Оглавление
John E. Boylan. Intermittent Demand Forecasting
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Intermittent Demand Forecasting. Context, Methods and Applications
Preface
Glossary
About the Companion Website
1 Economic and Environmental Context. 1.1 Introduction
1.2 Economic and Environmental Benefits
1.2.1 After‐sales Industry
1.2.2 Defence Sector
1.2.3 Economic Benefits
1.2.4 Environmental Benefits
1.2.5 Summary
1.3 Intermittent Demand Forecasting Software
1.3.1 Early Forecasting Software
1.3.2 Developments in Forecasting Software
1.3.3 Open Source Software
1.3.4 Summary
1.4 About this Book
1.4.1 Optimality and Robustness
1.4.2 Business Context
1.4.3 Structure of the Book
1.4.4 Current and Future Applications
1.4.5 Summary
1.5 Chapter Summary
Technical Note
Note 1.1 3D Printing
2 Inventory Management and Forecasting. 2.1 Introduction
2.2 Scheduling and Forecasting
2.2.1 Material Requirements Planning (MRP)
2.2.2 Dependent and Independent Demand Items
2.2.3 Make to Stock
2.2.4 Summary
2.3 Should an Item Be Stocked at All?
2.3.1 Stock/Non‐Stock Decision Rules
2.3.2 Historical or Forecasted Demand?
2.3.3 Summary
2.4 Inventory Control Requirements
2.4.1 How Should Stock Records be Maintained?
2.4.2 When are Forecasts Required for Stocking Decisions?
2.4.3 Summary
2.5 Overview of Stock Rules
2.5.1 Continuous Review Systems
2.5.2 Periodic Review Systems
2.5.3 Periodic Review Policies
2.5.4 Variations of the Periodic Policy
2.5.5 Summary
2.6 Chapter Summary
Technical Notes
Note 2.1 Order Overplanning
Note 2.2 Cessation of Replenishment and Stock Write Off
Note 2.3 External and Internal Lead Times
Note 2.4 Renewal Processes
Note 2.5 Optimisation of (R,S) and (s,Q) Systems
3 Service Level Measures. 3.1 Introduction
3.2 Judgemental Ordering
3.2.1 Rules of Thumb for the Order‐Up‐To Level
3.2.2 Judgemental Adjustment of Orders
3.2.3 Summary
3.3 Aggregate Financial and Service Targets
3.3.1 Aggregate Financial Targets
3.3.2 Service Level Measures
3.3.3 Relationships Between Service Level Measures
3.3.4 Summary
3.4 Service Measures at SKU Level
3.4.1 Cost Factors
3.4.2 Understanding of Service Level Measures
3.4.3 Potential Service Level Measures
3.4.4 Choice of Service Level Measure
3.4.5 Summary
3.5 Calculating Cycle Service Levels
3.5.1 Distribution of Demand Over One Time Period
3.5.2 Cycle Service Levels Based on All Cycles
3.5.3 Cycle Service Levels Based on Cycles with Demand
3.5.4 Summary
3.6 Calculating Fill Rates
3.6.1 Unit Fill Rates
3.6.2 Fill Rates: Standard Formula
3.6.3 Fill Rates: Sobel's Formula
3.6.4 Summary
3.7 Setting Service Level Targets
3.7.1 Responsibility for Target Setting
3.7.2 Trade‐off Between Service and Cost
3.7.3 Setting SKU Level Service Targets
3.7.4 Summary
3.8 Chapter Summary
Technical Note
Note 3.1 Fill Rate Expression of Zhang and Zhang
4 Demand Distributions. 4.1 Introduction
4.2 Estimation of Demand Distributions
4.2.1 Empirical Demand Distributions
4.2.2 Fitted Demand Distributions
4.2.3 Summary
4.3 Criteria for Demand Distributions
4.3.1 Empirical Evidence for Goodness of Fit
4.3.2 Further Criteria
4.3.3 Summary
4.4 Poisson Distribution
4.4.1 Shape of the Poisson Distribution
4.4.2 Summary
4.5 Poisson Demand Distribution
4.5.1 Poisson: A Priori Grounds
4.5.2 Poisson: Ease of Calculation
4.5.3 Poisson: Flexibility
4.5.4 Poisson: Goodness of Fit
4.5.5 Testing for Goodness of Fit
4.5.6 Summary
4.6 Incidence and Occurrence
4.6.1 Demand Incidence
4.6.2 Demand Occurrence
4.6.3 Summary
4.7 Poisson Demand Incidence Distribution
4.7.1 A Priori Grounds
4.7.2 Ease of Calculation
4.7.3 Flexibility
4.7.4 Goodness of Fit
4.7.5 Summary
4.8 Bernoulli Demand Occurrence Distribution
4.8.1 Bernoulli Distribution: A Priori Grounds
4.8.2 Bernoulli Distribution: Ease of Calculation
4.8.3 Bernoulli Distribution: Flexibility
4.8.4 Bernoulli Distribution: Goodness of Fit
4.8.5 Summary
4.9 Chapter Summary
Technical Notes
Note 4.1 Triangular Distribution Calculations
Note 4.2 Memoryless Property of the Poisson Process
Note 4.3 Chi‐square Test for Goodness of Fit
Note 4.4 Chi‐square Calculations by Shale et al. (2008)
