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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
INTERMITTENT DEMAND FORECASTING
The first text to focus on the methods and approaches of intermittent, rather than fast, demand forecasting
Intermittent Demand Forecasting is for anyone who is interested in improving forecasts of intermittent demand products, and enhancing the management of inventories. Whether you are a practitioner, at the sharp end of demand planning, a software designer, a student, an academic teaching operational research or operations management courses, or a researcher in this field, we hope that the book will inspire you to rethink demand forecasting. If you do so, then you can contribute towards significant economic and environmental benefits.
No prior knowledge of intermittent demand forecasting or inventory management is assumed in this book. The key formulae are accompanied by worked examples to show how they can be implemented in practice. For those wishing to understand the theory in more depth, technical notes are provided at the end of each chapter, as well as an extensive and up-to-date collection of references for further study. Software developments are reviewed, to give an appreciation of the current state of the art in commercial and open source software.
“Intermittent demand forecasting may seem like a specialized area but actually is at the center of sustainability efforts to consume less and to waste less. Boylan and Syntetos have done a superb job in showing how improvements in inventory management are pivotal in achieving this. Their book covers both the theory and practice of intermittent demand forecasting and my prediction is that it will fast become the bible of the field.”
—Spyros Makridakis, Professor, University of Nicosia, and Director, Institute for the Future and the Makridakis Open Forecasting Center (MOFC).
“We have been able to support our clients by adopting many of the ideas discussed in this excellent book, and implementing them in our software. I am sure that these ideas will be equally helpful for other supply chain software vendors and for companies wanting to update and upgrade their capabilities in forecasting and inventory management.”
—Suresh Acharya, VP, Research and Development, Blue Yonder.
“As product variants proliferate and the pace of business quickens, more and more items have intermittent demand. Boylan and Syntetos have long been leaders in extending forecasting and inventory methods to accommodate this new reality. Their book gathers and clarifies decades of research in this area, and explains how practitioners can exploit this knowledge to make their operations more efficient and effective.”
—Thomas R. Willemain, Professor Emeritus, Rensselaer Polytechnic Institute.
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Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
Glossary
About the Companion Website
1 Economic and Environmental Context
1.1 Introduction
1.2 Economic and Environmental Benefits
1.3 Intermittent Demand Forecasting Software
1.4 About this Book
1.5 Chapter Summary
Technical Note
2 Inventory Management and Forecasting
2.1 Introduction
2.2 Scheduling and Forecasting
2.3 Should an Item Be Stocked at All?
2.4 Inventory Control Requirements
2.5 Overview of Stock Rules
2.6 Chapter Summary
Technical Notes
3 Service Level Measures
3.1 Introduction
3.2 Judgemental Ordering
3.3 Aggregate Financial and Service Targets
3.4 Service Measures at SKU Level
3.5 Calculating Cycle Service Levels
3.6 Calculating Fill Rates
3.7 Setting Service Level Targets
3.8 Chapter Summary
Technical Note
4 Demand Distributions
4.1 Introduction
4.2 Estimation of Demand Distributions
4.3 Criteria for Demand Distributions
4.4 Poisson Distribution
4.5 Poisson Demand Distribution
4.6 Incidence and Occurrence
4.7 Poisson Demand Incidence Distribution
4.8 Bernoulli Demand Occurrence Distribution
4.9 Chapter Summary
Technical Notes
5 Compound Demand Distributions
5.1 Introduction
5.2 Compound Poisson Distributions
5.3 Stuttering Poisson Distribution
5.4 Negative Binomial Distribution
5.5 Compound Bernoulli Distributions
5.6 Compound Erlang Distributions
5.7 Differing Time Units
5.8 Chapter Summary
Technical Notes
6 Forecasting Mean Demand
6.1 Introduction
6.2 Demand Assumptions
6.3 Single Exponential Smoothing (SES)
6.4 Croston's Critique of SES
6.5 Croston's Method
6.6 Critique of Croston's Method
6.7 Syntetos–Boylan Approximation
6.8 Aggregation for Intermittent Demand
6.9 Empirical Studies
6.10 Chapter Summary
Technical Notes
7 Forecasting the Variance of Demand and Forecast Error
7.1 Introduction
7.2 Mean Known, Variance Unknown
7.3 Mean Unknown, Variance Unknown
7.4 Lead Time Variability
7.5 Chapter Summary
Technical Notes
8 Inventory Settings
8.1 Introduction
8.2 Normal Demand
8.3 Poisson Demand
8.4 Compound Poisson Demand
8.5 Variable Lead Times
8.6 Chapter Summary
Technical Notes
9 Accuracy and Its Implications
9.1 Introduction
9.2 Forecast Evaluation
9.3 Error Measures in Common Usage
9.4 Criteria for Error Measures
9.5 Mean Absolute Percentage Error and its Variants
9.6 Measures Based on the Mean Absolute Error
9.7 Measures Based on the Mean Error
9.8 Measures Based on the Mean Square Error
9.9 Accuracy of Predictive Distributions
9.10 Accuracy Implication Measures
9.11 Chapter Summary
Technical Notes
10 Judgement, Bias, and Mean Square Error
10.1 Introduction
10.2 Judgemental Forecasting
10.3 Forecast Bias
10.4 The Components of Mean Square Error
10.5 Chapter Summary
Technical Notes
11 Classification Methods
11.1 Introduction
11.2 Classification Schemes
11.3 ABC Classification
11.4 Extensions to the ABC Classification
11.5 Conceptual Clarifications
11.6 Classification Based on Demand Sources
11.7 Forecasting‐based Classifications
11.8 Chapter Summary
Technical Notes
12 Maintenance and Obsolescence
12.1 Introduction
12.2 Maintenance Contexts
12.3 Causal Forecasting
12.4 Time Series Methods
12.5 Forecasting in Context
12.6 Chapter Summary
Technical Notes
13 Non‐parametric Methods
13.1 Introduction
13.2 Empirical Distribution Functions
13.3 Non‐overlapping and Overlapping Blocks
13.4 Comparison of Approaches
13.5 Resampling Methods
13.6 Limitations of Simple Bootstrapping
13.7 Extensions to Simple Bootstrapping
13.8 Chapter Summary
Technical Notes
14 Model‐based Methods
14.1 Introduction
14.2 Models and Methods
14.3 Integer Autoregressive Moving Average (INARMA) Models
14.4 INARMA Parameter Estimation
14.5 Identification of INARMA Models
14.6 Forecasting Using INARMA Models
14.7 Predicting the Whole Demand Distribution
14.8 State Space Models for Intermittence
14.9 Chapter Summary
Technical Notes
15 Software for Intermittent Demand
15.1 Introduction
15.2 Taxonomy of Software
15.3 Framework for Software Evaluation
15.4 Software Features and Their Availability
15.5 Training
15.6 Forecast Support Systems
15.7 Alternative Perspectives
15.8 Way Forward
15.9 Chapter Summary
Technical Note
ReferencesReferences
Author Index
Subject Index
End User License Agreement
List of Tables
Chapter 3
Table 3.1 Order comprising five order lines.
