analysis of a forecasting production inventory system with stationary demand forecast evolution...

8/6/2019 Analysis of a Forecasting Production Inventory System With Stationary Demand Forecast Evolution Models Guillaume Roels 1233779442126234 3

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Analysis of a Forecasting-

Production-Inventory System withStationary Demand

L. Beril Toktay and Lawrence W. Wein

Presented by Guillaume Roels

Operations Research Center

This summary presentation is based on: Toktay, L. Beryl, and Lawrence M. Wein. "Analysis of a Forecasting-Production-Inventory System with Stationary Demand." Management Science47, no. 9 (2001).


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Objective

Minimize steady-state Inventory holding costs h

Shortage penalty costs b


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Recap: MMFE Model

Rolling horizon

Forecast

Forecast Update

Assumptions Stationary Demand with rate

Unbiased Forecasts

Uncorrelated Forecast Updates

H

,0, ,

t t i D i H + =

, , 1,t t i t t i t t iD D + + +=


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Production-Inventory Model

MRP-Type Release Policy:

Inventory Policy

1

, ,

0

HT

t t t i t t H t

i

R D e

+ +=

= + = +

,

1

H

t t t t i H

iQ I D s+

=+ =tI


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Production Policy

Forecast-corrected base-stock policy

State-dependent Optimal Policy

1

* 1

1 1

( )tt H t

t

t t H H t

C if s I C P I

s I if s I C

> + = +

1, 1, 1 1, 1( , , , , )t t t t t t H D D D + +


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Benchmark: Myopic Policy

Do not use available forecastinformation

Constant Inventory

t tR D=

t t mQ I s+ =


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In Heavy Traffic, the WIP has

an exponential distribution

Average Excess Capacity

2

2( )

TCv e e

=

+

Variance of the forecasts Variance of the production


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WIP at time n

time

units1

( )n

n t t

t

X R C =

=

1infn n t n t Q X X =

2 2R C


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Heavy traffic analysis 1

Consider a sequence of systems s.t.:( )

( )

( ) ( )

( ) 0

k

k

k k

k c

= +


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Outline

Model Steady-State Distribution of WIP

Base-Stock Levels Discussion

Conclusion


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Determination of the Base-

Stock levels 1

Myopic Policy

Newsboy quantity

considering the distr. of the WIP!

1

m Q

bs F

b h =

+

1ln 1m

bs

v h

= +


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Stock levels 2

MRP-type Policy

is the difference between: Total Forecast Error over the horizon Hand

Total Capacity

1

H W

bs F

b h

= +

0 1max{ , max }k H kW Q Y Y = +

0Y


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Stock levels 3

MRP-type policy: asymptotic

Proportional to the variance!

Good approximation when large

High utilization rate

0 0

* 21

2

a

H m Y Y

b h

s s v

= + +

/b h


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Outline



Conclusion


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Discussion

Correlation

is the system variability over Hnotresolved at the beginning of the horizon Preference for accurate early forecasts

Optimize over all planning horizons

Greater costs due to misspecification of the forecast model than

misuse of the information in production

*

m

v s

0

2

Y

1

, 1 ,

0

H

t t t t t H

i

R D

+ +=

= +


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Outline



Conclusion


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Conclusion

Integrated view Forecast

Production

Inventory

Lots of improvement for current MRP

systems Is heavy traffic of practical value?


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Thank you

Questions?

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