Forecasting – stock control interactions: a simulation intensive investigation

1. Centre for Operational Research and Applied Statistics Forecasting – stock control interactions: a simulation intensive investigation Aris A. Syntetos andZied M. Babai CORAS - University of Salford

2. Outline EPSRC project 1 Forecasting and stock control 2 Current investigations & preliminary results 3 Conclusions and further work 4

3. EPSRC project • On the Development of Theory-Informed Operationalised Definitions of Demand Patterns. (FOCUS ON INTERMITTENT DEMANDS) OBJECTIVES: • To identify, through analysing the interaction between forecasting and stock control, the key factors that influence the performance of the total system • To propose theoretically coherent demand categorisation rules for both forecasting and stock control purposes • To test the empirical validity and utility of the theoretical results on large sets of real world data • To provide a set of recommendations for industrial applications.

4. Methodology • Positivistic methodology  Development of universally applicable categorisation solutions • However, due to the complexity of the problem, the research strategy cannot be purely hypothetico-deductive • Established theory is applied to empirical data with the objective of identifying issues that are subsequently incorporated/reflected back to the theory. Knowledge is then deduced again and final recommendations/ conclusions will be made. • Semi-deductive research strategy (theory-data loops) - a very well-framed simulation-intensive exploratory investigation.

5. Industrial collaborators Brother International, UK Computer Science Corporation Valves Instrument Plus, Ltd

6. Forecasting and stock control Estimate the lead-time demand An appropriate demand forecasting method (Parametric and Non-parametric methods) 1st step An appropriate inventory control policy (Continuous / Periodic review policies) (Service level / Cost minimisation) Compute the parameters of the stock control policy 2nd step

7. Demand forecasting methods • Parametric Methods • Known distribution is assumed (eg Poisson, Negative Binomial) • Distribution parameters must be estimated • Examples: MA, SES, Croston‘s method • Non-Parametric Methods • No particular distribution is assumed • It is assumed that distribution observed in the past persists into the future • Examples: Bootstrapping methods

8. Stock control methods • Typically periodic review policies are used for intermittent demand items • (T,S) and (T,s,S) policies. • (T,S) policy: Review inventory position every T periods and order enough to bring up to the order-up-to-level S • (T,s,S) policy: Inventory position dropping to the re-oder point s triggers a new order Comments on the methods: • (T,S) is very simple and performs well for low ordering costs • (T,s,S) induces lower costs but the parameters are more complex to compute • Some heuristics have been proposed to compute these parameters • (Require only knowledge of mean and variance of the demand)

9. Current investigations • Investigation on parametric forecasting methods • Collaboration with Nezih Altay (University of Richmond, Virginia) • Investigation on non-parametric methods • Collaboration with John Boylan (Buckinghamshire New University) • Investigation and comparison of stock control methods • Collaboration with Richard Marett (Multipart) and Yves Dallerry (Ecole Centrale, Paris), IJPR • A new approach for the stock control of intermittent demand items • Collaboration with Ruud Teunter (Lancaster), JORS, EJOR • Demand classification related issues • Collaboration with Mark Keyes (Brother International), IMA

10. 1 of 5: Investigation on parametric forecasting methods • Which distribution should be hypothesised to represent the demand? • Which estimator to choose in order to forecast the demand? • Limited empirical work has been conducted on: • Comparing different demand estimators • Assessing the fit of demand distributions Current work: • Empirical investigation to test the statistical goodness-of-fit of many distributions on large intermittent demand datasets • The impact of the distributional assumptions on stock control

11. Investigation on parametric methods • Goodness-of-Fit results (experimentation on 4,588 SKUs from US Navy) Poisson distribution Negative Binomial distribution Normal distribution Gamma distribution

12. 2 of 5: Investigation on non-parametric methods • Investigate and compare non-parametric (bootstrapping) methods • Efron’s bootstrapping Approach • Porras and Dekker’s bootstrapping Approach • Willemain’s bootstrapping Approach • Compare parametric and non-parametric methods on stock control performance • Empirical results (experimentation on 1,308 SKUs from RAF,UK) • Considerable cost reductions achieved by employing the parametric approach • Better CSL achievedby employing the non-parametric approach

13. 3 of 5: Investigation and comparison of stock control methods • Comparison of stock control methods for intermittent demand items • (T,S) method • Power Approximation (Ehrhardt and Mosier, 1984) • Normal Approximation (Wagner, 1975) • Naddor Heuristic (Naddor, 1975) • Development of categorisation rules for inventory control purposes (experimentation on 5,000 SKUs from RAF, UK) • Empirical Results: • Naddor’s heuristic is overall the best performing heuristic when cost is considered • (T,S) is the worst performing one when ordering cost is considered • Consideration of both cost and service level results in similar performances being reported for all thee (T,s,S) heuristics. • Implementation related considerations imply that the Power Approximation is the preferred one.

14. Inventory level S Zm Time L Tm 4 of 5: A new stock control approach • Main assumption: Lead time is smaller than the inter-demand interval, L ≤ Tm • Estimating separately the inter-demand intervals and demand sizes, when demand occurs, directly for stock control purposes. • Empirical investigation to compare the inventory performance of the new approach to the classical one (experimentation on 2,455 SKUs from the RAF, UK)

15. A new stock control approach • Preliminary results: Considerable cost reductions achieved by employing the new approach. The cost reductions range (across all SKUs) from 14% to 22% • Almost no penalty in service levels • Extensions: • Further work is about to be submitted for peer review on the development of a generalised compound Bernoulli model • Theoretical developments for both cost and service level constraints

16. 5 of 5: Demand classification • Demand categorisation in a European spare parts Logistics network • In collaboration with Brother International, UK • Typical ABC classifications • An opportunity for considering pertinent qualitative issues and large scale applications • Demonstration of the tremendous scope for improving real world systems • Next steps to involve the application of theoretically sound solutions

17. Conclusions and further work • Project funded by the EPSRC, UK • Simulation intensive investigation that has been evolved around 5 areas • Parametric forecasting methods • Non-parametric methods • Stock control methods • Integrated forecasting – stock control solutions • Further insights into categorisation related issues • We have already started reflecting pertinent issues identified through our empirical investigations into theoretical developments • Exciting and very challenging second year of the project: attempt to synthesise our findings into robust, theoretically sound, inventory management solutions.

18. Thank you very much Questions …? http://www.mams.salford.ac.uk/CORAS/Projects/Forecasting/