Modeling the Evolution of Demand Forecasts with Application to Safety Stock Analysis in Production/Distribution Systems

Transcription

1 Modeling he Evoluion of Demand oreca wih Applicaion o Safey Sock Analyi in Producion/Diribuion Syem David Heah and Peer Jackon Preened by Kai Jiang Thi ummary preenaion baed on: Heah, D.C., and P.L. Jackon. "Modeling he Evoluion of Demand oreca wih Applicaion o Safey Sock Analyi in Producion/Diribuion Syem." IIE Tranacion 26, no. 3 (1994): 17-3.

2 Overview Problem Mehodology Key Reul

3 Muli-produc Muli-locaion Muli-period wih Capaciy and Tran-hipmen N=5 Produc Muli- Plan L=8 DC Demand of each produc a each DC

4 Planning Sequence of Even 2. Deerminiic LP derive producion plan Monh Monh 1 3. Implemen he curren monh producion plan Monh 2 1. A he end of he monh foreca demand M-monh ou 4. Roll horizon and re-foreca

5 Solving he Invenory Problem ind an economical afey ock facor for each produc a each DC for each monh A DP approach difficul A imulaion approach Ue MME o imulae foreca Ue a imilar LP o imulae deciion Tally co and ervice level for differen afey ock facor

6 The Maringale Model of oreca Evoluion (Addiive) Curren Monh Monh Monh 1 Monh 2 Monh uure Monh Monh 1 Monh 2 Monh 3 D, D,1 D,2 D i.i.d. mulivariae normal wih mean D 1,1 D 1,2 D 1,3 ε 1,1 = D 1,1 -D,1 ε 1,2 = D 1,2 -D,2 ε 1,3 = D 1,3 -D D 2,2 D 2,3 ε 2,2 = D 2,2 -D 1,2 ε 2,3 = D 2,3 -D 1,3

7 Juifying ε are i.i.d. mulivariae normal wih mean ε ε = D D,, 1, + = ( ε ), = Informaion e grow wih ime ε i uncorrelaed wih all ε u for u -1 and E[ε ]= ε i a aionary proce ε i normal

8 Why i i called a Maringale Model? Why i i called a Maringale Model? If foreca i condiional expecaion baed on curren informaion e ] [,, D D = E Then D D E D E E D E 1, 1, 1, 1, ],..., [ ],..., ],..., [ [ ],..., [ = = = Thu, D, i a maringale and ] [ ] [ 1,,, = D E D E ε i uncorrelaed wih -1 ] [, = E ε

9 Condiional Expecaion a Be Mean- Square Predicor of D, Uing he be Mean-quare predicor definiion of condiional probabiliy E[( D D ) w ] = E[( D D u,,, ) w ] =, Then w r. v. oberved a u E[( D D ) w ] = E[( D D ) w ] =, u,, u, Thu, rue alo under linear predicor

10 The Muliplicaive Model ν = log( D ) log( D, 1,, ) R exp( ) = D / D,,, 1, = ν ν ν + = ( ), = i.i.d. mulivariae normal wih mean of each coordinae being he negaive of one half of i variance

11 Characerize he Simulaion Syem The variance-covariance marix Σ for ε (MN Х MN) eimaed uing pa demand and foreca The iniial ae of he yem (D,, D,1,, D,M, D)

12 Why no Simulae he Time Serie of oreca Direcly Simulae he complicaed foreca proce baed on pa demand, compeior price, weaher foreca ec. i no more credible han auming he foreca proce i MME and eimaing he variance-covariance marix

13 Simulaing he oreca Evoluion Uing he Variance-covariance Marix Σ Properie of Σ Σ i ymmeric and PSD Σ = CC = (UD 1/2 )(UD 1/2 ) where D i he diagonal marix wih eigenvalue ored in decreaing order The andard mulivariae normal repreenaion: ε = CZ where Z i a andard normal random vecor

14 oreca Variabiliy Reolving Over Time The 1 column of C capure he 1 order magniude of ε The ign and value of enrie in he 1 column of C reveal how foreca variabiliy reolve over ime and how hey are correlaed e.g. C,1 = , C,41 = % variabiliy reolved in monh of ale, 38.3% variabiliy reolved 1 monh ou e.g. C,1 =.1616, C,41 =.3143, C,81 = -.88, C,121 = %, 49%, 4%, 34%

15 The Experimen Tradiional oreca Mehod (2 monh ou) 8 X 8 Σ from four year of pa foreca and acual demand daa Saiical oreca Mehod (4 monh ou) (16 X 16) Σ from wo year acual demand and imulaed foreca Iniial ae foreca for he year of fical year Co and ervice meric averaged over 1 2 imulaed year

16 The Reul Safey ock facor can be reduced wihou acrificing much fill rae, if uing he Saiical oreca Mehod reuling in ignifican co aving Reducing afey ock facor uing he Tradiional oreca Mehod doe no how much benefi More imporan o increae foreca accuracy han o increae capaciy

17 Recap MME o model foreca evoluion Simulae he yem uing MME Evaluae he performance of he wo yem wih wo differen foreca mehod