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Inventory Management in e to y a age e t Semiconductor Supply - - PowerPoint PPT Presentation

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Dagstuhl Seminar 16062 Modeling and Analysis of Semiconductor Supply Chains Schlo Dagstuhl, 66687 Wadern, Germany Schlo Dagstuhl, 66687 Wadern, Germany 07-12, February 2016 Inventory Management in e to y a age e t Semiconductor Supply

slide-1
SLIDE 1

Dagstuhl Seminar 16062 Modeling and Analysis of Semiconductor Supply Chains Schloß Dagstuhl, 66687 Wadern, Germany Schloß Dagstuhl, 66687 Wadern, Germany 07-12, February 2016

Inventory Management in e to y a age e t Semiconductor Supply Chains

Jei-Zheng Wu1,3, Chen-Fu Chien2,3, and Hui-Chun Yu3,4

1Department of Business Administration Soochow University Taiwan 1Department of Business Administration, Soochow University, Taiwan 2Department of Industrial Engineering and Engineering Management,

National Tsing Hua University, Taiwan

3NTHU-TSMC Center for Manufacturing Excellence, Taiwan 4Taiwan Semiconductor Manufacturing Company, Taiwan

09 F b 2016 09, February 2016

1

slide-2
SLIDE 2

Outline

 Basic Model not comprehensive  Basic Model, not comprehensive  Survival Analysis for Safety Stock Level (Inventory Days)

Inventory Age and Accounting Principles

 Inventory Age and Accounting Principles 2

slide-3
SLIDE 3

Semiconductor Manufacturing Process

 The rapid technology development and shortening

p gy p g product life cycle lead to high risk of product obsolescence.

 Manufacturers still need to hold a reasonable level of inventory to

satisfy customer under demand uncertainty and long lead-time.

 This study considers the work-in-process and inventory problem

  • f the semiconductor memory manufacturing which has the 3
  • f the semiconductor memory manufacturing which has the 3-

month approximately averaged lead time.

General Specific

(50 days) (5 days) (7 days) (22 days)

p f

3

slide-4
SLIDE 4

Features

Complex BOM and product substitution, but also various raw wafer release schedules (wafer start), turnaround times (TAT, lead times), production plans, safety stock strategies, and end lead times), production plans, safety stock strategies, and end product-demand forecasts.

Inventory on-hand and multi-period rolling mechanism

Postponement strategy, delayed differentiation

  • die-bank, wafer bank, via bank.

Although some manufacturers have set inventory banks

Although some manufacturers have set inventory banks through the manufacturing process. However, the stock points do not bring its role into full play.

It l fl t th t it ti b t l k d i i l i

  • It merely reflects the recent situation but lacks decisional meaning

The sale unit will not provide the accurate distribution of

  • demand. Inventory planners have to judge the demand.

4

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SLIDE 5

Inventory Days Research Motivation and Objectives Research Motivation and Objectives

 Existing study did not suggest inventory days (turnover) for  Existing study did not suggest inventory days (turnover) for

decision making

 Inventory turnover is practical but only applies for post-

y p y pp p evaluation in practice.

 This study aims to constructed an inventory-day-based multistage

inventory decision model for calculating the inventory level of all

  • f the stages of semiconductor manufacturing based on the

i t i l l i inventory survival analysis.

5

slide-6
SLIDE 6

Indices and Sets

i, j product group i, j t Day t m Month m N the set of network structure of FG corresponding to DB NN the set of non-network structure of FG k technology k l technology capacity balance level l T the set of days M th t f th NN the set of non network structure of FG corresponding to DB DBN the set of DB existing in network structure M the set of months K the set of technologies DMtm the set of day corresponding to month FG the set of inventory group of stage FG DBNN the set of DB existing in non-network structure BOM the set of product group f corresponding to the group g of its FG the set of inventory group of stage FG DB the set of inventory group of stage DB WB the set of inventory group of stage WB VB the set of inventory group of stage VB corresponding to the group g of its upper stage in the bill of material MAP the set of product group g corresponding to its technology k y g p g L the set of technology capacity balance level FL the set of FG corresponding to l corresponding to its technology k

6

slide-7
SLIDE 7

Parameters

tati turn-around time of product group i

i

g yi yield of product group i bit beginning on-hand inventory of product group i at day t

it

byit yielded beginning on-hand inventory of product group i at day t ri gross die of product group i

i

dit demand of product group i at day t ssldit inventory days of product group i at day t

t

sslit safety stock level of product group i at day t ckm capacity limit of technology k of month m bcpi inventory in the beginning of CP technology of product group i bdl technology capacity balance bound of level l rtl technology capacity balance ratio of level l

7

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SLIDE 8

Variables

Iit end on-hand inventory of the period of product group i at day t Iit end on hand inventory of the period of product group i at day t Sit amount of shortage of product group i at day t Fit receipt inventory from upper stage of product group i at day t Uit unmet amount of safety stock of product group i at day t Oit

  • ver amount of safety stock of product group i at day t

D ti t d d d f d t i t d t Dit estimated demand of product group i at day t WIPit the amount of work-in-process (WIP) of product group i at day t Hijt the amount of FG demand of product group i (corresponding to group j) Hijt the amount of FG demand of product group i (corresponding to group j) in network structure SSLit estimated safety stock level of product group i at day t Ckm technology capacity k used of month m BCPit inventory in the beginning of CP technology of product group i at day t PL t h l it b l f t f d t i t b l l l l

8

PLil technology capacity balance factor of product group i at balance level l

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SLIDE 9

Constraints relative to the Finished Goods Bank (FG) Finished Goods Bank (FG)

Fl b l f f t t k l l d th d h d i t

 Flow balance of safety stock level and the end on-hand inventory

, ,

it it it it

ssl O I U t i       T FG

, ,

it

it is i t s t ssld

ssl d t i

  

   

 

T FG

 Stock flow from the last period into this period

FG     i t I d S F b 1

 Estimated safety

stock level

B i th

it

FG        i t I d S F by

it it it it it

, 1 , FG T          

 

i t S I d I S F by

t i it it t i it it it

, 1 ,

) 1 ( ) 1 (

By summing the demand of product group at DB stage in the period of

9

i it

tat t i F      , , FG

in the period of inventory days up

slide-10
SLIDE 10

Demand of the product group at Die Bank group at Die Bank

 Network structure

i j

  • alternative BOM

 Network structure

  • Multi-Chip Package

H F  

  • substitutions
  • multi-chip

, ,( , ) , ,

ijt ijt it

H F t i j i j        T BOM FG DB

, ( , )