Table 3.2 Distribution of demand over one week.
Table 3.3 Probability distribution of total demand over two weeks.
Table 3.4 Cumulative distribution of total demand over two weeks.
Table 3.5 Distribution of total demand over two weeks conditional on non‐zero...
Table 3.6 Fill rates per time period.
Table 3.7 Distribution of lumpy demand over one week.
Table 3.8 Traditional fill rate calculation (
and
;
).
Table 3.9 Sobel's fill rate calculation (
,
,
).
Chapter 4
Table 4.1 Triangular distribution example.
Table 4.2 Poisson probabilities (
).
Table 4.3 Calculation of chi‐square goodness of fit statistic.
Table 4.4 Example of demand incidences.
Table 4.5 Weekly demand data.
Table 4.6 Sequence of demand occurrences (1) and non‐occurrences (0).
Table 4.7 Observed and estimated order incidences over four weeks.
Table 4.8 Critical values of the chi‐square distribution for degrees of freed...
Chapter 5
Table 5.1 Poisson (
) and stuttering Poisson (
and
probabilities (prob) an...
Table 5.2 Calculation of negative binomial probabilities (
and
).
Table 5.3 Percentages of SKUs with strong fit (demand per period).
Table 5.4 Percentages of SKUs with strong fit (lead time demand).
Table 5.5 Variables to be forecasted for four demand distributions.
Table 5.6 ‘Stars and bars’ diagrams.
Chapter 6
Table 6.1 SES bias (issue points only,
) as a percentage of average demand.
Table 6.2 Intermittent demand series (first eight periods).
Table 6.3 Series of demand sizes and demand intervals.
Table 6.4 Intermittent demand series (first 10 periods).
Table 6.5 Intermittent series (after demand occurrence in period zero).
Table 6.6 Croston's bias as a percentage of average demand.
Table 6.7 Bias correction factors.
Table 6.8 Bias of SES (
) as a percentage of average demand conditional on de...
Chapter 7
Table 7.1 Updating of mean and variance using SES.
Table 7.2 Updating of variance over protection interval: scaled and direct.
Table 7.3 Distributions of demand over gamma distributed lead times.
Chapter 8
Table 8.1 Safety factors for CSL targets, normal demand.
Table 8.2 Safety factors for fill rate (FR) targets, normal demand.
Table 8.3 Asymmetric effect of under‐ and over‐forecasting.
Table 8.4 Adjusted safety factors for cycle service levels.
Table 8.5 Cycle service level for Poisson demand ((
R
+
L
)
).
Table 8.6 Fill rate for Poisson distributed demand.
Table 8.7 Cycle service levels for stuttering Poisson distributed demand.
Table 8.8 Weighted cumulative probabilities.
Table 8.9 Adjusted safety factors for fill rates.
Table 8.10
component calculations for Poisson distributed demand.
Table 8.11
calculations for Poisson distributed demand.
Table 8.12 Fill rate calculations for Poisson demand.
Table 8.13
component calculations for stuttering Poisson demand.
Chapter 9
Table 9.1 Mean error, mean square error, mean absolute error, and mean absolu...
Table 9.2 Forecast value added (FVA) example.
Table 9.3 MAPEFF and sMAPE for intermittent demand.
Table 9.4 MAE : Mean ratios for multiple series.
Table 9.5 Mean absolute error for zero forecasts.
Table 9.6 Mean error (ME) and mean absolute error (MAE).
Table 9.7 Scaled mean error for multiple series.
Chapter 10
Table 10.1 Reported usage of forecast methods in practice.
Table 10.2 Judgemental adjustments: effect on cycle service levels.
Table 10.3 Cumulative forecast error (CFE).
Table 10.4 Mean square error (frequent zeroes).
Chapter 13
Table 13.1 Cumulative frequency percentages.
Table 13.2 Three‐month overlapping blocks (OB) and non‐overlapping blocks (NO...
Table 13.3 Resampling from previous observations.
Table 13.4 VZ resampling method (
).
Table 13.5 Most recent 10 observations from Table 13.2.
Table 13.6 Conditional probabilities of demand occurrence.
Table 13.7 Simple bootstrapping with Markov chain extension..
Table 13.8 Theta function calculation (
,
), overlap of one period.
Chapter 14
Table 14.1 INAR(1) process example.
Table 14.2 INMA(1) process example.
Table 14.3 Four simplest INARMA models.
Table 14.4 Empirical evidence on model identification.
Table 14.5 Conditional probabilities of demand at time
(
) given demand at t...
Table 14.6 Cumulative conditional probabilities at time
(
) given demand at ...
Table 14.7 Cumulative probabilities of demand over two periods (
), given dem...
Chapter 15
Table 15.1 Software implementation.
List of Illustrations
Chapter 1
Figure 1.1 Intermittent and lumpy demand.
Chapter 2
Figure 2.1 Bill of materials (BoM) example.
Figure 2.2 Periodic review and continuous review systems.
Figure 2.3 Continuous review
and
policies for unit sized transactions.
Figure 2.4 Periodic review
policy.
Chapter 3
Figure 3.1 Comparison of CSL and
.
Figure 3.2 Exchange curve.
Figure 3.3 RightStock Inventory Strategist.
Chapter 4
Figure 4.1 Monthly demand time series for an automotive SKU.
Figure 4.2 Demand frequencies for an automotive SKU.
Figure 4.3 Demand relative frequencies with triangle superimposed.