Note 4.5 Memoryless Property of the Bernoulli Process
5 Compound Demand Distributions. 5.1 Introduction
5.2 Compound Poisson Distributions
5.2.1 Compound Poisson: A Priori Grounds
5.2.2 Compound Poisson: Flexibility
5.2.3 Summary
5.3 Stuttering Poisson Distribution
5.3.1 Stuttering Poisson: A Priori Grounds
5.3.2 Stuttering Poisson: Ease of Calculation
5.3.3 Stuttering Poisson: Flexibility
5.3.4 Stuttering Poisson: Goodness of Fit for Demand Sizes
5.3.5 Summary
5.4 Negative Binomial Distribution
5.4.1 Negative Binomial: A Priori Grounds
5.4.2 Negative Binomial: Ease of Calculation
5.4.3 Negative Binomial: Flexibility
5.4.4 Negative Binomial: Goodness of Fit
5.4.5 Summary
5.5 Compound Bernoulli Distributions
5.5.1 Compound Bernoulli: A Priori Grounds
5.5.2 Compound Bernoulli: Ease of Calculation
5.5.3 Compound Bernoulli: Flexibility
5.5.4 Compound Bernoulli: Goodness of Fit
5.5.5 Summary
5.6 Compound Erlang Distributions
5.6.1 Compound Erlang Distributions: A Priori Grounds
5.6.2 Compound Erlang Distributions: Ease of Calculation
5.6.3 Compound Erlang‐2: Flexibility
5.6.4 Compound Erlang‐2: Goodness of Fit
5.6.5 Summary
5.7 Differing Time Units
5.7.1 Poisson Distribution
5.7.2 Compound Poisson Distribution
5.7.3 Compound Bernoulli and Compound Erlang Distributions
5.7.4 Normal Distribution
5.7.5 Summary
5.8 Chapter Summary
Technical Notes
Note 5.1 Form of Stuttering Poisson Distribution
Note 5.2 A Priori Models for the Negative Binomial
Note 5.3 Recursive Form of the Negative Binomial
Note 5.4 Kolmogorov–Smirnov Test
Note 5.5 Compound Bernoulli Distribution: Variance to Mean Ratio
Note 5.6 Computation of the Compound Erlang
Note 5.7 Condensed Poisson Distribution
6 Forecasting Mean Demand
6.1 Introduction
6.2 Demand Assumptions
6.2.1 Elements of Intermittent Demand
6.2.2 Demand Models
6.2.3 An Intermittent Demand Model
6.2.4 Summary
6.3 Single Exponential Smoothing (SES)
6.3.1 SES as an Error‐correction Mechanism
6.3.2 SES as a Weighted Average of Previous Observations
6.3.3 Practical Considerations
6.3.4 Summary
6.4 Croston's Critique of SES
6.4.1 Bias After Demand Occurring Periods
6.4.2 Magnitude of Bias After Demand Occurring Periods
6.4.3 Bias After Review Intervals with Demands
6.4.4 Summary
6.5 Croston's Method
6.5.1 Method Specification
6.5.2 Method Application
6.5.3 Summary
6.6 Critique of Croston's Method
6.6.1 Bias of Size‐interval Approaches
6.6.2 Inversion Bias
6.6.3 Quantification of Bias
6.6.4 Summary
6.7 Syntetos–Boylan Approximation
6.7.1 Practical Application
6.7.2 Framework for Correction Factors
6.7.3 Initialisation and Optimisation
6.7.4 Summary
6.8 Aggregation for Intermittent Demand
6.8.1 Temporal Aggregation
6.8.2 Cross‐sectional Aggregation
6.8.3 Summary
6.9 Empirical Studies
6.9.1 Single Series, Single Period Approaches
6.9.2 Single Series, Multiple Period Approaches
6.9.3 Summary
6.10 Chapter Summary
Technical Notes
Note 6.1 Stationary Mean and Local Level Models
Note 6.2 Simple Moving Averages
Note 6.3 SES Bias: End of Review Intervals with Demand
Note 6.4 Approximate Bias of Croston's Method
Note 6.5 SBA is Approximately Unbiased
Note 6.6 Revised Croston's Method
Note 6.7 Cross‐sectional Aggregation
7 Forecasting the Variance of Demand and Forecast Error. 7.1 Introduction
7.2 Mean Known, Variance Unknown
7.2.1 Mean Demand Unchanging Through Time
7.2.2 Relating Variance Over One Period to Variance Over the Protection Interval
7.2.3 Summary