/ , ,

i

jt ij t tat i i j

D H y t j

 

   

N

T DBN

 Non-network structure

  • Single-Chip Package

i j

g p g

, ( , )

/ , ,

i

jt i t tat i i j

D F y t j

 

   

NN

T DBNN

10

slide-11
SLIDE 11

Constraints relative to the Die Bank (DB) the Die Bank (DB)

 Flow balance of safety stock level

y and the end on-hand inventory

DB T       i t U I O SSL

it it it it

, , 1 , ,        t i I D F BCP b

it it it it i

DB

1 , ,

) 1 (

       t i I D I F BCP

it it t i it it

DB

 Estimated safety stock level

Equation of beginning on hand

1 , ,

) 1 (

     

t i I D I F BCP

it it t i it it

DB

i it

tat t i F      , , DB

 Estimated safety stock level

By summing the demand of product group at DB stage in the i d f i t d

Equation of beginning on-hand inventory of circuit probing process at DB stage

period of inventory days up

DB T      i t D SSL

is it

, ,

MAP DB     

) , ( , , k i i BCP bcp y

k

tat t it i i

t t t i BCP   DB

11

   i ssld t s t

it

i it

tat t i BCP     , , DB

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SLIDE 12

Constraints relative to the Wafer Bank (WB) the Wafer Bank (WB)

 Demand of the product group at WB  Stock flow from the last

period into this period

WB T

BOM

   

 

  

j t y F D

j i tat t s i is jt

, , /

) (

 Flow balance of safety stock level

BOM    j i tat t s

i

) , (

1 , ,       t i I D F by

it it it it

WB

1 , ,

) 1 (

       t i I D I F by

it it t i it it

WB

, ,

it

it is i t s t ssld

SSL D t i

  

   

 

T WB WB T       i t U I O SSL

it it it it

, ,

, ,

) 1 ( 

y

it it t i it it

i it

tat t i F      , , WB

12

it it it it

, ,

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SLIDE 13

Constraints relative to the Via Bank (VB) the Via Bank (VB)

 Demand of the product group at VB  Stock flow from the last

period into this period

VB T    

 

j t y F D

i is jt

, , /

 Flow balance of safety stock level

BOM

 

  

j y

j i tat t s i is jt

i

) , (

1 , ,       t i I D F by

it it it it

VB

1        t g I D I F by VB , ,

it

it is i t s t ssld

SSL D t i V

  

   

 

T B 1 , ,

) 1 (

      

t g I D I F by

it it t i it it

VB

i it

tat t i F      , , VB

13

VB T       i t U I O SSL

it it it it

, ,

slide-14
SLIDE 14

Capacity limit by different technology different technology

 Constraints about capacity limits Level Bound Ratio  Constraints about capacity limits

MAP M

BOM DM

   

 

   

) , ( , ,

) , ( ) , ( ,

k i m F C

k i m s tat t s is km

i

10 10 1 1000 1000 2 100000 100000 4

Capacity balance of technology

) , ( ) , ( ,

i

MAP M     ) , ( , , k i m ca C

km km

100000 100000 4 1000000000

  • 1

8  Capacity balance of technology

 

il i

PL S

Product Level PL F001 10 7.94 F001 1000

  FL T il t

, ) , ( ,    

 l l l il

bd l i bd PL FL

L

F001 100000 F001 1000000000 F002 10 47.86  Calculation of work-in-process

   

 l L

F002 10 47.86 F002 1000 F002 100000 F002 1000000000 14

, ,

i i

it it is is i t tat s t i t tat s t

WIP I F b t i

     

        

   

T FG DB WB VB

F002 1000000000

slide-15
SLIDE 15

Objectives j

 Objective

CO CL CS CB

M M M M   

j

  • cost of technology balance penalty cost (CB)

CO CL CS CB Min

CO CL CS CB

Μ M M M   

CO C CS C

  • shortage cost (CS)



 

DB L i l il l

PL rt CB *

  • shortage cost (CS)



 

FG T i t it

s CS

  • cost of inventory unsatisfying safety stock (CL)

     

   

it U it U it U it U

U M U M U M U M CL

4 3 2 1

  • cost of inventory excess of safety stock (CO)

     

        VB T WB T DB T FG T i t it U i t it U i t it U i t it U 4 3 2 1

     

O M O M O M O M CO

15

     

       

   

VB T WB T DB T FG T i t it O i t it O i t it O i t it O

O M O M O M O M CO

4 3 2 1

slide-16
SLIDE 16

How to determine the safety stock level using inventory days?? level using inventory days??

 Estimated safety stock level

y

By summing the demand of product group at the stage in the period of inventory days up

, ,

it

it is i t s t ssld

ssl d t i

  

   

 

T FG DB T     

  

i t D SSL

i ssld t s t is it

it

, ,

it it

, ,

it

it is i t s t ssld

SSL D t i

  

   

 

T WB

, ,

it is i t t ld

SSL D t i V

   

 

T B

16

it

i t s t ssld   

slide-17
SLIDE 17

Inventory Days How to Evaluate? How to Evaluate?

St d Sh t R i i C it S tti Study Shortage Remaining Capacity Setting Ben-Daya and Raouf （1993） ◎ Variation Hsu and Wang （2001） ◎ ◎ Variation Hsu and Wang （2001） ◎ ◎ Variation Zhao et al. （2001） ◎ ◎ ◎ Variation Boulaksil et al. （2009） ◎ ◎ Error Ruiz-Torres and Mahmoodi （2010） ◎ ◎ Variation Janssens and Ramaekers （2011） ◎ ◎ Error This study ◎ ◎ ◎ Turnover

Existing study did not suggest inventory days (turnover) for decision making

Inventory turnover is practical but only applies for post-evaluation in practice.

This study ◎ ◎ ◎ Turnover

y p y pp p p

This study aims to constructed an inventory-day-based multistage inventory decision model for calculating the inventory level of all of the stages of semiconductor manufacturing based on the inventory survival analysis semiconductor manufacturing based on the inventory survival analysis.

