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

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

- 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 n Positivistic methodology  Development of universally applicable categorisation solutions n However, due to the complexity of the problem, the research strategy cannot be purely hypothetico-deductive n 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. n 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 Compute the parameters of the stock control policy 1 st step 2 nd step An appropriate demand forecasting method (Parametric and Non-parametric methods) An appropriate inventory control policy (Continuous / Periodic review policies) (Service level / Cost minimisation)

- 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

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

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

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 achieved by employing the non-parametric approach

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.

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. S Time Inventory level L ZmZm TmTm  Empirical investigation to compare the inventory performance of the new approach to the classical one (experimentation on 2,455 SKUs from the RAF, UK)

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

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

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.

Thank you very much Questions …?