Improving Forecasting with Imperfect Advance Demand Information

1. Improving Forecasting with Imperfect Advance Demand Information Tarkan Tan Technische Universiteit Eindhoven October 23, 2007 Forecasting and Inventory Management: Bridging the Gap EPSRC project Meeting - London

2. Outline • Introduction • Related Literature • Advance Demand Information (ADI) • Analysis and Proposed Methodology • Incorporating ADI • Conclusions and Future Research

3. Introduction • B2B Production Environments • High demand volatility • Seasonality • Changing trends • Affected by individual clients • Some clients provide information on their future orders • subject to changes in time (imperfect Advance Demand Information - ADI) • Demand forecasting in such a make-to-stock production environment

4. Introduction • Motivation: • Dairy products company • 3 business lines: Food, Nutrition, and Pharma • Orders: single or call-off of a contract • Demand forecast is used in • Packaging- and raw material acquisition • Production planning • Financial forecasting and budget allocation • Milk allocation planning • Reserving inventory space

5. Introduction • ADI collection: • Customers have their own production plans • Some customers place their orders in advance: • minimize the risk of unmet orders • parts of contracts • time allowance for arranging transportation • 30% of the orders are known by the end of the previous month (57% for Pharma)

6. Preliminary Analysis

7. Introduction • If the order is known not to change => Perfect ADI • Impurity and uncertainty => Imperfect ADI • In our application, advance orders are never postponed or cancelled • The changes are in forms of increased orders • We made use of this observation, but similar methods can be devised for different forms of ADI

8. Introduction • In many B2B environments, judgmental forecasts are preferred to statistical forecasts • specific customer information (customers ceasing operations for a period, capacity extensions, etc.) • By personnel with in-depth customer information (Area Sales Managers - ASMs), for each Product-Customer Combination (PCC) • Labor-intensive and repeats itself • Little time to get available data

10. Forecast Accuracy per Area Sales Manager (ASM):

11. Preliminary Analysis • Forecasting System: • 12 months, rolling horizon, monthly updates • Group the forecasts according to the requirements • Define aggregation levels • Statistical forecast as an input to ASMs • Cap the number of product/customer combinations (PCC) for judgmental update

12. Literature Review • ADI • Review: Karaesmen, Liberopoulos, and Dallery (2003) • Imperfect ADI • DeCroix and Mookerjee (1997) • Van Donselaar, Kopczak, and Wouters (2001) • Treharne and Sox (2002) • Thonemann (2002) • Zhu and Thonemann (2004) • Tan, Güllü, and Erkip (2005, 2007) • Forecasting with ADI • Thomopoulos (1980) • Abuizam and Thomopoulos (2005)

13. ADI • some customers never change their orders • some others update (increase) in time • some others never provide any information • How can the placed order be classified? • "Perfect" ADI • Guaranteed by contracts • Analyze order history of PCC and build PCC profile • Those who never change their orders (reliable information) • Those who reach their historical maximum # of updates (Mij ) • Imperfect ADI • Those who have not reached Mij • No ADI

14. ADI • Production/inventory models with ADI: • Dividing the demand into two groups (observed and unobserved) => • independence violated (overlapping populations) • not making the best use of information • special patterns of ordering • timing or number of orders

15. Bayesian Updates • Dependence on distributional assumptions • Normal => (e.g.: 75 observed, demand ~ Normal with st dev = 25, prior forecast = 100, posterior forecast = 102) • Poisson (# orders)=> (e.g.: 91 and 100 observed, average # orders = 5.25, prior forecast = 467, posterior forecast = 564) • Updates are one-sided • Only the information as to the total observed demand (or total number of observed orders) is utilized • Information on the individual order patterns of the customers not taken into account

16. Analysis • How to make use of individual order patterns of the customers?

17. Proposed Methodology • Forecast for each PCC • Information from placed orders: • No Advance Demand Information (ADI) • "Perfect" ADI • Those who reached their historical maximum (Mi) • Imperfect ADI • Those who have not reached Mi

18. Imperfect ADI • Some Possible Methods: • Basic • Binomial • Number of orders • Right tail estimation • Non-stationary right tail estimation

19. Basic: Ft= max{FAt, Ot} Number of orders: Right tail estimation: Non-stationary right tail estimation:

20. Comparison of Methods (% Mean Absolute Error)

21. Monthly cycle Real-time Forecast agreement Statistical forecast ADI ASM input Evaluate accuracy Final Forecast Proposed Method

22. Model CaseFinal Forecast • Perfect ADI: ADI • No ADI: Forecast Agreement • Imperfect ADI: Forecast Agreement + ADI

23. Results (Example) • For a product which 5 customers order • PCC1, 2, and 3: • No ADI: F(PCC1-3) = 287 • PCC4: 91 observed, M=1 • Perfect ADI: F(PCC4) = 91 • PCC5: 100 observed (single order), M=3, F w/o info = 90, History: F1(PCC5)=180, D1=275; F2=90, D2=0; ... • Imperfect ADI: (NSRTE) F(PCC5) = 100 + Av(95-10, (-90-10)+, ...) = 120 • Ftotal = 287 + 91 + 120 = 498 (compare with 467 vs 564) • If PCC4 had ordered 33, Ftotal = 287+33+120 = 440

24. Results • 192 data points: • 78 x No ADI • 65 x Perfect ADI • 49 x Imperfect ADI

25. Results

26. Conclusions • A methodology to improve forecasting by making use of information • A number of methods for utilizing imperfect ADI • Takes individual ordering pattern histories and the current build-up of orders into account • Safety Stock Reduction: • Statistical forecast + ADI: 25% • Statistical forecast + ADI + ASM Update: 37%

27. Future Research • Different methods for utilizing imperfect ADI • Incorporating this kind of ADI directly in production/inventory planning • Lot sizing • Inventory rationing based on ADI