17

slide-18
SLIDE 18

Conventional Inventory Setting Considering Demand Uncertainty Considering Demand Uncertainty

U i D d V i ti Using Forecast Error

Uncertain

Using Demand Variation Using Forecast Error

( , )

D

D 

 

 

1 2

ˆ 1

t

Uncertain Inventory

Production

Uncertain Demand

Production Salesperson

( , )

D

D 

 

 

  

1 2

) ( ˆ 1 1 ˆ

j

i D i D t 

Uncertain Demand Inventory Setting J D Z

 Inventory Setting

Production

Demand Forecast

Salesperson

( , )

d

d 

Remaining Stock, C t S ti f ti

D

J D Z

 

  Setting

d

J d Z

 

  Forecast Customer Satisfaction Remaining Stock, Customer Satisfaction

18

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SLIDE 19

Forecast Error Comparison p

Absolute error Bias Mean squared error Mean absolute distance error

 

) ( ) ( ˆ

1 1

 

i D i D

t i

 

) ( ) ( ˆ

1 1 2

 

i D i D

t i

) ( ) ( ˆ

1 1

 

i D i D

t i

1

1

 t

i

1

1

 t

i

1

1

 t

i

Relative error Mean absolute percentage error Symmetric mean absolute percentage error

) ( ) ( ˆ

1

i D i D

t

) ( ) ( ˆ

1

i D i D

t

1 ) ( ) ( ) (

1

 

t i D i D i D

i

 

1 2 ) ( ) ( ˆ ) ( ) (

1

  

t i D i D i D i D

i

19

slide-20
SLIDE 20

Mean Absolute Deviation (E ) (MAD)

) ( ) ( ˆ

1 1

 

i D i D

t i

(Error) (MAD)

 The same error (100 units), but accuracy differs

1  t

 The same error (100 units), but accuracy differs

Prod A 1 2 3 4 5 6 7 8 9 10 11 12 Actual

10,200 20,000 22,000 20,000 20,000 30,000 3,000 23,000 23,000 23,000 30,000 23,000

Forecast

10,100 22,000 20,000 2,000 3,000 20,000 23,000 30,000 23,000 30,000 23,000 23,000

Error

100

  • Prod B

1 2 3 4 5 6 7 8 9 10 11 12 Actual

1,100 500 1,440 1,000 3,750 2,000 5,682 4,550 1,440

Actual

1,100 500 1,440 1,000 3,750 2,000 5,682 4,550 1,440

Forecast

1,200 2,200 17,000 1,000 17,000 100 2,700 170

E

100

20

Error

100

slide-21
SLIDE 21

Mean Absolute Percentage Deviation (Relative Error)

) ( ) ( ) ( ˆ

1 1

 

i D i D i D

t i

Deviation (Relative Error)

 When the denominator approaches to zero, the relative error

1  t

 When the denominator approaches to zero, the relative error

becomes less useful.

產品C 1 2 3 4 5 6 7 8 9 10 11 12

Prod C

產品C 1 2 3 4 5 6 7 8 9 10 11 12 Actual

1,200 2,200 7,000 1,000 1,000 100 2,700 170

Prod C

Forecast

40 56,110 20 240 16 60 4,238 50 95 2,847

預測誤差

  • 100%

Error

產品D 1 2 3 4 5 6 7 8 9 10 11 12 Actual

40 56 110 20 240 16 60 4 238 50 95 2 847

Prod D

Actual

40 56,110 20 240 16 60 4,238 50 95 2,847

Forecast

20 2,200 17,000 1,000 17,000 100 2,700 170 21

預測誤差

  • Error
slide-22
SLIDE 22

Inventory Turnover Estimation y

 Inventory turnover represents the actual demand that  Inventory turnover represents the actual demand that

must be fulfilled after a number of forecast periods.

  • Actual demand represents the should-be inventory level
  • denote the salesperson’s forecast demand
  • T1 denote the maximal time before fulfills

T d t th ti f th i i d d t th T +1

 

t D ˆ

  • T2 denote the proportion of the remaining demand to the T1+1

forecast at time t;

  • T1 +T2 express the inventory turnover

1 2

p y

1

T t

1 2

( ) J t T T  

   

1

ˆ arg max

t T T T j t

T D j D t

  

       

   

) 1 ( ˆ ˆ

2

1

  

T D j D t D T

t j

22

j t 

 

) 1 ( 1  T D

slide-23
SLIDE 23

Inventory Turnover Estimation 01 Inventory Turnover Estimation 01

2011 01 02 03 04 05 06 07 08 09 10 11 12 01 02 03 04 Actual

0 48,000 60,000 12,000 90,000 0 24,000

Forecast

0 10,000 10,000 10,000 100 100,000 100,000 100,000 100,000

  • Turnover
  • 1

2

0, (01) T T J    

M2 Forecast M3 Forecast M4 Forecast

1 2

, ( )