7.3 Mean Unknown, Variance Unknown
7.3.1 Mean and Variance Unchanging Through Time
7.3.2 Mean or Variance Changing Through Time
7.3.3 Relating Variance Over One Period to Variance Over the Protection Interval
7.3.4 Direct Approach to Estimating Variance of Forecast Error Over the Protection Interval
7.3.5 Implementing the Direct Approach to Estimating Variance Over the Protection Interval
7.3.6 Summary
7.4 Lead Time Variability
7.4.1 Consequences of Recognising Lead Time Variance
7.4.2 Variance of Demand Over a Variable Lead Time (Known Mean Demand)
7.4.3 Variance of Demand Over a Variable Lead Time (Unknown Mean Demand)
7.4.4 Distribution of Demand Over a Variable Lead Time
7.4.5 Summary
7.5 Chapter Summary
Technical Notes
Note 7.1 Variance of Demand Over the Protection Interval
Note 7.2 Variance of Forecast Errors Over the Protection Interval
Note 7.3 Backcasting for Initial MSE Estimation
8 Inventory Settings. 8.1 Introduction
8.2 Normal Demand
8.2.1 Order‐up‐to Levels for Four Scenarios
8.2.2 Scenario 1: Mean and Standard Deviation Known
8.2.3 Scenario 2: Mean Demand Unknown Standard Deviation Known
8.2.4 Scenario 3: Mean Demand Known Standard Deviation Unknown
8.2.5 Scenario 4: Mean and Standard Deviation Unknown
8.2.6 Summary
8.3 Poisson Demand
8.3.1 Cycle Service Level System when the Mean Demand is Known
8.3.2 Fill Rate System when the Mean Demand is Known
8.3.3 Poisson OUT Level when the Mean Demand is Unknown
8.3.4 Summary
8.4 Compound Poisson Demand
8.4.1 Stuttering Poisson OUT Level when the Parameters are Known
8.4.2 Negative Binomial OUT Levels when the Parameters are Known
8.4.3 Stuttering Poisson and Negative Binomial OUT Levels when the Parameters are Unknown
8.4.4 Summary
8.5 Variable Lead Times
8.5.1 Empirical Lead Time Distributions
8.5.2 Summary
8.6 Chapter Summary
Technical Notes
Note 8.1: OUT Levels for Normally Distributed Demand
Note 8.2: Calculations of CSLs for Different OUT Levels
Note 8.3: Adjusted Safety Factors for Fill Rates
Note 8.4: CSL+ Calculations for Poisson Demand
Note 8.5: Fill Rate Calculations for Poisson Demand
Note 8.6: Calculations for Stuttering Poisson Demand
9 Accuracy and Its Implications. 9.1 Introduction
9.2 Forecast Evaluation
9.2.1 Only One Step Ahead?
9.2.2 All Points in Time?
9.2.3 Summary
9.3 Error Measures in Common Usage
9.3.1 Popular Forecast Error Measures
9.3.2 Calculation of Forecast Errors
9.3.3 Mean Error
9.3.4 Mean Square Error
9.3.5 Mean Absolute Error
9.3.6 Mean Absolute Percentage Error (MAPE)
9.3.7 100% Minus MAPE
9.3.8 Forecast Value Added
9.3.9 Summary
9.4 Criteria for Error Measures
9.4.1 General Criteria
9.4.2 Additional Criteria for Intermittence
9.4.3 Summary
9.5 Mean Absolute Percentage Error and its Variants
9.5.1 Problems with the Mean Absolute Percentage Error
9.5.2 Mean Absolute Percentage Error from Forecast
9.5.3 Symmetric Mean Absolute Percentage Error
9.5.4 MAPEFF and sMAPE for Intermittent Demand
9.5.5 Summary
9.6 Measures Based on the Mean Absolute Error
9.6.1 MAE : Mean Ratio
9.6.2 Mean Absolute Scaled Error
9.6.3 Measures Based on Absolute Errors
9.6.4 Summary
9.7 Measures Based on the Mean Error
9.7.1 Desirability of Unbiased Forecasts
9.7.2 Mean Error
9.7.3 Mean Percentage Error
9.7.4 Scaled Bias Measures
9.7.5 Summary
9.8 Measures Based on the Mean Square Error
9.8.1 Scaled Mean Square Error
9.8.2 Relative Root Mean Square Error
9.8.3 Percentage Best
9.8.4 Summary