Figure 4.4 Actual relative frequencies and triangular probabilities.
Figure 4.5 Poisson distribution for varying mean (
) values.
Figure 4.6 Poisson probabilities and actual relative frequencies.
Figure 4.7 Variance and mean of weekly order frequencies.
Chapter 5
Figure 5.1 Geometric distribution (
).
Figure 5.2 Standard deviation and mean of demand sizes. Source: Johnston et ...
Figure 5.3 Frequency distribution of order sizes. Source: Johnston et al. 20...
Figure 5.4 Logarithmic distribution (
= 0.33, 0.66, 0.99).
Figure 5.5 Exponential distributions. (a) Probability density; (b) Cumulativ...
Figure 5.6 Erlang distributions.
Figure 5.7 Normal distribution (poor approximation).
Figure 5.8 Normal distribution (better approximation).
Chapter 6
Figure 6.1 Weights of previous observations. (a)
. (b)
.
Figure 6.2 SES response to a step‐change. (a)
. (b)
.
Figure 6.3 SES bias for issue points only (
).
Figure 6.4 Forecast initialisation and optimisation.
Figure 6.5 ADIDA forecasting framework.
Figure 6.6 Comparison of model forms.
Chapter 8
Figure 8.1 Standard normal distribution.
Figure 8.2 Normally distributed demand and OUT levels.
Chapter 9
Figure 9.1 Errors and absolute (‘Abs’) errors.
Figure 9.2 Non‐uniform distributions of randomised PITs.
Figure 9.3 Exchange curves.
Chapter 10
Figure 10.1 Cumulative demands and forecasts.
Figure 10.2 Squared error decomposition.
Figure 10.3 (Extended) squared error decomposition.
Chapter 11
Figure 11.1 Customer demand and forecasting.
Figure 11.2 Categorisation of non‐normal demand patterns.
Figure 11.3 Categorisation based on sources of demand characteristics.
Figure 11.4 Categorisation by mean square error: SES (issue points,
) vs. C...
Figure 11.5 Categorisation by mean square error: SES vs. SBA.
Chapter 12
Figure 12.1 Maintenance generated demand and forecasting.
Figure 12.2 Life cycle stages.
Figure 12.3 TSB and Croston forecasts.
Figure 12.4 Forecasting in context.
Figure 12.5 Inventory‐forecasting interactions.
Chapter 13
Figure 13.1 Intermittent series.
Figure 13.2 Cumulative frequency percentages: three‐month overlapping blocks...
Figure 13.3 Proportional reduction in variance of CDF estimates by using OB ...
Figure 13.4 Cumulative frequency percentages (OB, NOB, and bootstrap).
Chapter 14
Figure 14.1 Demand transitions from one period to the next.
Guide
Cover
Table of Contents
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Intermittent Demand Forecasting
Context, Methods and Applications
John E. Boylan
Lancaster University
Lancaster, UK
Aris A. Syntetos
Cardiff University
Cardiff, UK
This edition first published 2021
© 2021 John Wiley & Sons Ltd
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.
The right of John E. Boyan and Aris A. Syntetos to be identified as the authors of this work has been asserted in accordance with law.
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The contents of this work are intended to further general scientific research, understanding, and discussion only and are not intended and should not be relied upon as recommending or promoting scientific method, diagnosis, or treatment by physicians for any particular patient. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of medicines, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each medicine, equipment, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
Library of Congress Cataloging‐in‐Publication Data applied for
ISBN 978-1-119-97608-0 (hardback); LCCN - 2021011006
Cover Design: Wiley
Cover Image: Mata Atlantica - Atlantic Forest in Brazil © FG Trade/Getty Images, Turbine © Brasil2/Getty Images
For Jan and Rachel
Preface
The images on the front of this book highlight a crucial tension for all advanced economies. There is a desire to travel more and consume more, but also a growing awareness of the detrimental effects that this is having on the environment. There is a belated realisation that those of us living in countries with developed economies need to consume less and waste less.
Waste can occur at all stages of the supply chain. Consumers may buy food they never eat or clothes they never wear. Retailers and wholesalers may order goods from manufacturers that never sell. These wastages can be significantly reduced by better demand forecasting and inventory management. Some items conform to regular demand patterns and are relatively easy to forecast. Other items, with irregular and intermittent demand patterns, are much harder.
Wastage can be addressed by changes in production, moving away from built‐in obsolescence and towards products that can be maintained and repaired economically. For this to be an attractive proposition, spare parts need to be readily available. Unfortunately, these items are often the most difficult to forecast because many of them are subject to the sporadic nature of intermittent demand. Although there have been significant advances in intermittent demand forecasting over recent decades, these are not all available in commercial software. In the final chapter of this book, we highlight the progress that has been made, including methods that are freely available in open source software.
The reasons for the slow adoption of new forecasting methods and approaches in commercial software are varied. We believe that one of the reasons is a lack of appreciation of the benefits that may accrue. Because intermittent demand items are so difficult to forecast, it may be thought that highly accurate forecasting methods can never be found. This may be true. However, it is possible to find more accurate methods, which can contribute towards significant improvements in inventory management.
There is also a need for greater awareness of the methods that have been developed in recent years. Information on them is scattered amongst a variety of academic journals, and some of the articles are highly technical. Therefore, we have set ourselves the challenge of synthesizing this body of knowledge. We have endeavoured to bring together the main strands of research into a coherent whole, and assuming no prior knowledge of the subject.
There are various perspectives from which demand forecasting can be addressed. One option would be to take an operations management view, with a focus on forecasting and planning processes. Another would be to take a more statistical perspective, starting with mathematical models and working through their properties. While some of our material has been influenced by these orientations, the dominant perspective of this book is that of operational research (OR). The start point of OR should always be the real‐life situation that is encountered. This means that it is essential to gain an in‐depth understanding of inventory systems and how forecasts inform these decisions. Such an appreciation enables a sharper focus on forecasting requirements and the appropriate criteria for a ‘good forecast’.