  • ecast

3

  • ec s
  • ec s

M1 Forecast M5 Forecast

23 10,000 10,000 10,000 100

slide-24
SLIDE 24

Inventory Turnover Estimation 02 Inventory Turnover Estimation 02

2011 01 02 03 04 05 06 07 08 09 10 11 12 01 02 03 04 Actual

0 48,000 60,000 12,000 90,000 0 24,000

Forecast R1

0 10,000 10,000 10,000 100 0 100,000 100,000 100,000 100,000

  • 1

Forecast R2

  • 48,000

100,000 100,000 100,000 100,000

  • Turnover
  • 1

(02) 1 T T J

M3 Forecast

1 2

1, (02) 1 T T J    

M2 Forecast M4 Forecast M5 Forecast

48,000

24 48,000 100,000

slide-25
SLIDE 25

Inventory Turnover Estimation 03 Inventory Turnover Estimation 03

2011 01 02 03 04 05 06 07 08 09 10 11 12 01 02 03 04 Actual

0 48,000 60,000 12,000 90,000 0 24,000

R1

10,000 10,000 10,000 100 0 100,000 100,000 100,000 100,000

  • Forecast R2
  • 48,000

100,000 100,000 100,000 100,000

  • R3
  • 20,000 80,000

4,000 24,000 0 100,000 4,000 24,000 4,000 0 -

  • Turnover

1

  • 1.5

1 2

1, 0.5 (03) 1.5 T T J    

M3 Forecast M4 Forecast M5 Forecast

20,000 40,000

25 20,000 80,000 4,000

, ,

slide-26
SLIDE 26

Inventory Turnover Estimation 04 Inventory Turnover Estimation 04

2011 01 02 03 04 05 06 07 08 09 10 11 12 01 02 03 04 Actual

0 48,000 60,000 12,000 90,000 24,000

R1

10,000 10,000 10,000 100 100,000 100,000 100,000 100,000

  • ForecastR2
  • 48,000 100,000

100,000 100,000 100,000

  • R3
  • 20,000

80,000 4,000 24,000 100,000 4,000 24,000 4,000

  • R4
  • 2,000

4,000 24,000 100,000 100,000 100,000 100,000 0 -

Turnover

1 1.5

  • 2.25

M6 Forecast

1 2

2, .25 (04) 2.25 T T J    

M4 F M5 Forecast M4 Forecast

2 000 4 000 6 000

26

2,000 4,000 6,000

2,000 4,000 24,000

slide-27
SLIDE 27

Inventory Turnover Estimation 05

2011 01 02 03 04 05 06 07 08 09 10 11 12 01 02 03 04

Inventory Turnover Estimation 05

2011 01 02 03 04 05 06 07 08 09 10 11 12 01 02 03 04 Actual

0 48,000 60,000 12,000 90,000 0 24,000

R1

10,000 10,000 10,000 100 0 100,000 100,000 100,000 100,000

  • R2
  • 48,000

100,000 0 100,000 100,000 100,000

  • Forecast

R2

48,000 100,000 0 100,000 100,000 100,000

R3

  • 20,000

80,000 4,000 24,000 0 100,000 4,000 24,000 4,000

  • R4
  • 2,000

4,000 24,000 100,000 100,000 100,000 100,000

  • R5
  • 100

100 100 100 100 100 100 100 100 100 100 100

Turnover

1 1.5 2.25

  • right

censored

M5 Forecast M8 Forecast M11 Forecast M2 Forecast

(05) 12 J 

M6 Forecast M9 Forecast M12 Forecast M3 Forecast

(05) 12 J 

M7 Forecast M10 Forecast M1 Forecast M4 Forecast

27

slide-28
SLIDE 28

Survival Analysis for Inventory Days Inventory Days

 Inventory days data possess the characteristics of  Inventory days data possess the characteristics of

  • temporal scale
  • small sample size (non-normal, nonparametric)
  • right-censored

 Survival analysis is an convincing methodology applied in the

i i i i i f i i biomedical, reliability, and others for dealing with temporal scale, small sample size, and right-censored. Y t i l l i i i th i t t

 Yet, survival analysis is scare in the inventory management area. 28

slide-29
SLIDE 29

Survival analysis y

 Time-to-event  Time to event  Example :

”Observe” an event elapsing time p g

Start

Event

 Event in Survival analysis :

Start

Time

Event

  • consumption
  • death

di

The elapsing time of actual value (shippment) being consumed by forecast

  • disease
  • relapse

29

slide-30
SLIDE 30

Right Censor g

 Censoring: we don’t know survival time exactly.  Censoring: we don t know survival time exactly.  Why censor?

1. study ends – no event y 2. lost to follow-up 3. Withdraw

 Example :

  • Tracing time from heartache to death

 Right-censored: true survival time is equal to or greater than

  • bserved survival time.

30

slide-31
SLIDE 31

Survival Function aka Empirical Distribution Function aka Empirical Distribution Function

 S(t) = survival function = P(T > t)

  • T = survival time (T ≥ 0) (random variable)
  • The probability of an individual’s survival time over a time point t

Ch t i ti f S(t)

 Characteristic of S(t):

  • t ≥ 0, temporal data
  • Monotonic decreasing
  • Monotonic decreasing
  • S(0) = 1
  • S(t) approaches zero when t becomes very large

( ) pp y g

Estimate of S(t)

31

slide-32
SLIDE 32

Kaplan-Meier (K-M) estimator p ( )

 Properties

   

1 ˆ ( ) 1 1

i

n i F t P T t S t

           

 Properties

(1) is an unbiased and consistent estimator of ) ( ˆ t S ) (t S

) (

   

( ) 1 1

i

t t

F t P T t S t n i

          

(2) G d f l

m i t t t p n p t S t S Var

i i i j j j j

, , 2 , 1 , ) 1 ( )] ( ˆ [ )) ( ˆ (

) 1 ( ) ( 1 2

        

 

Greenwoods formula (3)

m i t t t d n n d t S t S Var

i i i j

, , 2 , 1 , ) ( )] ( ˆ [ )) ( ˆ (

) 1 ( ) ( 2

      

d n n

j j j j

) (

1

 ( ) ( ) ( ) 1

ˆ ˆ ( ) ( | ), 1,2, ,

i i j j j i i i i i

S t P T t T t i m

     

Number of deaths at time ti

1 1 1 1 1

(1 ) (1 ( )) (1 ) (1 ) ? ˆ ( ) ( | ) ( )

i i i i i

i i i i i d d i i i n n j j j j j i i

p q h t n d S t P T t T t S t

     

                  

Number of survivors (i) Hazard Censor or not

32

( 1) ( ) ( ) ( 1)

?( ) ( | ) ( )

i i i i i

S t P T t T t S t n

 

     

until time ti at time ti

slide-33
SLIDE 33

Kaplan-Meier Estimation Procedure

1

i

n i

 

 

1 ˆ ( )

i

t t

n i P T t S t n i

           

5 1.0 1.0

  • 3

1 5 1/5 0 8 0 8 0 179 3 1 5 1/5 0.8 0.8 0.179 5 1 4 1/4 0.75 0.6 0.219 8 1 2 1/2 0.5 0.3 0.239

Censored data provides ti l d f l

Confidence level

partial and useful information about the distribution

33

6

slide-34
SLIDE 34

Inventory Survival Analysis Procedure

1

i

n i

 

Time Censor Count 0 00 1 11 Product Time Count Total Prob S(t) F(t) A 0 00 11 25 0 56 0 56 0 44

   

1 ˆ ( ) 1 1

i

t t

n i F t P T t S t n i

              

