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.
Preface xix Glossary xxi About the Companion Website xxiii 1 Economic and Environmental Context 1 1.1 Introduction 1 1.2 Economic and Environmental Benefits 3 1.2.1 After-sales Industry 3 1.2.2 Defence Sector 4 1.2.3 Economic Benefits 5 1.2.4 Environmental Benefits 5 1.2.5 Summary 6 1.3 Intermittent Demand Forecasting Software 6 1.3.1 Early Forecasting Software 6 1.3.2 Developments in Forecasting Software 6 1.3.3 Open Source Software 7 1.3.4 Summary 7 1.4 About this Book 7 1.4.1 Optimality and Robustness 7 1.4.2 Business Context 8 1.4.3 Structure of the Book 9 1.4.4 Current and Future Applications 10 1.4.5 Summary 10 1.5 Chapter Summary 11 Technical Note 11 2 Inventory Management and Forecasting 13 2.1 Introduction 13 2.2 Scheduling and Forecasting 13 2.2.1 Material Requirements Planning (MRP) 13 2.2.2 Dependent and Independent Demand Items 14 2.2.3 Make to Stock 15 2.2.4 Summary 15 2.3 Should an Item Be Stocked at All? 15 2.3.1 Stock/Non-Stock Decision Rules 16 2.3.2 Historical or Forecasted Demand? 18 2.3.3 Summary 18 2.4 Inventory Control Requirements 19 2.4.1 How Should Stock Records be Maintained? 19 2.4.2 When are Forecasts Required for Stocking Decisions? 22 2.4.3 Summary 24 2.5 Overview of Stock Rules 25 2.5.1 Continuous Review Systems 25 2.5.2 Periodic Review Systems 26 2.5.3 Periodic Review Policies 28 2.5.4 Variations of the (R, S) Periodic Policy 29 2.5.5 Summary 30 2.6 Chapter Summary 30 Technical Notes 31 3 Service Level Measures 33 3.1 Introduction 33 3.2 Judgemental Ordering 34 3.2.1 Rules of Thumb for the Order-Up-To Level 34 3.2.2 Judgemental Adjustment of Orders 34 3.2.3 Summary 35 3.3 Aggregate Financial and Service Targets 35 3.3.1 Aggregate Financial Targets 36 3.3.2 Service Level Measures 36 3.3.3 Relationships Between Service Level Measures 38 3.3.4 Summary 39 3.4 Service Measures at SKU Level 39 3.4.1 Cost Factors 39 3.4.2 Understanding of Service Level Measures 40 3.4.3 Potential Service Level Measures 40 3.4.4 Choice of Service Level Measure 41 3.4.5 Summary 42 3.5 Calculating Cycle Service Levels 42 3.5.1 Distribution of Demand Over One Time Period 43 3.5.2 Cycle Service Levels Based on All Cycles 44 3.5.3 Cycle Service Levels Based on Cycles with Demand 45 3.5.4 Summary 47 3.6 Calculating Fill Rates 48 3.6.1 Unit Fill Rates 48 3.6.2 Fill Rates: Standard Formula 49 3.6.3 Fill Rates: Sobel’s Formula 51 3.6.4 Summary 53 3.7 Setting Service Level Targets 53 3.7.1 Responsibility for Target Setting 53 3.7.2 Trade-off Between Service and Cost 54 3.7.3 Setting SKU Level Service Targets 55 3.7.4 Summary 56 3.8 Chapter Summary 56 Technical Note 57 4 Demand Distributions 59 4.1 Introduction 59 4.2 Estimation of Demand Distributions 60 4.2.1 Empirical Demand Distributions 60 4.2.2 Fitted Demand Distributions 62 4.2.3 Summary 64 4.3 Criteria for Demand Distributions 64 4.3.1 Empirical Evidence for Goodness of Fit 64 4.3.2 Further Criteria 64 4.3.3 Summary 65 4.4 Poisson Distribution 65 4.4.1 Shape of the Poisson Distribution 66 4.4.2 Summary 67 4.5 Poisson Demand Distribution 67 4.5.1 Poisson: A Priori Grounds 67 4.5.2 Poisson: Ease of Calculation 67 4.5.3 Poisson: Flexibility 68 4.5.4 Poisson: Goodness of Fit 69 4.5.5 Testing for Goodness of Fit 70 4.5.6 Summary 72 4.6 Incidence and Occurrence 72 4.6.1 Demand Incidence 72 4.6.2 Demand Occurrence 73 4.6.3 Summary 74 4.7 Poisson Demand Incidence Distribution 75 4.7.1 A Priori