In this book, the first three chapters focus on the inventory management context in which forecasting occurs, including the inventory policies and the service level measures that are appropriate for intermittent demand. Recognising the interconnection between inventory policies, demand distributions, and forecasting methods, the next two chapters focus on demand distributions, including evidence from studies of real‐world data. The following two chapters concentrate on forecasting methods, with discussion of practical issues that must be addressed in their implementation. We then turn to the linkage between forecasts and inventory availability, and review how forecast accuracy should be measured and how its implications for inventories should be assessed. We also look at how stock keeping units should be classified for forecasting purposes, and examine methods designed specifically to address maintenance and obsolescence. The next two chapters deal with methods that can tackle more challenging demand patterns. We conclude with a review of forecasting software requirements and our views on the way forward.
We are grateful to those pioneers who inspired us to study this subject, and who have given us valuable advice over the years, especially John Croston, Roy Johnston, and Tom Willemain. We would like to express our thanks to those who commented on draft chapters of this book: Zied Babai, Stephen Disney, Robert Fildes, Thanos Goltsos, Matteo Kalchschmidt, Stephan Kolassa, Nikos Kourentzes, Mona Mohammadipour, Erica Pastore, Fotios Petropoulos, Dennis Prak, Anna‐Lena Sachs, and Ivan Svetunkov; and to Nicole Ayiomamitou and Antonis Siakallis who helped with the figures.
Lancaster and Cardiff
January 2021
John E. Boylan
Aris A. Syntetos
Glossary
ADIDA
aggregate–disaggregate intermittent demand approach
AIC
Akaike information criterion
AR
autoregressive
ARIMA
autoregressive integrated moving average
ARMA
autoregressive moving average
APE
absolute percentage error
BO
backorder
BoM
bill of materials
BS
Brier score
CDF
cumulative distribution function
CFE
cumulative forecast error
CSL
cycle service level (all replenishment cycles)
cycle service level (replenishment cycles with some demand)
CV
coefficient of variation
EDF
empirical distribution function
ERP
enterprise resource planning
FMECA
failure mode, effects, and criticality analysis
FR
fill rate
FSS
forecast support system
FVA
forecast value added
HES
hyperbolic exponential smoothing
INAR
integer autoregressive
INARMA
integer autoregressive moving average
INMA
integer moving average
IP
inventory position
KS
Kolmogorov–Smirnov (test)
LTD
lead‐time demand
MA
moving average
MAD
mean absolute deviation
MAE
mean absolute error
MAPE
mean absolute percentage error
MAPEFF
mean absolute percentage error from forecast
MASE
mean absolute scaled error
ME
mean error
MMSE
minimum mean square error
MPE
mean percentage error
MPS
master production schedule
MRO
maintenance, repair, and operations
MRP
material requirements planning
MSE
mean square error
MSOE
multiple source of error
MTO
make to order
MTS
make to stock
NBD
negative binomial distribution
NN
neural network
NOB
non‐overlapping blocks
OB
overlapping blocks
OUT
order up to
PIS
periods in stock
PIT
probability integral transform
RMSE
root mean square error
rPIT
randomised probability integral transform
S&OP
sales and operations planning
SBA
Syntetos–Boylan Approximation (method)
SBC
Syntetos–Boylan–Croston (classification)
SCM
supply chain management
SES
single (or simple) exponential smoothing
SKU
stock keeping unit
SLA
service level agreement
SMA
simple moving average
sMAPE
symmetric mean absolute percentage error
sMSE
scaled mean square error
SOH
stock on hand
SOO
stock on order
SSOE
single source of error
TSB
Teunter–Syntetos–Babai (method)
VZ
Viswanathan–Zhou (method)
WMH
Wright Modified Holt (method)
WSS
About the Companion Website
This book is accompanied by a companion website.
www.wiley.com/go/boylansyntetos/intermittentdemandforecasting
This website includes:
Datasets (with accompanying information)
Links to R packages
1Economic and Environmental Context
1.1 Introduction
Demand forecasting is the basis for most planning and control activities in any organisation. Unless a forecast of future demand is available, organisations cannot commit to staffing levels, production schedules, inventory replenishment orders, or transportation arrangements. It is demand forecasting that sets the entire supply chain in motion.
Demand will typically be accumulated in some pre‐defined ‘time buckets’ (periods), such as a day, a week, or a month. The determination of the length of the time period that constitutes a time bucket is a very important decision. It is a choice that should relate to the nature of the industry and the volume of the demand itself but it may also be dictated by the IT infrastructure or software solutions in place. Regardless of the length of the time buckets, demand records eventually form a time series, which is a sequence of successive demand observations over time periods of equal length.
On many occasions, demand may be observed in every time period, resulting in what is sometimes referred to as ‘non‐intermittent demand’. Alternatively, demand may appear sporadically, with no demand at all in some periods, leading to an intermittent appearance of demand occurrences. Should that be the case, contribution to revenues is naturally lower than that of faster‐moving demand items. Intermittent demand items do not attract much marketing attention, as they will rarely be the focus of a promotion, for example. However, they have significant cost implications for a simple reason: there are often many of them!
Service or spare parts are very frequently characterised by intermittent demand patterns. These items are essentially components or (sub‐) assemblies contributing to the build‐up of a final product. However, they face ‘independent demand’, which is demand generated directly from customers, rather than production requirements for a particular number of units of the final product. In the after‐sales environment (or ‘aftermarket’), we deal exclusively with ‘independent demand’ items. Service parts facing intermittent demand may represent a large proportion of an organisation's inventory investment. In some industries, this proportion may be as high as 60% or 70% (Syntetos 2011). The management of these items is a very important task which, when supported by intelligent inventory control mechanisms, may yield dramatic cost reductions.
Industries that rely heavily on after‐sales support, including the automotive, IT, and electronics sectors, are dominated by intermittent demand items. The contributions of the after‐sales services to the total revenues of organisations in these industries have been reported to be as high as 60% (Johnston et al. 2003). This signifies an opportunity not only to reduce costs but also to increase revenues through a careful balancing of keeping enough in stock to satisfy customers but not so much as to unnecessarily increase inventory investments. There are tremendous economic benefits that may be realised through the reappraisal of managing intermittent demand items.
There are also significant environmental benefits to be realised by such a reappraisal. Because of their inherent slow movement, intermittent demand items are at the greatest risk of obsolescence. The problem is exacerbated by the greatly reduced product life cycles in modern industry. This affects the planning process for all intermittent demand items (both final products and spare parts used to sustain the operation of final products). Better forecasting and inventory decisions may reduce overall scrap and waste. Furthermore, the sustained provision of spare parts may also reduce premature replacement of the original equipment.