0.00 1 11 0.31 2 0.31 1 2 0.80 1 1 A 0.00 11 25 0.56 0.56 0.44 A 0.31 2 12 0.83 0.47 0.53 A 0.80 1 10 0.90 0.42 0.58 A 0.97 1 9 0.89 0.37 0.63 0.97 1 1 0.98 4 0.98 1 1 1.58 1 1 A 0.98 1 4 0.75 0.28 0.72 A 1.58 1 3 0.67 0.19 0.81 A 1.80 1 2 0.50 0.09 0.91

Calculate the inventory turnover and sort the data in Giving confidence

1.80 1 1 12.00 1

the increasing order Giving confidence level to determine the inventory months

if 1

it it

ssld SSL    if 1

it

it it is i t s t ssld

ssld SSL D

  

    

ssldit

34

it

slide-35
SLIDE 35

Estimation for Different Products using Empirical Distribution Function using Empirical Distribution Function

Product 0.6 0.7 0.8 0.9 Product 0.6 0.7 0.8 0.9

A23 0.74 0.96 1.10 1.95 A24 0.00 0.19 0.24 0.48 A25 0.20 0.30 0.68 1.01 A26 0.99 0.99 0.99 0.99 6 10 40 12 00 12 00 A01 0.00 0.00 12.00 12.00 A02 0.00 0.50 0.96 2.60 A03 0.78 1.02 2.60 3.15 A04 1.00 1.00 1.00 1.68 A27 5.67 10.40 12.00 12.00 A28 12.00 12.00 12.00 12.00 A29 1.46 1.49 2.18 2.35 A30 1.81 4.25 11.11 11.68 A31 1 23 1 51 1 64 2 09 A05 0.00 0.00 0.00 12.00 A06 12.00 12.00 12.00 12.00 A07 12.00 12.00 12.00 12.00 A08 0.55 0.94 1.48 2.02 A31 1.23 1.51 1.64 2.09 A32 1.33 1.33 1.33 1.33 A33 1.03 1.05 1.45 3.06 A34 0.00 0.00 0.00 0.00 A35 0 96 1 00 1 33 12 00 A09 0.70 0.70 2.37 2.37 A10 1.77 1.80 1.90 2.43 A11 0.00 0.00 0.00 0.00 A12 0.94 1.08 1.71 2.56 A35 0.96 1.00 1.33 12.00 A36 0.53 0.53 1.27 1.27 A37 1.28 1.62 2.85 12.00 A38 1.00 1.00 1.19 1.26 A39 12 00 12 00 12 00 12 00 A13 0.90 0.90 12.00 12.00 A14 2.45 5.84 12.00 12.00 A15 1.04 1.14 1.74 1.78 A16 0.80 0.97 1.22 2.00 A39 12.00 12.00 12.00 12.00 A40 1.00 1.00 1.00 1.00 A41 0.44 0.72 1.00 1.08 A42 0.00 0.68 1.31 3.34 A43 0 00 0 00 0 00 0 38 A17 0.50 0.93 1.10 1.58 A18 1.00 1.15 1.54 2.36 A19 1.00 1.97 1.97 1.97 A20 0.82 1.00 1.35 1.84

35

A43 0.00 0.00 0.00 0.38 A44 1.13 1.32 2.24 5.53 A45 1.02 1.35 1.51 2.06 A21 12.00 12.00 12.00 12.00 A22 0.41 0.41 1.02 1.02

slide-36
SLIDE 36

Case Study

 Planning Horizon: 12 months – 22 VBs, 26 WBs, 46 DBs, 151 FGs

g

 Parameters

  • Turn around time, TAT

Yi ld G di

  • Yield, Gross die
  • Confidence Level to set up safety stock
  • Actual Inventory Settings

y g

  • Backlog, Rolling
  • Shipping
  • Begin on hand inventory BOH
  • Begin-on-hand inventory, BOH

Tech Product # of Var. # of Const. T h1

FG-151 WB-26 604 706 285 215

Tech1

FG 151 DB-46 WB 26 VB-12 604,706 285,215

Tech2

FG-127 DB-48 WB- 22 VB-7 438,642 204,775 36

Tech3

FG-66 DB-54 WB-22 VB-10 528,108 243,795

slide-37
SLIDE 37

Inventory Equivalent y q

Technology Time VB WB DB FG M1 1 000 0 189 1 362 0 860

 Inventory amount of Tech1

M1 1.000 0.189 1.362 0.860 M2 1.031 0.244 1.223 0.937 M3 0.932 0.328 1.176 0.970 M4 0 957 0 320 1 202 0 979

 Inventory amount of

Tech1 VB in the first month is linearly

M4 0.957 0.320 1.202 0.979 M5 1.056 0.276 1.225 0.925 M6 1.103 0.317 1.176 0.748 M1 1.816 0.626 1.427 0.796

transformed to 1 so do others

Tech2

M1 .8 6 0.6 6 . 7 0.796 M2 1.693 0.659 1.680 0.889 M3 1.699 0.717 1.783 0.935 M4 1.748 0.784 1.877 0.716 M5 1.789 0.807 2.043 0.484 M6 1.679 0.873 2.094 0.477 M1 0.150 0.037 0.159 0.130

Tech3

M2 0.087 0.035 0.158 0.132 M3 0.108 0.027 0.143 0.138 M4 0.155 0.025 0.144 0.137

37

M5 0.110 0.025 0.144 0.136 M6 0.088 0.025 0.141 0.113

slide-38
SLIDE 38

Parameter

Demand Amount

Capacity Limits

Tech Time Capacity limits M1 0.576 M2 0 576

Tech 1 2 3 4 5 6 7 8 9 10 11 12 Tech1

0 312 0 743 0 697 0 603 0 682 0 659 0 700 0 678 0 713 0 757 0 745 0 798 Tech1 M2 0.576 M3 0.648 M4 0.646 M5 0.442 M6

Tech1

0.312 0.743 0.697 0.603 0.682 0.659 0.700 0.678 0.713 0.757 0.745 0.798

Tech2

0.236 0.561 0.580 0.527 0.594 0.596 0.632 0.611 0.650 0.672 0.632 0.664

Tech3

0.038 0.103 0.092 0.084 0.092 0.086 0.092 0.090 0.097 0.103 0.099 0.104 

Begin on Hand (BOH)

M6 0.537 Tech2 M1 0.956 M2 0.956 M3 0.648 Tech2 M4 0.646 M5 0.785 M6 0.598 M1 0.053

