1. 1 Intermittent demand Forecasting & Inventory control Ruud Teunter

2. 2 Typical intermittent demand pattern

3. 3 RAF data-set (5,000 items) MinimumAverageMaximum Demand size1161330 Demands per year0.513 Lead time1 months9 months24 months Price0.3p£108£4962

4. 4 What forecasting method to use? Zero forecast Simple moving average Exponential smoothing Croston’s method Syntetos-Boylan variation of Croston’s method Levén-Segerstedt variation of Croston’s method Bootstrapping

5. 5 Croston’s Method (1972) If a demand occurs 1.Re-estimate mean demand size (S) using Exponential Smoothing: S SES 2.Re-Estimate mean demand interval (I1) using Exponential Smoothing: I SES 3. Re-estimate mean demand : D = S SES / I SES Else if demand does not occur Do not re-estimate ^ ^ ^^ ^

6. 6 Bias in Croston’s method E[D] = E[S/ I ] > E[S] / E[ I ] Bias increases with variation of I Bias increases with smoothing constant α Syntetos-Boylan variation corrects for bias

7. 7 Syntetos-Boylan Approximation Forecast of Mean Demand = (1 -  /2) S SES I SES  = smoothing constant for I Comments As easy to apply as Croston’s Method Slight bias remains (downwards) ^ ^

8. 8 Traditional performance measures Accuracy (MAD, MSE) of next period forecast

9. 9 Results Traditional performance measures

10. 10 Zero forecast – Example

11. 11 Forecaster

12. 12 And stock controller

13. 13 Inventory performance measure Service Level Accuracy

14. 14 Inventory policy parameters RAF uses the order-up-to S policy Assume normal lead time demand L: Lead time k: safety factor for achieving target stock- out service level (Normally distributed lead time demand) Forecast1.25 ∙ MAD or √(MSE)

15. 15 Service Level Accuracy

16. 16 Initial Demand Size! Inventory Time S Lead Time Initial Demand Size (Additional) Lead Time Demand

17. 17 Forecasted number of periods between demands Include Initial Demand Size

18. 18 Conclusions Dangerous to focus on standard accuracy measures (MAD, MSE) only Although bias relates measures (Mean Error - ME) would have helped Standard forecasting methods (MA, SES) do not provide enough information for intermittent demand Original Croston, SB Croston variant, and Bootstrapping have similar performance for RAF sata set