The area of intermittent demand forecasting has been neglected by researchers and practitioners for too long. From a business perspective, this may be explained in terms of the lack of focus on intermittent demand items by the marketing function of organisations. However, the tough economic conditions experienced from around 2010 onwards have resulted in a switch of emphasis from revenue maximisation to cost minimisation. This switch repositions intermittent demand items as the focus of attention in many companies, as part of the drive to dramatically cut down costs and remain competitive. In addition, the more recent emergence of the after‐sales business as a major determinant of companies' success has also led to the recognition of intermittent demand forecasting as an area of exceptional importance.
Following a seminal contribution in this area by John Croston in 1972, intermittent demand forecasting received very little attention by researchers over the next 20 years. This was in contrast to the extensive research conducted on forecasting faster‐moving demand items. Research activity grew rapidly from the mid‐1990s onwards, and we have now reached a stage where a comprehensive body of knowledge, both theoretical and empirical, has been developed in this area. This book aims to provide practitioners, students, and academic researchers with a single point of reference on intermittent demand forecasting. Although there are considerable openings for further advancements, the current state of knowledge offers organisations significant opportunities to improve their intermittent demand forecasting. Numerous reports, to be discussed in more detail later in this chapter, indicate that intermittent demand forecasting is one of the major problems facing modern organisations. Specialised software packages offer some forecasting support to companies but they often lag behind new developments. There are great benefits that have not yet been achieved in this area, and we hope that this book will make a contribution towards their realisation.
There are three main audiences for this book:
Supply chain management
(
SCM
) practitioners, broadly defined, who wish to realise the full benefits of managing intermittent demand items.
Software designers wanting to incorporate new developments in forecasting into their software.
Students and academics wishing to learn and incorporate into their curricula, respectively, the state of the art in intermittent demand forecasting.
In summary, business pressures to reduce costs and environmental pressures to reduce scrap (often introduced in the form of prescribed policies imposed by national governments or the EU for example) render intermittent demand items, and forecasting their requirements, one of the most important areas in modern organisations.
There are great benefits associated with forecasting intermittent demand more accurately, and those benefits are far from being realised. This may be explained by the well reported innovation–adoption gap, which arises from the divergence between innovations and real‐world practices. Organisational practices typically lag behind software developments, and software developments typically lag behind the state of the art in the academic literature. It is the aim of this book to bridge these gaps and show how intelligent intermittent demand forecasting may result in significant economic and environmental benefits.
In the remainder of this chapter, we first discuss in more detail the potential benefits that may be realised through improved intermittent demand forecasting. We then provide an overview of the current state of supply chain software packages and enterprise resource planning (ERP) solutions with regard to intermittent demand forecasting. This is followed by a section where we elaborate on both the structure of this book and the perspective that we take regarding the material presented here. We close with a summary of the chapter.
1.2 Economic and Environmental Benefits
Intermittent demand for products appears sporadically, with some time periods showing no demand at all. Moreover, when demand occurs, the demand size may be constant or variable, perhaps highly so, leading to what is often termed ‘lumpy demand’. Later in this chapter, we discuss why forecasting sporadic and lumpy demand patterns is a very difficult task. Specific characterisations of intermittent demand series are considered in detail in Chapters 4 and 5.
1.2.1 After‐sales Industry
Intermittent demand items dominate service and repair parts inventories in many industries (Boylan and Syntetos 2010). A survey by Deloitte Research (2006) benchmarked the service businesses of many of the world's largest manufacturing companies with combined revenues reaching more than $1.5 trillion; service operations accounted for an average of 25% of revenues. In addition to their contribution to revenues, these items present a distinct opportunity for cost reductions. Maintenance, repair, and operations (MRO) inventories typically account for as much as 40% of the annual procurement budget (Donnelly 2013). Increased revenues and reduced costs naturally lead to increased profits. Many organisations have repeatedly testified to the importance of after‐sales services for their businesses and the profits they generate. Companies such as Beretta, Canon, DAF Trucks, Electrolux, EPTA, GE Oil & Gas, and Lavapiu have reported contributions of the after‐sales services to their total profit of up to 50% (Syntetos 2011). Comparable numbers have been reported by Gaiardelli et al. (2007), Kim et al. (2007), and Glueck et al. (2007), while after‐sales service has been identified as a key profit lever in the manufacturing sector (Manufacturing Management 2018).
Intermittent demand items are at the greatest risk of obsolescence. Many case studies (e.g. Molenaers et al. 2012) have documented large proportions of ‘dead’ (obsolete) stock in a variety of industries, with serious environmental implications. However, under‐stocking situations may be as harmful, given the potentially high criticality of the items involved. In civil aviation, for example, lack of spare parts is one of the major causes of ‘aircraft on ground’ events (problems serious enough to prevent aircraft from flying). Badkook (2016) found that a quarter of the aircraft in an (un‐named) airline's Boeing 777 fleet were affected by such aircraft on ground events over a year.
1.2.2 Defence Sector
Defence inventories, which are highly reliant on spare parts, have been repeatedly identified as a high risk area with a direct impact on a nation's economy. In the United States for example, the Department of Defense (DoD) manages around five million secondary items. These include repairable components, subsystems, assemblies, consumable repair parts, and bulk items. They reported that, as of September 2017, the value of the inventory was $93 billion (GAO 2019). Although a matter of concern, there had been no substantial reductions in inventory values over the previous decade (being, for example, $95 billion in 2013 and 2010; GAO 2012, 2015).
A major determinant of the performance of an inventory system is the forecasting method(s) being used to predict demand. Inaccurate forecasts lead to either excess inventory or shortfalls, depending on the direction of the forecast error. Over‐forecasting can lead to holding stocks that are simply not needed. According to the US Government Accountability Office (GAO 2011, p. 11), ‘Our recent work identified demand forecasting as the leading reason why the services and DLA [Defense Logistics Agency] accumulate excess inventory’.
