faculteit technologie management Improving Forecasting with Imperfect Advance Demand Information Tarkan Tan Technische Universiteit Eindhoven October.

/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


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

Outline


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


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


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)


Preliminary AnalysisOrder lead time distribution

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 >10

Order lead time (weeks)

Fre

qu

en

cy

0%

20%

40%

60%

80%

100%

Frequency

Cumulative %


• 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


• 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



Forecast Accuracy per Area Sales Manager (ASM):

-100%

-50%

0%

50%

100%

150%

200%

250%

300%

350%

400%

1 2 3 4 5 6

Month

Fo

rec

as

t E

rro

r


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


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)


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


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


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


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

Analysis

Product/customer M Feb March April May June July42411-9156/51645 12 288000 240000 264000 264000 288000 19200047654-9120/50582 5 89613 64000 25600 19200 4560046663-5367/58880 3 4400041639-4841/51032 4 37440 18720 18720 3200041610-4879/50291 5 21120 17280 24960 18560 11160 1984046604-5399/51137 3 31000 1700042022-5342/50669 2 20000 60000 20000 38175 2000042030-5319/51245 1 54800 9815042024-5346/50842 3 34000 16000 0 28000 900042022-5342/50881 2 10000 20000 10000 20000 10000 1000041500-5316/50130 4 3000 2000 8000 1600096677-5301/51085 2 700042301-7356/50713 2 0 5200 29100 0 0 1920043437-5350/54520 1 0 0 0 32000 0 042023-5383/57255 1 0 0 0 15000 0 042066-5365/50660 2 1700041509-5317/50159 1 1000 100041509-5317/50453 error12072-9010/51552 10 exception, >5 deliveries per month47105-9158/50051 5 24068 24039 2402942024-5346/50669 2 40000 80000 80000 40000 60000 6000042065-9115/50524 143136-5383/50018 2 11000 2400041500-5316/51187 5 10000 10000 18000 2000042024-5346/50506 1 12000 0 20000 0 14000 042027-5343/50658 1 10000 10000 10000 1000042411-9156/58890 5 0 0 123000 120000 12000042411-9090/51611 5 121320 95140 31420 157120 12190042411-9095/50627 18 exception, > 5 deliveries per month43437-5350/52250 3 20000 18000 70000 43000 1800041509-5317/51130 3 32000 44000 4400046057-5334/50130 5 11000 15000 16000


• 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

Proposed Methodology


Imperfect ADI

• Some Possible Methods:– Basic

– Binomial

– Number of orders

– Right tail estimation

– Non-stationary right tail estimation


Basic: Ft = max{FAt, Ot}

Number of orders:

Right tail estimation:

Non-stationary right tail estimation:

})(,max{

M

NOiitttt

t

pNOiQOFAF

otherwiseFA

cFAOifODwOF

t

t

iitttiit

t

1

)(

1

1

)()(t

ittiiitt FAOFDwOF


Comparison of Methods (% Mean Absolute Error)

PCC1 PCC2 PCC3 PCC4 Average

Basic 21.4 36.6 33.8 23 28.7

# orders 13.6 38.3 31.3 36.2 29.8

Right tail 22.9 32.8 33.8 23 28.1

Right tail non-stat

17.6 34 35.1 23.5 27.6


Proposed Method

Statistical forecast

ASM inpu

t

Forecast agreement

Evaluate accuracy

ADI

Final Forecast

Monthly cycle Real-time


Model

Case Final ForecastPerfect ADI: ADINo ADI: Forecast AgreementImperfect ADI: Forecast Agreement + ADI


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


Results

192 data points:78 x No ADI65 x Perfect ADI49 x Imperfect ADI

Product/customer M Feb March April May June July

42411-9156/51645 12 288000 240000 264000 264000 288000 19200047654-9120/50582 5 89613 64000 25600 19200 4560046663-5367/58880 3 4400041639-4841/51032 4 37440 18720 18720 3200041610-4879/50291 5 21120 17280 24960 18560 11160 1984046604-5399/51137 3 31000 1700042022-5342/50669 2 20000 60000 20000 38175 2000042030-5319/51245 1 54800 9815042024-5346/50842 3 34000 16000 0 28000 900042022-5342/50881 2 10000 20000 10000 20000 10000 1000041500-5316/50130 4 3000 2000 8000 1600096677-5301/51085 2 700042301-7356/50713 2 0 5200 29100 0 0 1920043437-5350/54520 1 0 0 0 32000 0 042023-5383/57255 1 0 0 0 15000 0 042066-5365/50660 2 1700041509-5317/50159 1 1000 100041509-5317/50453 error12072-9010/51552 10 exception, >5 deliveries per month47105-9158/50051 5 24068 24039 2402942024-5346/50669 2 40000 80000 80000 40000 60000 6000042065-9115/50524 143136-5383/50018 2 11000 2400041500-5316/51187 5 10000 10000 18000 2000042024-5346/50506 1 12000 0 20000 0 14000 042027-5343/50658 1 10000 10000 10000 1000042411-9156/58890 5 0 0 123000 120000 12000042411-9090/51611 5 121320 95140 31420 157120 12190042411-9095/50627 18 exception, > 5 deliveries per month43437-5350/52250 3 20000 18000 70000 43000 1800041509-5317/51130 3 32000 44000 4400046057-5334/50130 5 11000 15000 16000


ResultsProduct/customer Feb March April May June July

42411-9156/51645 288000 240000 264000 264000 288000 19200047654-9120/50582 89613 94248 89309 83745 97548 8437246663-5367/58880 55836 43123 40408 39837 45240 5024541639-4841/51032 66028 55083 25742 55449 61693 5875341610-4879/50291 38055 39323 39040 42410 40480 3943246604-5399/51137 31419 24748 20000 20000 20000 2000042022-5342/50669 20000 60000 20000 38175 20000 3698642030-5319/51245 54800 0 0 0 98150 042024-5346/50842 34000 22503 0 28336 31294 2053942022-5342/50881 10000 20000 10000 20000 10000 1000041500-5316/50130 9888 11200 18300 13363 13095 4876096677-5301/51085 991 7760 6052 6833 8454 1284842301-7356/50713 0 5200 29100 0 0 1920043437-5350/54520 0 0 0 32000 0 042023-5383/57255 0 0 0 15000 0 042066-5365/50660 0 0 0 10449 17000 041509-5317/50159 0 7588 1000 8469 6601 100041509-5317/50453 101237 183506 232137 404647 348027 25518612072-9010/51552 250000 245157 376577 501245 495084 52072347105-9158/50051 37215 75482 74566 60366 60817 6275142024-5346/50669 40000 80000 80000 40000 60000 6000042065-9115/50524 0 0 32898 0 0 3277343136-5383/50018 28638 26744 33590 20263 31824 2205541500-5316/51187 22652 19724 33105 31014 37323 3835642024-5346/50506 12000 0 20000 0 14000 042027-5343/50658 10000 10000 10000 10000 10000 1000042411-9156/58890 0 0 123000 120000 120000 14965242411-9090/51611 131512 119105 0 31420 158009 12718042411-9095/50627 651690 758465 768730 882731 839678 89330043437-5350/52250 38886 33053 41539 70000 43336 3609841509-5317/51130 34309 48377 48118 51380 60428 046057-5334/50130 26113 28352 25437 19774 22602 24462


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%


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

faculteit technologie management Improving Forecasting with Imperfect Advance Demand Information Tarkan Tan Technische Universiteit Eindhoven October.

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