Stage Tech1 Tech2 Tech3 VB 0.477 0.518 0.117 WB 0.097 0.307 0.023

Tech3 M2 0.053 M3 0.086 M4 0.091 M5 0.111

DB 2.440 1.721 0.146 FG 0.775 0.554 0.101

Inventory amount of Tech1 VB in the first month is

38

M6 0.196

Inventory amount of Tech1 VB in the first month is linearly transformed to 1 so do others

slide-39
SLIDE 39

Results: VB and WB Qty1 (CL: 90%) Qty2 (CL: 80%) Qty1 (CL: 90%), Qty2 (CL: 80%)

 Inventory amount of Tech1 VB in the first month is linearly

Tech Time Case This study This study （Qty） （Qty1） （Qty2） Tech Time Case This study This study （Qty） （Qty1） （Qty2）

VB WB y y transformed to 1 so do others

Tech1 M1 1.000 0.999 0.767 M2 1.031 1.268 1.181 M3 0.932 1.822 1.618 M4 0.957 2.228 1.845 Tech1 M1 0.189 0.091 0.089 M2 0.244 0.099 0.091 M3 0.328 0.133 0.121 M4 0.320 0.304 0.323 M5 1.056 2.278 1.908 M6 1.103 2.090 1.938 M1 1.816 1.413 1.360 M2 1.693 1.759 1.712 M5 0.276 0.457 0.469 M6 0.317 0.523 0.460 M1 0.626 0.260 0.258 M2 0.659 0.311 0.309 Tech2 M3 1.699 2.195 2.098 M4 1.748 2.400 2.290 M5 1.789 2.646 2.498 M6 1.679 2.846 2.545 Tech2 M3 0.717 0.424 0.414 M4 0.784 0.450 0.442 M5 0.807 0.448 0.432 M6 0.873 0.480 0.465 6 Tech3 M1 0.150 0.146 0.129 M2 0.087 0.139 0.140 M3 0.108 0.149 0.145 M4 0.155 0.176 0.170 6 Tech3 M1 0.037 0.028 0.026 M2 0.035 0.048 0.038 M3 0.027 0.058 0.041 M4 0.025 0.056 0.036

39

M4 0.155 0.176 0.170 M5 0.110 0.200 0.194 M6 0.088 0.261 0.221 M4 0.025 0.056 0.036 M5 0.025 0.061 0.039 M6 0.025 0.066 0.043

slide-40
SLIDE 40

Results: DB and FG Qty1 (CL: 90%) Qty2 (CL: 80%) Qty1 (CL: 90%), Qty2 (CL: 80%)

 Inventory amount of Tech1 VB in the first month is linearly

Tech Time Case This study This study （Qty） （Qty1） （Qty2） Tech Time Case This study This study （Qty） （Qty1） （Qty2）

DB FG

 Inventory amount of Tech1 VB in the first month is linearly

transformed to 1 so do others

（Qty） （Qty1） （Qty2） Tech1 M1 1.362 2.015 2.064 M2 1.223 2.275 2.525 M3 1.176 1.692 1.927 M4 1 202 1 107 1 365 （Qty） （Qty1） （Qty2） Tech1 M1 0.860 0.961 0.798 M2 0.937 1.043 0.773 M3 0.970 0.942 0.683 M4 0 979 0 948 0 687

G

M4 1.202 1.107 1.365 M5 1.225 0.680 1.004 M6 1.176 0.460 0.809 M1 1.427 1.261 1.205 M2 1 680 1 608 1 518 M4 0.979 0.948 0.687 M5 0.925 1.009 0.758 M6 0.748 1.050 0.820 M1 0.796 0.520 0.520 M2 0 889 0 441 0 441 Tech2 M2 1.680 1.608 1.518 M3 1.783 1.284 1.242 M4 1.877 0.964 1.050 M5 2.043 0.677 0.756 M6 2 094 0 481 0 465 Tech2 M2 0.889 0.441 0.441 M3 0.935 0.379 0.380 M4 0.716 0.498 0.381 M5 0.484 0.606 0.503 M6 0 477 0 625 0 655 M6 2.094 0.481 0.465 Tech3 M1 0.159 1.261 1.205 M2 0.158 0.204 0.200 M3 0.143 0.193 0.184 M6 0.477 0.625 0.655 Tech3 M1 0.130 0.115 0.105 M2 0.132 0.101 0.092 M3 0.138 0.084 0.075

40

M4 0.144 0.156 0.156 M5 0.144 0.136 0.140 M6 0.141 0.117 0.121 M4 0.137 0.080 0.071 M5 0.136 0.081 0.071 M6 0.113 0.085 0.074

slide-41
SLIDE 41

WIP Comparisons

Suggested WIP Actual WIP

x100%

p

Confidence Level 90% 80% Technology Time VB WB DB FG VB WB DB FG

Actual WIP

Tech1

M1

100% 48% 148% 112% 77% 47% 152% 93%

M2

123% 40% 186% 111% 115% 37% 206% 83%

M3

196% 40% 144% 97% 174% 37% 164% 70% Tech1

M4

233% 95% 92% 97% 193% 101% 114% 70%

M5

216% 165% 56% 109% 181% 170% 82% 82%

M6

189% 165% 39% 141% 176% 145% 69% 110%

M1

78% 40% 88% 65% 75% 41% 84% 65% Tech2

M1

78% 40% 88% 65% 75% 41% 84% 65%

M2

104% 47% 96% 50% 101% 47% 90% 50%

M3

129% 59% 72% 41% 123% 58% 70% 41%

M4

137% 57% 51% 70% 131% 56% 56% 53%

M4

137% 57% 51% 70% 131% 56% 56% 53%

M5

148% 55% 33% 125% 140% 53% 37% 104%

M6

170% 55% 23% 131% 152% 53% 22% 137%

M1

98% 75% 88% 88% 87% 70% 84% 80% Tech3

M1

98% 75% 88% 88% 87% 70% 84% 80%

M2

161% 136% 129% 77% 162% 108% 126% 70%

M3

139% 216% 122% 61% 135% 152% 116% 55%

M4

113% 230% 109% 59% 109% 149% 109% 52%

M5

182% 246% 95% 60% 176% 160% 97% 52%

M6

298% 268% 81% 75% 252% 174% 84% 65% 41

slide-42
SLIDE 42

WIP Equivalent (sum over 6 months) (sum over 6 months)