Unfortunately, progress in improving forecasting and inventory management has been slow in many industries, with the defence industry being a case in point. The GAO of the United States reported, ‘Since 1990, we have identified DoD [Department of Defense] supply chain management as a high‐risk area due in part to ineffective and inefficient inventory management practices and procedures, weaknesses in accurately forecasting the demand for spare parts, and other supply chain challenges. Our work has shown that these factors have contributed to the accumulation of billions of dollars in spare parts that are excess to current needs’ (GAO 2015, p. 2). Progress in inventory management has been made since then, especially with regard to the visibility of physical inventories, receipt processing, and cargo tracking (GAO 2019). These improvements in information systems have led to inventory management being removed from the list of high‐risk areas. However, it is notable that no claims have yet been made for corresponding improvements in demand forecasting.
1.2.3 Economic Benefits
Moving beyond the after‐sales industry, and the defence sector, we now examine the potential benefits that may result from intelligent intermittent demand forecasting for the wider economy. Purchased goods inventories and their management are significant concerns for firms wishing to remain competitive and survive in the marketplace. According to the 26th Annual State of Logistics report (CSCMP 2015, statistics referring to 2014), the United States alone has been sitting on approximately $2 trillion worth of goods held for sale. According to the same report, the inventory carrying costs (taxes, obsolescence, depreciation, and insurance) are estimated to be around $0.5 trillion (i.e. about 25% of the value of the goods). The total value of inventory was equivalent to approximately 14% of the US gross domestic product (GDP) in 2014. Although similar statistics have not been given in subsequent publications, the 30th Annual State of Logistics Report (CSCMP 2019) revealed that inventory carrying costs in the United States increased by 14.8% between 2014 and 2018.
These figures show that a huge amount of capital is tied up in warehouses. They also indicate that small improvements in managing inventories may be translated into considerable cost benefits. We should, therefore, not be surprised to learn that firms, from manufacturing to wholesale to retail, are currently intensifying their search for more efficient and effective inventory management approaches. Their aim is to minimise not only their direct investments in purchased goods inventory but also the indirect cost incurred in managing this inventory. In a make to stock (MTS) environment (discussed in Section 1.4.2), if there is no decoupling in terms of the ownership and location of the inventories, then these indirect costs become more significant the longer the stock remains unsold. The high volumes of stocks of intermittent demand items, and their high risk of obsolescence, should put them very high up the list of priorities for modern businesses.
1.2.4 Environmental Benefits
Obsolescence is a very important topic for supply chain management. The complexity of supply chains, in conjunction with increasingly reduced product life cycles, is resulting in high levels of obsolescence. Molenaers et al. (2012) discussed a case study where 54% of the parts stocked at a large petrochemical company had seen no demand for the last five years. Syntetos et al. (2009b) evaluated the inventory practices employed in the European spare parts logistics network of a Japanese manufacturer. They found one case, reported in Sweden, where some parts in stock had not ‘moved’ at all over the preceding 10 years. The value of the on‐hand excess (spare parts) inventory of the US Air Force, Navy, and Army has been estimated to be of $1.7 billion, $1.4 billion, and $2.5 billion, respectively (GAO 2015). Much of this excess stock is at risk of obsolescence.
When obsolescent (or ‘dead’) stock is created, there is considerable environmental waste. Firstly, there is an environmental cost associated with producing goods that are never used. Secondly, there are environmental costs of transporting these goods to national, regional, or local stocking points. Finally, there are environmental costs of disposing of these stocks. The prevention of the accumulation of dead stock relies on accurate demand forecasts. Consequently, more accurate and robust forecasting methods may be translated to significant reductions in wastage or scrap, with considerable environmental benefits.
1.2.5 Summary
More accurate forecasting of intermittent demand presents organisations with a distinct opportunity to reduce costs and address major issues on their environmental agenda. In the after‐sales context, intelligent intermittent demand forecasting is of paramount importance, as many items have demand patterns that are intermittent in nature. Other inventory settings that are dominated by spare parts (e.g. the military, public utilities, and aerospace) would also benefit directly from more accurate intermittent demand forecasting methods.
1.3 Intermittent Demand Forecasting Software
Given the relevance of intelligent forecasting methods in modern organisations, it is vital that they are included in software solutions. The continuous update of software to reflect research developments in the area of intermittent demand forecasting is of great financial and environmental importance. Forecasting software solutions are briefly reviewed in this section and revisited in greater detail in Chapter 15.
1.3.1 Early Forecasting Software
Early forecasting software solutions in the 1950s and 1960s were based on single exponential smoothing (SES) (a method that is discussed in detail in Chapter 6), meaning that intermittent demand items were not treated any differently from fast‐moving items. SES is a method devised for fast‐moving items that exhibit no trend or seasonality. It is a very practical forecasting method for these items, and is included in the vast majority of (inventory) forecasting software applications. It is still used for intermittent demand, although we shall see in Chapter 6 that it is not a natural method for these items and it does suffer from some major weaknesses.
1.3.2 Developments in Forecasting Software
Software packages have since moved on, with most, but not all, packages offering methods that are designed for intermittent demand. Croston's (1972) method, for example, was developed specifically for intermittent demand items, and 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 and Optimisation [SAP APO] and SAP Digital Manufacturing).
Similarly, more recent developments in demand categorisation (rules that distinguish between various types of demand patterns and signify when a pattern should be treated as intermittent) have also been adopted in some commercial software (e.g. Blue Yonder, Syncron International), allowing their clients the capability to achieve some dramatic inventory cost reductions (Research Excellence Framework 2014). However, the adoption of recent developments has not been widespread, and there are many software packages that have limited functionality. Overall, there have been rather minor improvements in commercial software since around 2000 despite some major improvements in empirically tested theory since that time.
1.3.3 Open Source Software
Another important development, to be discussed in detail in Chapter 15, is the availability of open source software of recently proposed intermittent demand forecasting methods. This enables companies to incorporate them in their own in‐house developed solutions, or for commercial software companies to extend their repertoire of methods more readily. Furthermore, sophisticated database systems are enabling companies to ‘slice and dice’ their data more easily. This means that data may be examined more readily by segments, such as geographical regions or product groupings, in forecasting and planning software (e.g. Forecast Pro, Smoothie). This provides the groundwork for implementing developments in forecasting at different levels of aggregation (to be discussed in detail in Chapter 6). However, whilst software solutions are moving ahead by embracing slicing and dicing, they do not do so in terms of new forecasting methods (including those that take advantage of slicing and dicing). There are significant opportunities offered by open source software and modern data analytics to improve the forecasting functionality of commercial software.