Grounds 75 4.7.2 Ease of Calculation 75 4.7.3 Flexibility 76 4.7.4 Goodness of Fit 76 4.7.5 Summary 79 4.8 Bernoulli Demand Occurrence Distribution 79 4.8.1 Bernoulli Distribution: A Priori Grounds 79 4.8.2 Bernoulli Distribution: Ease of Calculation 80 4.8.3 Bernoulli Distribution: Flexibility 81 4.8.4 Bernoulli Distribution: Goodness of Fit 81 4.8.5 Summary 82 4.9 Chapter Summary 82 Technical Notes 83 5 Compound Demand Distributions 87 5.1 Introduction 87 5.2 Compound Poisson Distributions 88 5.2.1 Compound Poisson: A Priori Grounds 89 5.2.2 Compound Poisson: Flexibility 89 5.2.3 Summary 89 5.3 Stuttering Poisson Distribution 90 5.3.1 Stuttering Poisson: A Priori Grounds 91 5.3.2 Stuttering Poisson: Ease of Calculation 91 5.3.3 Stuttering Poisson: Flexibility 93 5.3.4 Stuttering Poisson: Goodness of Fit for Demand Sizes 93 5.3.5 Summary 95 5.4 Negative Binomial Distribution 96 5.4.1 Negative Binomial: A Priori Grounds 96 5.4.2 Negative Binomial: Ease of Calculation 96 5.4.3 Negative Binomial: Flexibility 97 5.4.4 Negative Binomial: Goodness of Fit 98 5.4.5 Summary 99 5.5 Compound Bernoulli Distributions 100 5.5.1 Compound Bernoulli: A Priori Grounds 100 5.5.2 Compound Bernoulli: Ease of Calculation 100 5.5.3 Compound Bernoulli: Flexibility 100 5.5.4 Compound Bernoulli: Goodness of Fit 101 5.5.5 Summary 101 5.6 Compound Erlang Distributions 101 5.6.1 Compound Erlang Distributions: A Priori Grounds 103 5.6.2 Compound Erlang Distributions: Ease of Calculation 104 5.6.3 Compound Erlang-2: Flexibility 104 5.6.4 Compound Erlang-2: Goodness of Fit 104 5.6.5 Summary 105 5.7 Differing Time Units 105 5.7.1 Poisson Distribution 106 5.7.2 Compound Poisson Distribution 106 5.7.3 Compound Bernoulli and Compound Erlang Distributions 107 5.7.4 Normal Distribution 108 5.7.5 Summary 110 5.8 Chapter Summary 110 Technical Notes 111 6 Forecasting Mean Demand 117 6.1 Introduction 117 6.2 Demand Assumptions 118 6.2.1 Elements of Intermittent Demand 119 6.2.2 Demand Models 119 6.2.3 An Intermittent Demand Model 120 6.2.4 Summary 121 6.3 Single Exponential Smoothing (SES) 121 6.3.1 SES as an Error-correction Mechanism 122 6.3.2 SES as aWeighted Average of Previous Observations 122 6.3.3 Practical Considerations 125 6.3.4 Summary 126 6.4 Croston’s Critique of SES 126 6.4.1 Bias After Demand Occurring Periods 126 6.4.2 Magnitude of Bias After Demand Occurring Periods 128 6.4.3 Bias After Review Intervals with Demands 128 6.4.4 Summary 129 6.5 Croston’s Method 129 6.5.1 Method Specification 129 6.5.2 Method Application 130 6.5.3 Summary 131 6.6 Critique of Croston’s Method 132 6.6.1 Bias of Size-interval Approaches 132 6.6.2 Inversion Bias 132 6.6.3 Quantification of Bias 133 6.6.4 Summary 134 6.7 Syntetos–Boylan Approximation 134 6.7.1 Practical Application 134 6.7.2 Framework for Correction Factors 135 6.7.3 Initialisation and Optimisation 135 6.7.4 Summary 138 6.8 Aggregation for Intermittent Demand 138 6.8.1 Temporal Aggregation 138 6.8.2 Cross-sectional Aggregation 141 6.8.3 Summary 142 6.9 Empirical Studies 143 6.9.1 Single Series, Single Period Approaches 143 6.9.2 Single Series, Multiple Period Approaches 144 6.9.3 Summary 145 6.10 Chapter Summary 145 Technical Notes 146 7 Forecasting the Variance of Demand and Forecast Error 151 7.1 Introduction 151 7.2 Mean Known, Variance Unknown 151 7.2.1 Mean Demand Unchanging Through Time 152 7.2.2 Relating Variance Over One Period to Variance Over the Protection Interval 152 