 Inventory amount of Tech1 VB in the first month is linearly  Inventory amount of Tech1 VB in the first month is linearly

transformed to 1 so do others

Stage WIP Equivalent WIP Ratio Actual 90% CL 80% CL 90% CL 80% CL

(b) (c)

(a) (b) (c) 90% CL 80% CL VB

17.199 25.015 22.757 145.44% 132.32%

(a) (a)

WB

6.314 4.285 4.098 67.87% 64.90%

DB

19.158 16.573 17.937 86.51% 93.63%

FG

10.505 9.570 7.888 91.10% 75.09%

Total

53.176 55.443 52.680 104.26% 99.07%

42

slide-43
SLIDE 43

Monetary Value Comparison y p

 Unit Value of Tech1 VB is linearly transformed to 1 so do others  Unit Value of Tech1 VB is linearly transformed to 1 so do others Inventory Unit Value Actual WIP 90% CL Equivalent 80% CL Equivalent Actual 90% CL 80% CL Value WIP Value 90% CL Value 80% CL Value stage Tech1 Tech2 Tech3 Tech1 Tech2 Tech3 Tech1 Tech2 Tech3 Tech1 Tech2 Tech3 VB 1 000 0 895 0 789 6 078 10 424 0 696 10 684 13 259 1 072 9 256 12 503 0 999 15 956 23 396 21 234 VB 1.000 0.895 0.789 6.078 10.424 0.696 10.684 13.259 1.072 9.256 12.503 0.999 15.956 23.396 21.234 WB 1.250 1.118 0.987 1.674 4.466 0.174 1.606 2.362 0.318 1.554 2.320 0.224 7.257 4.9620 4.757 DB 1.408 1.276 1.145 7.364 10.904 0.890 8.229 6.276 2.068 9.694 6.237 2.006 25.301 21.962 23.904 FG 2.757 2.362 5.783 5.420 4.297 0.787 5.953 3.070 0.547 4.520 2.880 0.488 29.643 26.827 22.086 Total 6.415 5.651 8.704 20.536 30.091 2.547 26.472 24.967 4.005 25.024 23.94 3.717 78.158 77.148 71.982 43

slide-44
SLIDE 44

Inventory Saving Comparisons

I t i ($TWD)

y g p

 Inventory saving ($TWD)

Confidence Level Stock Point 90% 80% VB

  • $248,158,333
  • $176,010,733

VB $248,158,333 $176,010,733 WB $76,605,167 $83,432,250 DB $111 454 717 $46 639 750 DB $111,454,717 $46,639,750 FG $94,148,775 $252,164,900 Total $34 050 325 $206 226 167 Total $34,050,325 $206,226,167

44

slide-45
SLIDE 45

Summary

The proposed inventory model can help deal with the multi-chip p p y p p package problem with network flow representations.

This study considers the four storage banks for delayed differentiation so that risk of storing inventory can be minimized so that risk of storing inventory can be minimized.

The inventory level information based on inventory days can be constructed to provide the suggestion of wafer start planning, as well as the setting of safety stock level at each stage, and help decision maker understand the response ability for customers’ need.

Inventory survival analysis is developed to suggest inventory levels

Inventory survival analysis is developed to suggest inventory levels.

The proposed inventory model can also support the decision maker automating the decision process, in addition, to reveal the information f d i i i i lif th tifi i l l l ti ti d

  • f decision experience, simplify the artificial calculation time and

improve the efficiency of decision.

45

slide-46
SLIDE 46

Extensions St h ti Li P i Stochastic Linear Programming

 To reduce the complexity of joint probabilities for the  To reduce the complexity of joint probabilities for the

stochastic programming, we may group similar survivals

Prob. 0 6 Prob. 0.6 0.3 0.5 0.3

ssldit ld

0.1

ld

0.2 1 0 2 5 5 0

ssld1

0.2 3.0 6.0

ssld2

1.0 2.5 5.0 MAP M

BOM DM

   

 

   

) , ( , ,

) , ( ) , ( ,

k i m F C

k i m s tat t s is km

i

(M M M Μ )

r r r r r

Mi CB CS CL CO

i

, ,( , )

k m m k km

C ca m i A k C      M MAP

46

CB CS CL CO

(M M M Μ )

r r r r r r

Min CB CS C p L CO

  

S

slide-47
SLIDE 47

Grouping: Identifying Similar Patterns Identifying Similar Patterns

47

slide-48
SLIDE 48

Are Two Survival Functions Equivalent?

  • Comparisons with Graphs

p p

A

  • Hypotheses

B

yp

) ( ) ( : . . ) ( ) ( :

2 1 1 2 1

t S t S H s v t S t S H   ) ( ) ( : . . ) ( ) ( :

2 1 1 2 1

t S t S H s v t S t S H   ) ( ) ( : . . ) ( ) ( :

2 1 1 2 1

t S t S H s v t S t S H  ) ( ) ( : . . ) ( ) ( :

2 1 1 2 1

t S t S H s v t S t S H  

48

slide-49
SLIDE 49

Nonparametric Methods for Comparing Survival Functions Comparing Survival Functions

Chi Pair Chi-square Kolmogorov-Smirnov(K-S) Wilcoxon Mann-Whitney No Censored Data? Kruskal Wallis(K W) Multiple Chi-square Censored Data? Kruskal-Wallis(K-W) Log-Rank Multiple Pair Peto-Wilcoxon Yes Generalized Wilcoxon Test

49

Multiple Log-Rank

slide-50
SLIDE 50

Grouping p g

 If all above issues are confirmed :

S bj i Censor

 If all above issues are confirmed :

Graph Subjective Cross but not obvious Log－rank

Grouping based on Domain Knowledge

No censor Not significant K－S test Graph g

g

Same Group Graph

  • r

Not significant C d b i Compared with

  • ther items
  • r

Multiple Significant Cross and obvious No cross but not obvious No cross and

  • bvious
  • ther items

Significant Same Group

50

  • bvious

K－S test Different and test

slide-51
SLIDE 51

Inventory Goods Will Perish y

 Goods may perish according to fixed/random expiration dates  Goods may perish according to fixed/random expiration dates  Perishability properties of inventory

  • direct spoilage, e.g., vegetable, fruit and fresh food etc.