1.3.4 Summary
There have been some very promising advances in the area of intermittent demand forecasting, some of which have found their way into software applications. However, much still remains to be done in terms of software companies keeping up with important methods that have recently been developed and particularly those that have been empirically tested and shown to yield considerable benefits.
1.4 About this Book
In this section we briefly review the stance taken, the scope of discussion, and the structure of the book.
1.4.1 Optimality and Robustness
Intermittent demand patterns are very difficult to model and forecast. It is the genuine lack of sufficient information associated with these items (due to the presence of zero demands) that may preclude the identification of series' components such as trend and seasonality. Demand histories are also very often limited, which makes things even worse. Demand arrives sporadically and, when it does so, it may be of a quantity that is difficult to predict. The actual demand sizes (positive demands) may sometimes be almost constant or consistently small in magnitude. Alternatively, they may be highly variable, leading to ‘erratic’ demand. Intermittence coupled with erraticness leads to what is known as ‘lumpy’ demand. The graph in Figure 1.1 shows examples of intermittent and lumpy demand patterns, based on annual demand history for two service parts used in the aerospace industry.
From Figure 1.1, two things become apparent: (i) the annual demand history contains only five positive demand observations and (ii) variability refers to both the demand arrivals (how often demand arrives) and the size of the demand, when demand occurs. The lack of information associated with intermittent demand patterns coupled with this dual source of variability calls for simplifying assumptions when modelling these patterns. A common simplifying assumption is that the demand is non‐seasonal. Such simplifications may impede the development of solutions that are optimal in a statistical sense, but do allow for the development of methods that potentially are very robust and easy to implement. Robustness is defined here as a ‘sufficiently good’ performance across a wide range of possible conditions. Optimality is defined, for particular conditions, as the ‘best’ performance.
Figure 1.1 Intermittent and lumpy demand.
Source: Boylan and Syntetos (2008). ©2008, Springer Nature.
We shall return to robustness and statistical optimality in later chapters but, for the time being, it is sufficient to say that robustness is essential in practical applications. While optimality is desirable, it should not be at the expense of robustness. Many of the methods to be discussed in this book have been found to be robust by such software companies as Blue Yonder, LLamasoft, Slimstock, and Syncron International, helping their customers to dramatically reduce inventory costs.
1.4.2 Business Context
With robustness in mind, this book presents a range of approaches to intermittent demand forecasting that are applicable in any industrial make to stock (MTS) setting. In addition to an MTS setting, unless otherwise specified, we focus on single stock keeping unit (SKU), single stocking location environments, as explained below.
Make to stock. In an MTS environment, customers are willing to wait no more than the time it takes to deliver the particular item to them and so the item needs to be available in stock, ready to be dispatched, or, in the case of retailing, it needs to be available on the shelf. In this case, demand is not known and needs to be predicted. The alternative environment is known as make to order (MTO), where the products are not assumed to be in stock, and the customer must wait until the manufacturer assembles the product for them. In this case, customer demand is known and does not need to be predicted. This situation is common for some products (e.g. furniture) but not for others (e.g. automotive or aerospace spare parts). There is also a move to 3D printing of products in some industries, which is a form of MTO but with shorter delays (Technical Note 1.1).
Single stock keeping unit (SKU) approaches. We are looking at forecasting the requirements (and managing the inventories) of single SKUs. Although some of the methods to be discussed in this book rely upon collective considerations (across a group of SKUs), the rest of the material considers single SKU problems. This is because higher levels of aggregation are, typically, not associated with intermittent demand. Consider, for example, 10 intermittent demand items, all of which are replenished from the same supplier. It makes sense to consider the aggregate demand of those items to facilitate efficient transportation arrangements. However, although demand at the individual SKU level may be intermittent, aggregate demand (across all 10 SKUs), most probably, will not be intermittent.
Single stocking location approaches. We focus on determining inventory replenishment requirements at each single location, without taking into account interactions between locations. As such, we do not consider the possibility of satisfying demand by lateral transshipments of stocks between stores. This is because these decisions relate explicitly to joint inventory‐transportation optimisation, which is beyond the scope of this book. Further, and as discussed above, aggregate demand (across different locations in this case) is typically not associated with intermittence.
We should also mention that, although the term ‘demand’ is being used in this book when referring to forecasting, demand will not always be known and, in this case, actual sales must be used as a proxy. The terms ‘demand’ and ‘sales’ are used interchangeably in this book although, strictly speaking, the latter is often used as an approximation for the former.
1.4.3 Structure of the Book
This book starts by contextualising intermittent demand forecasting in the wider scholarship and practice of inventory management. We begin in Chapter 2 with a discussion of inventory management and some of its implications for forecasting. Then, in Chapter 3, we examine the service drivers of inventory performance. The focus shifts in Chapters 4 and 5 to the characterisation of intermittent demand patterns by demand distributions. This forms a natural foundation for the next two chapters, which focus on forecasting methods. Chapter 8 takes us back to inventory replenishment and the linkage between forecasting and inventory control. In the next chapter, we move on to the measurement of forecasting accuracy and inventory performance. Forecasting accuracy assessment is a notoriously difficult problem for intermittent series, and the chapter highlights the traps for the unwary and gives some pointers to good practice.
Although the main emphasis of this book is on forecasting, classification methods are also important in practical applications. In Chapter 10, we lay some of the groundwork for classification methods, discussed in Chapter 11, which have been designed specifically to address intermittence. In the next chapter, we turn our attention to obsolescence and forecasting methods that are particularly suited to this stage of the life cycle. Chapter 13 presents an alternative perspective on demand forecasting, concentrating on methods that do not assume any particular form of demand distribution. By contrast, Chapter 14 delves more deeply into methods that are based on demand distributions. The book closes with Chapter 15, which contains a discussion of software solutions for intermittent demand forecasting.