9.9 Accuracy of Predictive Distributions
9.9.1 Measuring Predictive Distribution Accuracy
9.9.2 Probability Integral Transform for Continuous Data
9.9.3 Probability Integral Transform for Discrete Data
9.9.4 Summary
9.10 Accuracy Implication Measures
9.10.1 Simulation Outline
9.10.2 Forecasting Details
9.10.3 Simulation Details
9.10.4 Comparison of Simulation Results
9.10.5 Summary
9.11 Chapter Summary
Technical Notes
Note 9.1 Amended Definitions of MAPE and sMAPE
Note 9.2 The Mean Arctangent Absolute Percentage Error
Note 9.3 Probability Integral Transform: Fractional Allocation of Counts
Note 9.4 Randomised Probability Integral Transform
Note 9.5 Calculation of the Brier Score
10 Judgement, Bias, and Mean Square Error. 10.1 Introduction
10.2 Judgemental Forecasting
10.2.1 Evidence on Prevalence of Judgemental Forecasting
10.2.2 Judgemental Biases
10.2.3 Effectiveness of Judgemental Forecasts: Evidence for Non‐intermittent Items
10.2.4 Effectiveness of Judgemental Forecasts: Evidence for Intermittent Items
10.2.5 Summary
10.3 Forecast Bias
10.3.1 Monitoring and Detection of Bias
10.3.2 Bias as an Expectation of a Random Variable
10.3.3 Response to Different Causes of Bias
10.3.4 Summary
10.4 The Components of Mean Square Error
10.4.1 Calculation of Mean Square Error
10.4.2 Decomposition of Expected Squared Errors
10.4.3 Decomposition of Expected Squared Errors for Independent Demand
10.4.4 Summary
10.5 Chapter Summary
Technical Notes
Note 10.1 Bias–Variance Decomposition
Note 10.2 Extended Bias–Variance Decomposition
11 Classification Methods. 11.1 Introduction
11.2 Classification Schemes
11.2.1 The Purpose of Classification
11.2.2 Classification Criteria
11.2.3 Summary
11.3 ABC Classification
11.3.1 Pareto Principle
11.3.2 Service Criticality
11.3.3 ABC Classification and Forecasting
11.3.4 Summary
11.4 Extensions to the ABC Classification
11.4.1 Composite Criterion Approach
11.4.2 Multi‐criteria Approaches
11.4.3 Classification for Spare Parts
11.4.4 Summary
11.5 Conceptual Clarifications
11.5.1 Definition of Non‐normal Demand Patterns
11.5.2 Conceptual Framework
11.5.3 Summary
11.6 Classification Based on Demand Sources
11.6.1 Demand Generation
11.6.2 A Qualitative Classification Approach
11.6.3 Summary
11.7 Forecasting‐based Classifications
11.7.1 Forecasting and Generalisation
11.7.2 Classification Solutions
11.7.3 Summary
11.8 Chapter Summary
Technical Notes
Note 11.1 Classification Rule for SES and SBA
Note 11.2 Refined Classification Rules
12 Maintenance and Obsolescence. 12.1 Introduction
12.2 Maintenance Contexts
12.2.1 Summary
12.3 Causal Forecasting
12.3.1 Causal Forecasting for Maintenance Management
12.3.2 Summary
12.4 Time Series Methods
12.4.1 Forecasting in the Presence of Obsolescence
12.4.2 Forecasting with Granular Maintenance Information
12.4.3 Summary
12.5 Forecasting in Context
12.6 Chapter Summary
Technical Notes
Note 12.1 Preventive and Corrective Maintenance
Note 12.2 On‐condition Monitoring
Note 12.3 Deterioration, Perishability, and Obsolescence
Note 12.4 Forecasting of Spare Parts Based on Component Repairs
13 Non‐parametric Methods
13.1 Introduction
13.2 Empirical Distribution Functions
13.2.1 Assumptions
13.2.2 Length of History
13.2.3 Summary
13.3 Non‐overlapping and Overlapping Blocks
13.3.1 Differences Between the Two Methods
13.3.2 Methods and Assumptions
13.3.3 Practical Considerations
13.3.4 Performance of Non‐overlapping Blocks Method