7.2.3 Summary 153 7.3 Mean Unknown, Variance Unknown 153 7.3.1 Mean and Variance Unchanging Through Time 154 7.3.2 Mean or Variance Changing Through Time 155 7.3.3 Relating Variance Over One Period to Variance Over the Protection Interval 156 7.3.4 Direct Approach to Estimating Variance of Forecast Error Over the Protection Interval 158 7.3.5 Implementing the Direct Approach to Estimating Variance Over the Protection Interval 160 7.3.6 Summary 160 7.4 Lead Time Variability 161 7.4.1 Consequences of Recognising Lead Time Variance 161 7.4.2 Variance of Demand Over a Variable Lead Time (Known Mean Demand) 162 7.4.3 Variance of Demand Over a Variable Lead Time (Unknown Mean Demand) 163 7.4.4 Distribution of Demand Over a Variable Lead Time 164 7.4.5 Summary 165 7.5 Chapter Summary 165 Technical Notes 166 8 Inventory Settings 169 8.1 Introduction 169 8.2 Normal Demand 170 8.2.1 Order-up-to Levels for Four Scenarios 170 8.2.2 Scenario 1: Mean and Standard Deviation Known 170 8.2.3 Scenario 2: Mean Demand Unknown Standard Deviation Known 172 8.2.4 Scenario 3: Mean Demand Known Standard Deviation Unknown 175 8.2.5 Scenario 4: Mean and Standard Deviation Unknown 176 8.2.6 Summary 177 8.3 Poisson Demand 177 8.3.1 Cycle Service Level System when the Mean Demand is Known 177 8.3.2 Fill Rate System when the Mean Demand is Known 178 8.3.3 Poisson OUT Level when the Mean Demand is Unknown 179 8.3.4 Summary 181 8.4 Compound Poisson Demand 181 8.4.1 Stuttering Poisson OUT Level when the Parameters are Known 181 8.4.2 Negative Binomial OUT Levels when the Parameters are Known 183 8.4.3 Stuttering Poisson and Negative Binomial OUT Levels when the Parameters are Unknown 183 8.4.4 Summary 184 8.5 Variable Lead Times 184 8.5.1 Empirical Lead Time Distributions 184 8.5.2 Summary 185 8.6 Chapter Summary 185 Technical Notes 186 9 Accuracy and Its Implications 193 9.1 Introduction 193 9.2 Forecast Evaluation 194 9.2.1 Only One Step Ahead? 194 9.2.2 All Points in Time? 194 9.2.3 Summary 195 9.3 Error Measures in Common Usage 195 9.3.1 Popular Forecast Error Measures 195 9.3.2 Calculation of Forecast Errors 197 9.3.3 Mean Error 197 9.3.4 Mean Square Error 198 9.3.5 Mean Absolute Error 198 9.3.6 Mean Absolute Percentage Error (MAPE) 198 9.3.7 100% Minus MAPE 199 9.3.8 Forecast Value Added 199 9.3.9 Summary 200 9.4 Criteria for Error Measures 200 9.4.1 General Criteria 200 9.4.2 Additional Criteria for Intermittence 201 9.4.3 Summary 201 9.5 Mean Absolute Percentage Error and its Variants 201 9.5.1 Problems with the Mean Absolute Percentage Error 202 9.5.2 Mean Absolute Percentage Error from Forecast 202 9.5.3 Symmetric Mean Absolute Percentage Error 203 9.5.4 MAPEFF and sMAPE for Intermittent Demand 204 9.5.5 Summary 205 9.6 Measures Based on the Mean Absolute Error 205 9.6.1 MAE: Mean Ratio 205 9.6.2 Mean Absolute Scaled Error 206 9.6.3 Measures Based on Absolute Errors 207 9.6.4 Summary 208 9.7 Measures Based on the Mean Error 208 9.7.1 Desirability of Unbiased Forecasts 209 9.7.2 Mean Error 209 9.7.3 Mean Percentage Error 210 9.7.4 Scaled Bias Measures 210 9.7.5 Summary 211 9.8 Measures Based on the Mean Square Error 211 9.8.1 Scaled Mean Square Error 212 9.8.2 Relative Root Mean Square Error 212 9.8.3 Percentage Best 213 9.8.4 Summary 213 9.9 Accuracy of Predictive Distributions 214 9.9.1 Measuring Predictive Distribution Accuracy 214 9.9.2 Probability Integral Transform for Continuous Data 215 9.9.3 Probability Integral