p g , g , g ,

  • physical depletion, e.g., gasoline and alcohol etc.
  • deterioration such as radiation changing, negative spoiling and lose of

ffi i i t l t i t d di i efficacy in inventory, e.g., electronic components and medicine

  • Substituted by newer generation products, e.g., USB memory stick

i h bl d l l

( ) ( ) dP t P t dt Ddt   

Perishable rate Demand rate Inventory level

2

( ) ( ) ( )

t

dP t P t dt Ddt D P t C e   

  

Differential equation

2

( ) 

Differential equation

51

slide-52
SLIDE 52

Both Finished Goods and Raw Material May Perish with Different Rates Perish with Different Rates

tradeoff between holding cost and fixed ordering/producing cost

52

slide-53
SLIDE 53

Perishable product and Perishable raw materials system Perishable raw materials system

1

min ( ) TC T PSC PHC PDC   

1 ( ) ln(1 )

T

De D T T

 

 

[1 (1 ) ] ( ) 1

T

De D r T

ar T

  

  

  

1

min ( ) TC T PSC PHC PDC RPC RHC RDC     

1( )

ln(1 ) T T r   

Inventory D

1

T

e  

Product r-D r-D- λP(t)

  • D- λP(t)

D Raw materials Time

  • D

Raw materials β-r a- ε R(t) β-r a β β-ε R(t) Time t1 t2 T2 T1

53

slide-54
SLIDE 54

Assumptions p

  • 1. Production rate and demand rate is constant and given.
  • 2. Finished products from production are immediately available.

p f p y

  • 3. Products start to perish only after they are stocked as inventory.
  • 4. Perished product and perishable raw material can be resold
  • 5. Perishable rate of products and raw material are positive.
  • 6. Product perishable rate is constant.

7 R t i l i h bl t i t t

  • 7. Raw material perishable rate is constant.

54

slide-55
SLIDE 55

Extensions Inventory Age and Accounting Principles Inventory Age and Accounting Principles

 International Financial Reporting Standards, No. 2.  International Financial Reporting Standards, No. 2.

  • The worldwide accounting principle for the reduction of inventory

to market allowance

  • Inventory write-down for inventory with different ages
  • Using accrued provision rates

Complex BOM and product substitution but also various

 Complex BOM and product substitution, but also various

raw wafer release schedules (wafer start), turnaround times (TAT, lead times), production plans, safety stock times (TAT, lead times), production plans, safety stock strategies, and end product-demand forecasts.

 Inventory on-hand and multi-period rolling mechanism

y p g

 Postponement strategy, delayed differentiation

  • die-bank, wafer bank, via bank

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SLIDE 56

Inventory Age: Constraints relative to the Finished Goods Bank (FG) the Finished Goods Bank (FG)

 Flow balance of safety stock level and the end on-hand inventory  Flow balance of safety stock level and the end on hand inventory

, ,

it it it it

ssl O I U t i       T FG , ,

it ita

I I t i    

T FG

 Stock flow from the last period into this period

FG        i t I d S F by

it it it it it

, 1 ,

a A 

it it it it it

FG T          

 

i t S I d I S F by

t i it it t i it it it

, 1 ,

) 1 ( ) 1 (

0, ,0

it i

F i t tat      FG

1 ,

, 1, ,

it it it a a a a it i a t

by F S D I t i a

        FG A 1 by F S I D S I t i a            T FG A

, ,

it ita a A

d D t i

   

T FG

, 1, , 1, , 1,

1, ,

it it it i t it i a a a a a a t it a

by F S I D S I t i a

  

           T FG A

56

0, ,0 ,

it i a

F i tat a t       FG A

slide-57
SLIDE 57

Inventory Age: WIP level and accrued provision rate for write-down provision rate for write-down

 Calculation of work-in-process  Calculation of work-in-process

, , ,

it it is is i t tat s a t i t a tat s t a a

WIP I F b t i a

     

         

   

T FG DB WB A VB

age S1 S2 S3 S4

 The write-down objective function

  • With Accrued Provision Rates

i i

i t tat s t i t tat s t     g 1

0 % 0 % 0 % 0 %

2

0 % 0 % 0 % 0 %

3

0 % 0 % 0 % 0 %

4

2 % 2 % 0 % 0 %

  • With Accrued Provision Rates

accrued provision rate for inventory age a

5

2 % 2 % 0 % 0 %

6

2 % 2 % 0 % 0 %

7

10 % 5 % 0 % 0 %

8

10 % 10 % 0 % 0 %



accrued provision rate for inventory age a

9

10 % 15 % 0 % 0 %

10

20 % 20 % 2 % 0 %

11

20 % 25 % 2 % 0 %

12

20 % 30 % 2 % 2 %

min

it a i i a a t

P IP CW

 



T A 13

50 % 35 % 40 % 2 %

14

50 % 40 % 50 % 2 %

15

50 % 45 % 60 % 90 %

16

50 % 50 % 70 % 100 % 57

accumulated cost for product i

17

50 % 55 % 80 % 100 %

18

50% 60 % 90 % 100 %

18+ 100 % 100 % 100 % 100 %

slide-58
SLIDE 58

Further Questions

Will be there more inventory staying in the upstream such as y y g p die bank, wafer bank, or via bank because of the compliance with inventory write-down accounting rules? What accrue provision rates make the cost structure more

What accrue provision rates make the cost structure more stable over time.

The more stages for controlling of delayed differentiation, the better?

58

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SLIDE 59

References

Wu*, J.-Z., Yu, H.-C., and Chien, C.-F. (2014/12), “Inventory survival analysis for semiconductor memory manufacturing,” Proceedings of Winter Simulation Conference: Modeling and Analysis of Semiconductor Manufacturing (MASM), Savannah, 2591-2599, GA, USA, December 7-10.

Wu*, J.-Z., Chien, C.-F. and Tsou, Y.-C. (2014/08), “Multistage semiconductor memory inventory model based on survival analysis,” IEEE International Conference on Automation Science and Engineering, 613-618, Taipei, Taiwan, August 18-22.

Wu*, J.-Z. (2013/05), “Inventory write-down prediction for semiconductor manufacturing considering inventory age, accounting principle, and product g g y g g structure with real settings,” Computers & Industrial Engineering, 65(1), 128- 136.

59

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SLIDE 60

Thanks for your attention atte t o

Jei-Zheng Wu Department of Business Administration Department of Business Administration, Soochow University, Taiwan

60