13.3.5 Performance of Overlapping Blocks Method
13.3.6 Summary
13.4 Comparison of Approaches
13.4.1 Time Series Characteristics Favouring Overlapping Blocks
13.4.2 Empirical Evidence on Overlapping Blocks
13.4.3 Summary
13.5 Resampling Methods
13.5.1 Simple Bootstrapping
13.5.2 Bootstrapping Demand Sizes and Intervals
13.5.3 VZ Bootstrap and the Syntetos–Boylan Approximation
13.5.4 Extension of Methods to Variable Lead Times
13.5.5 Resampling Immediately After Demand Occurrence
13.5.6 Summary
13.6 Limitations of Simple Bootstrapping
13.6.1 Autocorrelated Demand
13.6.2 Previously Unobserved Demand Values
13.6.3 Summary
13.7 Extensions to Simple Bootstrapping
13.7.1 Discrete‐time Markov Chains
13.7.2 Extension to Simple Bootstrapping Using Markov Chains
13.7.3 Jittering
13.7.4 Limitations of Jittering
13.7.5 Further Developments
13.7.6 Empirical Evidence on Bootstrapping Methods
13.7.7 Summary
13.8 Chapter Summary
Technical Notes
Note 13.1 Calculation of the Theta Function
Note 13.2 General Expression for the Variance of the OB Estimate
Note 13.3 General Condition for OB Outperformance
14 Model‐based Methods. 14.1 Introduction
14.2 Models and Methods
14.2.1 A Simple Model for Single Exponential Smoothing
14.2.2 Critique of Weighted Least Squares
14.2.3 ARIMA Models
14.2.4 The ARIMA(0,1,1) Model and SES
14.2.5 Summary
14.3 Integer Autoregressive Moving Average (INARMA) Models
14.3.1 Integer Autoregressive Model of Order One, INAR(1)
14.3.2 Integer Moving Average Model of Order One, INMA(1)
14.3.3 Mixed Integer Autoregressive Moving Average Models
14.3.4 Summary
14.4 INARMA Parameter Estimation
14.4.1 Parameter Estimation for INAR(1) Models
14.4.2 Parameter Estimation for INMA(1) Models
14.4.3 Parameter Estimation for INARMA(1,1) Models
14.4.4 Summary
14.5 Identification of INARMA Models
14.5.1 Identification Using Akaike's Information Criterion
14.5.2 General Models and Model Identification
14.5.3 Summary
14.6 Forecasting Using INARMA Models
14.6.1 Forecasting INAR(1) Mean Demand
14.6.2 Forecasting INMA(1) Mean Demand
14.6.3 Forecasting INARMA(1,1) Mean Demand
14.6.4 Forecasting Using Temporal Aggregation
14.6.5 Summary
14.7 Predicting the Whole Demand Distribution
14.7.1 Protection Interval of One Period
14.7.2 Protection Interval of More Than One Period
14.7.3 Summary
14.8 State Space Models for Intermittence
14.8.1 Croston's Demand Model
14.8.2 Proposed State Space Models
14.8.3 Summary
14.9 Chapter Summary
Technical Notes
Note 14.1 INARMA(1,1) Cumulative Forecasts
Note 14.2 INAR(1) Conditional Probabilities
Note 14.3 Normal Approximation to Order‐up‐to Level for an INAR(1) Process
15 Software for Intermittent Demand. 15.1 Introduction
15.2 Taxonomy of Software
15.2.1 Proprietary Software
15.2.2 Open Source Software
15.2.3 Hybrid Solutions
15.2.4 Summary
15.3 Framework for Software Evaluation
15.3.1 Key Aspects of Software Evaluation
15.3.2 Additional Criteria
15.3.3 Summary
15.4 Software Features and Their Availability
15.4.1 Software Features for Intermittent Demand
15.4.2 Availability of Software Features
15.4.3 Summary
15.5 Training
15.5.1 Summary
15.6 Forecast Support Systems
15.6.1 Summary
15.7 Alternative Perspectives
15.7.1 Bayesian Methods
15.7.2 Neural Networks
15.7.3 Summary
15.8 Way Forward
15.9 Chapter Summary
Technical Note
Note 15.1: Evolution of ERP Systems
References
Author Index. a
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