Transform for Discrete Data 215 9.9.4 Summary 217 9.10 Accuracy Implication Measures 218 9.10.1 Simulation Outline 218 9.10.2 Forecasting Details 218 9.10.3 Simulation Details 219 9.10.4 Comparison of Simulation Results 220 9.10.5 Summary 221 9.11 Chapter Summary 221 Technical Notes 221 10 Judgement, Bias, and Mean Square Error 225 10.1 Introduction 225 10.2 Judgemental Forecasting 225 10.2.1 Evidence on Prevalence of Judgemental Forecasting 226 10.2.2 Judgemental Biases 226 10.2.3 Effectiveness of Judgemental Forecasts: Evidence for Non-intermittent Items 229 10.2.4 Effectiveness of Judgemental Forecasts: Evidence for Intermittent Items 230 10.2.5 Summary 231 10.3 Forecast Bias 232 10.3.1 Monitoring and Detection of Bias 232 10.3.2 Bias as an Expectation of a Random Variable 234 10.3.3 Response to Different Causes of Bias 235 10.3.4 Summary 236 10.4 The Components of Mean Square Error 236 10.4.1 Calculation of Mean Square Error 236 10.4.2 Decomposition of Expected Squared Errors 236 10.4.3 Decomposition of Expected Squared Errors for Independent Demand 238 10.4.4 Summary 239 10.5 Chapter Summary 240 Technical Notes 240 11 Classification Methods 243 11.1 Introduction 243 11.2 Classification Schemes 244 11.2.1 The Purpose of Classification 244 11.2.2 Classification Criteria 245 11.2.3 Summary 245 11.3 ABC Classification 246 11.3.1 Pareto Principle 246 11.3.2 Service Criticality 246 11.3.3 ABC Classification and Forecasting 247 11.3.4 Summary 248 11.4 Extensions to the ABC Classification 248 11.4.1 Composite Criterion Approach 249 11.4.2 Multi-criteria Approaches 250 11.4.3 Classification for Spare Parts 250 11.4.4 Summary 251 11.5 Conceptual Clarifications 251 11.5.1 Definition of Non-normal Demand Patterns 251 11.5.2 Conceptual Framework 252 11.5.3 Summary 253 11.6 Classification Based on Demand Sources 254 11.6.1 Demand Generation 254 11.6.2 A Qualitative Classification Approach 254 11.6.3 Summary 255 11.7 Forecasting-based Classifications 255 11.7.1 Forecasting and Generalisation 256 11.7.2 Classification Solutions 257 11.7.3 Summary 258 11.8 Chapter Summary 259 Technical Notes 260 12 Maintenance and Obsolescence 263 12.1 Introduction 263 12.2 Maintenance Contexts 264 12.2.1 Summary 265 12.3 Causal Forecasting 265 12.3.1 Causal Forecasting for Maintenance Management 266 12.3.2 Summary 268 12.4 Time Series Methods 268 12.4.1 Forecasting in the Presence of Obsolescence 269 12.4.2 Forecasting with Granular Maintenance Information 272 12.4.3 Summary 273 12.5 Forecasting in Context 273 12.6 Chapter Summary 275 Technical Notes 276 13 Non-parametric Methods 279 13.1 Introduction 279 13.2 Empirical Distribution Functions 280 13.2.1 Assumptions 281 13.2.2 Length of History 281 13.2.3 Summary 282 13.3 Non-overlapping and Overlapping Blocks 282 13.3.1 Differences Between the Two Methods 282 13.3.2 Methods and Assumptions 284 13.3.3 Practical Considerations 284 13.3.4 Performance of Non-overlapping Blocks Method 285 13.3.5 Performance of Overlapping Blocks Method 285 13.3.6 Summary 286 13.4 Comparison of Approaches 286 13.4.1 Time Series Characteristics Favouring Overlapping Blocks 286 13.4.2 Empirical Evidence on Overlapping Blocks 287 13.4.3 Summary 289 13.5 Resampling Methods 289 13.5.1 Simple Bootstrapping 289 13.5.2 Bootstrapping Demand Sizes and Intervals 290 13.5.3 VZ Bootstrap and the Syntetos–Boylan Approximation 292 13.5.4 Extension of Methods to Variable Lead Times 293 13.5.5 Resampling Immediately