ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/chapter 18 (inventory...

12
1 ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888 88 yyy8y8y8y y88y8y sissygsg iisisss g3 1133 g3s3 133 ssisisssrigrssgrsg sr iisisss ssssssssss ssssss 3 sgsgssssg sgs g3sggsss gysgssgy3 sssss ssss ss sssgss sg s gssss gsg gss sg ggsgss g3sggsss3 ggsss ssgsggsg gssss ssgs3 ssssgg gssssgss3 sgysgs3 gsggsggsssgs3 sssr sgsggsss ssgsggsg gssss ysgssssss3 gsss3 gggsss3 sssr sgsssss ggssgsss3 ssgsgsgsssss ggssgsss3 sgisgggsssss3 gs gsssgssss sg gsgggsssggsgg sysssgs ssggss gsssggsss gss3 ssss3 sssg3 sssr sgsgssss sssggsssss ssssis3 sgss3 ggsgss gggss3 sssr g ssss ssggss s ssgssssg gssssy sgysgssgy gsssss gsg ssgsggsg gssss ssss ssgssssy ss sgsssgsgs ss sss gsssss ssyss ss gsssss gsg sgsssgss sgs gsgggsssggsgg ssyss sgysgssgsss sgs ssgstsss ssggsgsgs

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Page 1: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

1

ssssssssss ssssss

sgsgsgsgs sg gsgssgsss gggsgssgsggysy ygsysgsssy

8888888888

yyy8y8y8y8y88y8y

sissygsg iisisss

g 3 1133 g3s3 133

ssisisssrigrssgrsg

sr iisisss ssssssssss ssssss 3

sgsgssssg sgs g3sggsss

� gysgssgy3 sssss ssss ss sssgss sg s �gssss� gsg gss sg ggsgss

� g3sggsss3� ggs�ss ssgsggsg gssss �ssgs3 �ssssgg gssssgss3 sgysgs3 gsggsggsssgs3 sssr�

� sgsggs�ss ssgsggsg gssss �ysgsss�sss3 gsss3 gggsss3 sssr�

� �sgsssss ggssgsss3 ssgs�gsgsssss ggssgsss3 �sgi�sg�ggsssss3 gs� gsssgssss sg gsgggsssggsgg sysssgs

� ssggss gsssggsss �gss3 ssss3 �sssg3 sssr�

� �sgsgssss sssggsssss �ssssis3 �sgss3 ggsgss gggss3 sssr�

� g ssss ssggss �s ssgssssg gssssy sgysgssgy gsssss gsg ssgsggsg gssss ssss ssgssssy ss sgsssgsgs ss sss �gsssss� ssyss

� ss gsssss gsg ��sgsssgss� sgs �gsgggsssggsgg� ssyss sgysgssgsss sgs ssgstsss ssggsgsgs

Page 2: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

3

sr iisisss ssssssssss ssssss

sssgssssgssssss

� syss� ssggssggs3 ssgssggsgs ysr gsgsssss

� �ssggsgg ssgsisg3 sggsgsss ysr gsgsss

� sgsgs ssggssggs3 ssssggsgsssss ys ssssssssss

� �ssissggsgg ssggssggs3 �ssissggsgg ssss�ss ys �ssissggsgg gss ssss�ss

� sss ssgs ssggssggs3 ssssggsgsssss ysr ssssssssss

� ssss sgs gsysggs ssggssggs� �ggsssss ssss3 c gsg ggss

� sssgg ssss3 K gsg sgssg

� �ssssgg ssss3 h gsg ggss gsg ssgs (hccccc sg gsgy sssss)

� sssgssgs ssss3 p gsg ggss gsg ssgs

� sssysgs yssgs

� ssss gsysggs

� ssssggs gssssg

sr iisisss ssssssssss ssssss

lssss gll sssss

� sgsgs sssggs ss s ssgsssgs gsss cgsg ssgs

� �ssggss sssgssgss sgs gss ssss�ss

� ssgsssgs ssss ssgs l

� ssssssg ysgss�sss sgs sgssg �gsgsssy Q sgs gssgssg ssyss lccc l

Page 3: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

sr iisisss ssssssssss ssssss 5

gll nsgggsssssg

� ss sssss ssss gsg ggss ssgs ss T

3

*

3

**

* *

2 3( )

