1. /faculteit technologie management 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. /faculteit technologie management Introduction Related Literature Advance Demand Information (ADI) Analysis and Proposed Methodology Incorporating ADI Conclusions and Future Research Outline

3. /faculteit technologie management 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. /faculteit technologie management 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. /faculteit technologie management 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. /faculteit technologie management Preliminary Analysis

7. /faculteit technologie management 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 Introduction

8. /faculteit technologie management 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 Introduction

9. /faculteit technologie management

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

11. /faculteit technologie management 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. /faculteit technologie management 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. /faculteit technologie management 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 (M ij ) –Imperfect ADI Those who have not reached M ij –No ADI

14. /faculteit technologie management 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. /faculteit technologie management 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. /faculteit technologie management How to make use of individual order patterns of the customers? Analysis

17. /faculteit technologie management Forecast for each PCC Information from placed orders: –No Advance Demand Information (ADI) –"Perfect" ADI Those who reached their historical maximum (M i ) –Imperfect ADI Those who have not reached M i Proposed Methodology

18. /faculteit technologie management Imperfect ADI Some Possible Methods: –Basic –Binomial –Number of orders –Right tail estimation –Non-stationary right tail estimation

19. /faculteit technologie management Basic: F t = max{FA t, O t } Number of orders: Right tail estimation: Non-stationary right tail estimation:

20. /faculteit technologie management Comparison of Methods (% Mean Absolute Error) PCC1PCC2PCC3PCC4Average Basic21.436.633.82328.7 # orders13.638.331.336.229.8 Right tail22.932.833.82328.1 Right tail non-stat17.63435.123.527.6

21. /faculteit technologie management Proposed Method Statistical forecast ASM input Forecast agreement Evaluate accuracy ADI Final Forecast Monthly cycleReal-time

22. /faculteit technologie management Model CaseFinal Forecast  Perfect ADI: ADI  No ADI: Forecast Agreement  Imperfect ADI:Forecast Agreement + ADI

23. /faculteit technologie management 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: F 1 (PCC5)=180, D 1 =275; F 2 =90, D 2 =0;... Imperfect ADI: (NSRTE) F(PCC5) = 100 + Av(95-10, (-90-10) +,...) = 120 –F total = 287 + 91 + 120 = 498 (compare with 467 vs 564) If PCC4 had ordered 33, F total = 287+33+120 = 440

24. /faculteit technologie management Results 192 data points: 78 x No ADI 65 x Perfect ADI 49 x Imperfect ADI

25. /faculteit technologie management Results

26. /faculteit technologie management 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. /faculteit technologie management Conclusions Some other possible methods: –Weighted right tail estimator FA t = O t + Σ t-1 w i (D i -O t ) + (w i = α i ) –Weighted non-stationary right tail estimator FA t = O t + Σ t-1 w i (D i-i -O t-i )(w i = α i ) – Order build-up estimator FA t-i,t = O t-i,t / p t-i,t – Number of orders distribution estimator FA t = O t + Q Σ Nt+1 M ip(i)

28. /faculteit technologie management 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