand Forecasting and Inventory Control" online for free, without having to search again every time where you left off. Put a bookmark, and you can go to the page where you finished reading at any time.

Light

Font size:

↓

↑

Georgia Tahoma Arial Verdana

Reset

Interval:

↓

↑

Bookmark:

Make

1234567...102

Nezih Altay and Lewis A. Litteral (eds.) Service Parts Management Demand Forecasting and Inventory Control 10.1007/978-0-85729-039-7_1

Springer-Verlag London Limited 2011

1. Intermittent Demand: Estimation and Statistical Properties

Aris A. Syntetos 1

(1)

University of Salford, Salford, UK

(2)

Buckinghamshire New University, Buckinghamshire, UK

Aris A. Syntetos (Corresponding author)

Email:

John E. Boylan

Email:

Abstract

Intermittent demand patterns are very difficult to forecast and they are, most commonly, associated with spare parts requirements. Croston () showed that there is scope for improving the accuracy of Crostons method. Since then two bias-corrected Croston procedures have been proposed in the academic literature that aim at advancing the practice of intermittent demand forecasting. In this paper, these estimators as well as Crostons method and SES are presented and analysed in terms of the following statistical properties: (i) their bias (or the lack of it); and (ii) the variance of the related estimates (i.e. the sampling error of the mean). Detailed derivations are offered along with a thorough discussion of the underlying assumptions and their plausibility. As such, we hope that our contribution may constitute a point of reference for further analytical work in this area as well as facilitate a better understanding of issues related to modelling intermittent demands.

Keywords

Intermittent demand Parametric forecasting Statistical bias Forecast variance

1.1 Introduction

Intermittent demand patterns are very difficult to forecast and they are, most commonly, associated with spare parts requirements. Croston () proved the inappropriateness of single exponential smoothing (SES) in an intermittent demand context and he proposed a method that relies upon separate forecasts of the inter-demand intervals and demand sizes, when demand occurs. His method for forecasting intermittent demand series is increasing in popularity. The method is incorporated in statistical forecasting software packages (e.g. Forecast Pro), and demand planning modules of component based enterprise and manufacturing solutions (e.g. Industrial and Financial Systems-IFS AB). It is also included in integrated real-time sales and operations planning processes (e.g. SAP Advanced Planning & Optimisation-APO 4.0).

An earlier paper (Syntetos and Boylan

In this paper, these estimators as well as Crostons method and SES are presented and analysed in terms of the following statistical properties: (i) their bias (or the lack of it); and (ii) the variance of the related estimates (i.e. the sampling error of the mean). Detailed derivations are offered along with a thorough discussion of the underlying assumptions and their plausibility. As such, we hope that our contribution may constitute a point of reference for further analytical work in this area as well as facilitate a better understanding of issues related to modelling intermittent demands.

Parametric approaches to intermittent demand forecasting rely upon a lead-time demand distributional assumption and the employment of an appropriate forecasting procedure for estimating the moments of the distribution. However, a number of non-parametric procedures have also been suggested in the literature to forecast intermittent demand requirements (e.g. Willemain et al..

The remainder of this chapter is structured around two main sections: in the next section we discuss issues related to the bias of intermittent demand estimates, followed by a discussion on the issue of variance. Some concluding remarks are offered in the last section of the chapter and all the detailed derivations are presented in the Appendices.

1.2 The Bias of Intermittent Demand Estimates

1.2.1 Crostons Critique of Exponential Smoothing

Croston (), proved the inappropriateness of exponential smoothing as a forecasting method when dealing with intermittent demands and he expressed in a quantitative form the bias associated with the use of this method when demand appears at random with some time periods showing no demand at all.

He first assumes deterministic demands of magnitude occurring every p review intervals. Subsequently the demand Y t is represented by:

(1)

where n = 0,1,2 and p 1.

Conventional exponential smoothing updates estimates every inventory review period whether or not demand occurs during this period. If we are forecasting one period ahead, , the forecast of demand made in period t , is given by:

(2)

where is the smoothing constant value used, 0 1, and e t is the forecast error in period t .

Under these assumptions if we update our demand estimates only when demand occurs the expected demand estimate per time period is not , i.e. the population expected value, but rather:

(3)

where = 1 .

Croston then refers to a stochastic model of arrival and size of demand, assuming that demand sizes, Z t , are normally distributed, N (, 2), and that demand is random and has a Bernoulli probability 1/ p of occurring in every review period (subsequently the inter demand intervals, p t , follow the geometric distribution with a mean p ). Under these conditions the expected demand per unit time period is:

(4)

If we isolate the estimates that are made after a demand occurs, Croston showed that these exponentially smoothed estimates have the biased expected value:

(5)

The error, expressed as a percentage of the average demand, is shown to be 100( p 1) and reveals an increase in estimation error produced by the Bernoulli arrival of demands as compared with constant inter-arrival intervals.

1.2.2 Crostons Method

Croston, assuming the above stochastic model of arrival and size of demand, introduced a new method for characterising the demand per period by modelling demand from constituent elements. According to his method, separate exponential smoothing estimates of the average size of the demand and the average interval between demand incidences are made after demand occurs. If no demand occurs, the estimates remain the same. If we let:

Next page

1234567...102

Light

Font size:

↓

↑

Georgia Tahoma Arial Verdana

Reset

Interval:

↓

↑

Bookmark:

Make

Similar books «Service Parts Management: Demand Forecasting and Inventory Control»

Look at similar books to Service Parts Management: Demand Forecasting and Inventory Control. We have selected literature similar in name and meaning in the hope of providing readers with more options to find new, interesting, not yet read works.

Sandy Markin

SAP Integrated Business Planning: Functionality and Implementation

Edward H. Frazelle

Inventory Strategy

Nita H. Shah

Soft Computing in Inventory Management

John E. Boylan

Intermittent Demand Forecasting: Context, Methods and Applications

Pujolle

Management, Control and Evolution of IP Networks

Farrokh Sassani

Industrial Engineering Foundations: Bridging the Gap Between Engineering and Management

Ennis Siemsen

Demand Forecasting for Managers

Rana

Three Lines Forecasting Forex Price Action

Bill Price

The Best Service is No Service: How to Liberate Your Customers from Customer Service, Keep Them Happy, and Control Costs

Mark A. Moon

Demand and Supply Integration: The Key to World-Class Demand Forecasting

Arthur V. Hill

The Encyclopedia of Operations Management: A Field Manual and Glossary of Operations Management Terms and Concepts

V. Gardiner

Water Demand Forecasting

Discussion, reviews of the book Service Parts Management: Demand Forecasting and Inventory Control and just readers' own opinions. Leave your comments, write what you think about the work, its meaning or the main characters. Specify what exactly you liked and what you didn't like, and why you think so.