After Demand Occurrence 293 13.5.6 Summary 294 13.6 Limitations of Simple Bootstrapping 294 13.6.1 Autocorrelated Demand 294 13.6.2 Previously Unobserved Demand Values 295 13.6.3 Summary 296 13.7 Extensions to Simple Bootstrapping 296 13.7.1 Discrete-time Markov Chains 296 13.7.2 Extension to Simple Bootstrapping Using Markov Chains 297 13.7.3 Jittering 299 13.7.4 Limitations of Jittering 300 13.7.5 Further Developments 300 13.7.6 Empirical Evidence on Bootstrapping Methods 300 13.7.7 Summary 302 13.8 Chapter Summary 302 Technical Notes 303 14 Model-based Methods 305 14.1 Introduction 305 14.2 Models and Methods 305 14.2.1 A Simple Model for Single Exponential Smoothing 306 14.2.2 Critique ofWeighted Least Squares 307 14.2.3 ARIMA Models 307 14.2.4 The ARIMA(0,1,1) Model and SES 308 14.2.5 Summary 309 14.3 Integer Autoregressive Moving Average (INARMA) Models 309 14.3.1 Integer Autoregressive Model of Order One, INAR(1) 310 14.3.2 Integer Moving Average Model of Order One, INMA(1) 312 14.3.3 Mixed Integer Autoregressive Moving Average Models 312 14.3.4 Summary 313 14.4 INARMA Parameter Estimation 313 14.4.1 Parameter Estimation for INAR(1) Models 313 14.4.2 Parameter Estimation for INMA(1) Models 314 14.4.3 Parameter Estimation for INARMA(1,1) Models 314 14.4.4 Summary 315 14.5 Identification of INARMA Models 315 14.5.1 Identification Using Akaike’s Information Criterion 315 14.5.2 General Models and Model Identification 316 14.5.3 Summary 317 14.6 Forecasting Using INARMA Models 317 14.6.1 Forecasting INAR(1) Mean Demand 318 14.6.2 Forecasting INMA(1) Mean Demand 318 14.6.3 Forecasting INARMA(1,1) Mean Demand 319 14.6.4 Forecasting Using Temporal Aggregation 319 14.6.5 Summary 319 14.7 Predicting the Whole Demand Distribution 319 14.7.1 Protection Interval of One Period 320 14.7.2 Protection Interval of More Than One Period 320 14.7.3 Summary 322 14.8 State Space Models for Intermittence 322 14.8.1 Croston’s Demand Model 323 14.8.2 Proposed State Space Models 324 14.8.3 Summary 325 14.9 Chapter Summary 325 Technical Notes 325 15 Software for Intermittent Demand 329 15.1 Introduction 329 15.2 Taxonomy of Software 330 15.2.1 Proprietary Software 330 15.2.2 Open Source Software 332 15.2.3 Hybrid Solutions 333 15.2.4 Summary 333 15.3 Framework for Software Evaluation 333 15.3.1 Key Aspects of Software Evaluation 334 15.3.2 Additional Criteria 335 15.3.3 Summary 336 15.4 Software Features and Their Availability 336 15.4.1 Software Features for Intermittent Demand 336 15.4.2 Availability of Software Features 337 15.4.3 Summary 338 15.5 Training 339 15.5.1 Summary 340 15.6 Forecast Support Systems 340 15.6.1 Summary 341 15.7 Alternative Perspectives 341 15.7.1 Bayesian Methods 342 15.7.2 Neural Networks 342 15.7.3 Summary 343 15.8 Way Forward 343 15.9 Chapter Summary 345 Technical Note 345 References 347 Author Index 365 Subject Index 367
John E. Boylan is Professor of Business Analytics at Lancaster University, an Editor-in-Chief of the Journal of the Operational Research Society, and President of the International Society for Inventory Research. Aris A. Syntetos is Professor of Operational Research and Operations Management at Cardiff University, an Editor-in-Chief of the IMA Journal of Management Mathematics, and Director of the International Institute of Forecasters.
Reviews for Intermittent Demand Forecasting: Context, Methods and Applications
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
