John E. Boylan - Intermittent Demand Forecasting

1 Cover

2 Title Page Intermittent Demand Forecasting Context, Methods and Applications John E. Boylan Lancaster University Lancaster, UK Aris A. Syntetos Cardiff University Cardiff, UK

3 Copyright

4 Dedication

5 Preface

6 Glossary

7 About the Companion Website

8 1 Economic and Environmental Context1.1 Introduction 1.2 Economic and Environmental Benefits 1.3 Intermittent Demand Forecasting Software 1.4 About this Book 1.5 Chapter Summary Technical Note

9 2 Inventory Management and Forecasting2.1 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

10 3 Service Level Measures3.1 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

11 4 Demand Distributions4.1 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

12 5 Compound Demand Distributions5.1 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

13 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

14 7 Forecasting the Variance of Demand and Forecast Error7.1 Introduction 7.2 Mean Known, Variance Unknown 7.3 Mean Unknown, Variance Unknown 7.4 Lead Time Variability 7.5 Chapter Summary Technical Notes

15 8 Inventory Settings8.1 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

16 9 Accuracy and Its Implications9.1 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

17 10 Judgement, Bias, and Mean Square Error10.1 Introduction 10.2 Judgemental Forecasting 10.3 Forecast Bias 10.4 The Components of Mean Square Error 10.5 Chapter Summary Technical Notes

18 11 Classification Methods11.1 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

19 12 Maintenance and Obsolescence12.1 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

20 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

21 14 Model‐based Methods14.1 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

22 15 Software for Intermittent Demand15.1 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

23 ReferencesReferences

24 Author Index

25 Subject Index

26 End User License Agreement

1 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 ( , , ).

2 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...

3 Chapter 5Table 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.

4 Chapter 6Table 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...