1.4.4 Current and Future Applications
Recent IT developments have greatly expanded the areas of application of intelligent intermittent demand forecasting methods. Data at a very low level of granularity have become available, which means that environments where traditionally intermittence would not be a problem now become natural candidates for further consideration. Take the retailing sector as an example: this is a traditionally fast demand environment where even the slower moving items sell in considerable volumes every day, making intermittent demand forecasting redundant. However, the current availability and utilisation of data for replenishment purposes, as often as three times per day, means that more items have intermittent demand. Although daily demand may not be intermittent, half‐daily demand could be, and demand over a third of a day most probably will be.
Another factor in retail, highlighted by Boylan (2018), is the broadening of product ranges in larger retail outlets, with grocery stores introducing more clothing lines, for example. These items will often be slower moving than staple food ranges, thereby increasing the proportion of intermittent items. Recent discussions with major supermarkets in the United Kingdom such as Sainsbury's and Tesco indicate that intermittent demand forecasting has become one of their major problems.
Intermittent series occur in many other settings. For example, the planning of inventories for emergency relief must address highly intermittent and lumpy demand. Indeed, the benefits of good forecasting and planning (for any type of series) apply just as much to charitable and not‐for‐profit organisations as they do for profit‐making wholesalers and retailers. Support for the promotion and realisation of these wider benefits is being offered at the time of writing by the ‘Forecasting for Social Good’ (www.f4sg.org) and ‘Democratising Forecasting’ initiatives launched in 2018 by Dr Bahman Rostami‐Tabar.
Nikolopoulos (2021) made a strong case for the use of intermittent forecasting methods for series that are not intermittent but have sporadic peaks. These time series can be decomposed into two subseries: a baseline series and one containing more extreme values. Standard time series or causal methods can be used for the former. The latter include rare but expected events (‘grey swans’) and truly unexpected special events (‘black swans’) (Taleb 2007) and can be addressed using intermittent forecasting methods, at least as a benchmark against which other methods may be compared. Methods to address intermittence have their origins in inventory planning, but Nikolopoulos (2021) argued that these forecasting methods can be used more widely in business, finance, and economics or, indeed, in any other discipline. This line of enquiry will not be pursued in this book, although it seems a very promising direction for future research.
1.4.5 Summary
The material presented in this book reflects the authors' emphasis on robust solutions that may perform well under a wide range of differing conditions. We present the state of the art in intermittent demand forecasting, paying particular attention to the interface between forecasting and stock control. There is a very considerable market for the application of those methods, and this can only expand as more highly granular data become available.
1.5 Chapter Summary
The associated cost of inventories of purchased goods has been estimated to be between 25% and 35% of the value of those goods (e.g. Chase et al. 2006): a firm carrying $20 million in purchased goods inventory would, accordingly, incur additional costs of $5–7 million. These are costs that, once reduced, can significantly improve the firm's net profits (Wallin et al. 2006). The total cost of purchased goods inventory can be quite alarming, calling for innovative approaches to cut it down. Intelligent intermittent demand forecasting offers such opportunities.
In the defence environment, Henry L. Hinton Jr, Assistant Comptroller General, National Security and International Affairs Division, stated, ‘Our work continues to show weaknesses in DoD's inventory management practices that are detrimental to the economy’ (GAO 1999, p. 1). Sixteen years later, only minor improvements were reported (GAO 2015), and public announcements on the poor management of defence inventories and the resulting detrimental impacts on the economy constitute a recurring issue in the news. Similarly, the expansion of the after‐sales industry and the increasing importance of commercial service operations have not been adequately reflected in the development of ERP and supply chain software packages, the functionality of which has often been judged to be inadequate (Syntetos et al. 2009b). In addition to the after‐sales and MRO environment and the military sector, intermittent demand items dominate the inventories in a wide range of industries, calling for improved solutions for their cost‐effective management.
There have been rather minor improvements in practical applications in this area since around 2000, but there have been major improvements in empirically tested theory since that time. Many of these theoretical advancements have not yet been incorporated in commercial software, and hence, there are major opportunities for improving real‐world applications. We hope this book will help towards moving in that direction.
Technical Note
Note 1.1 3D Printing
An alternative form of MTO, enabled by advances in additive manufacturing, is 3D Printing (3DP) an item on demand. In this case, decision‐making relates to the level of investment in 3DP machinery/technology that may ‘print’ the requested number of items upon demand. Potentially, this is very appealing in the case of spare parts and is currently being explored by various organisations seeking to cut down their inventories. For example, in 2018 the Dutch Army initiated a collaboration with the 3DP company DiManEx to examine spare part supply challenges. At the time of writing, there is no empirical evidence on the effect of 3DP on spare parts inventory management and how this compares with MTS approaches.
2Inventory Management and Forecasting
2.1 Introduction
In the previous chapter, we showed that the management of intermittent demand items is an important task for many organisations. These items require certain operational decisions to be taken at the level of an individual stock keeping unit (SKU) including whether to stock the item at all and, if so, how much to stock. Both of these decisions will be addressed in this chapter. We discuss the major inventory replenishment policies and their appropriateness for intermittent demand items. This is the foundation for inventory forecasting and is an essential component of all software dedicated to inventory management. We also consider what forecasts are important when demand is intermittent. The interface between forecasting and stock control has been rather neglected in the academic literature although it is vital in real‐world inventory applications.
2.2 Scheduling and Forecasting
Before discussing the integration of forecasting and inventory control for intermittent demand items, a distinction needs to be made between the inventory management practices required for dependent and independent demand items.
2.2.1 Material Requirements Planning (MRP)
The design and construction of any physical product is captured in its bill of materials (BoM) which, as illustrated in Figure 2.1, shows the product's assemblies (middle level) and components (bottom level). Demand at the top level, corresponding to the end product, is defined as ‘independent’, whereas demand at lower levels in the hierarchy is dependent on demand at higher levels.
If a company has a ‘make to stock’ policy, then immediate availability and thus shipment of the end products (also known as “finished goods”) is promised to the customers. If a company operates a ‘make to order’ (MTO) policy, then immediate availability of the end products is not offered, but rather a delivery date is promised. In both policies, all the components and assemblies are produced or procured in time for the end product to reach the client by the promised time.
Figure 2.1 Bill of materials (BoM) example.
To meet delivery targets, a scheduling procedure is required and this is the backbone of the principal inventory methodology for dependent demand items, called material requirements planning (