2 3

( ) 3) (gll3 sssgsgss sgssg )gsgsssy)

3

3 (gl 3 sssgsgss sgssg sgssgyss)

( ) 3 (gsgsggg ssss)

K cQ hQ K hQT Q c

Q Q

T Q K h KQ

Q Q h

Q Kt

h

T Q c hQ c hK

+ ++ + + +

+ = + + = +

+ +

+ + + +

sr iisisss ssssssssss ssssss 6

g3sggss

� � � gsgggsssggsgg ssggsgy ggssgsss sss s�g sgssisgsr ss � ssss sgs ssssg sss ss s gsss sg 3))) gsg gsgssr ss sgssisgs sgs ggssgsss sg ssssss sgs sssgs ss s gs3ss ssss sg 133))) ss sssgg sss gsgggsssggsgg sysssgr ss ggss ggssgssssg ssss ss 1) gsg ssss sgssisgr ss ssssgssss sssssgg ssss gsg ssss sgssisg ss )r ) gsg gsgssr sss ss sss sgssgss ssss ssis?

*

**

* *

3)))3 133)))3 1)3 )r )

3( 3))))(133)))) 35333

)r )

35333 r3 gsgsss

3)))

( ) 3)))(1)) )r )(35333 ) 335 3r )

K c h

Q

Qt

T Q c hQ

+ + + +

+

+ +

+ + + + +

Page 4: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

sr iisisss ssssssssss ssssss 3

gll sssss tsss sssgssgs

� sgggsss ssss gssggss sssgssgss sgs ssss�ss ss s ssss sg p gsg ggss gsg ssgs

� ss �ssss ssis ss Q sgs sss sgysgssgy ssyss gss sgssg sg sgssg ss gssssyss ss S

� ss sssss ssss gsg ggss ssgs ss gs� s gggssssg sg 3 sssssssg ysgss�sss T)Q)S)

sr iisisss ssssssssss ssssss

sssgsssg

3 3 3 3

3 3

3 3 3

3

3

2 3 ( ) 2 3 ( )( 3 )

2 3 3

( 3 ) ( ))

( 3 ) ( ) ( ))

3 3

1 13 3

K cQ hS p Q S K hS p Q ST Q S c

Q Q Q Q

T Q S hS p Q S S S S ph p p

S Q Q Q Q Q p h

T Q S K hS p Q S p Q S

Q Q Q Q Q

K h p p p pp

Q p h p h p

ù ù ù ù+ + + = =û û û û+ + + + +

ö ö ö ö- =+ = + + = + = +÷ ÷ ÷ ÷- +ø ø ø ø

- = =+ = = + = +

-

ö ö ö ö= = + = = =÷ ÷ ÷ ÷+ + +ø ø ø ø

3

3

** * * *

* *

*

*

3) )

3 3 3

3 (gs3sggg sssgssgs)

2 (ggsgsgsssg sg ssgs tsss gs sssgssgs)

2

K p

h hQ p h

K p h p K p Q K p hQ S Q t

h p p h h p h p h p

K hQ S

p p h

S p

Q p h

ö ö ö ö+ = = + +÷ ÷ ÷ ÷+ø ø ø ø

ß

ö ö+ ++ + + + +÷ ÷+ +ø ø

= ++

++

Page 5: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

5

sr iisisss ssssssssss ssssss 3

gll sssss tsss lgsgsssy ssssggs

� g sss � s3sggss3 sgggsss ssss sss ggss ssss gsg sysgy sgssisg ss c1 11 sg ssss sssg 1)3))) sgssisgs sgs ggssgsss3 c3 1) sg ggssgssssg ss sstssg 1)3))) sgs )3))) sgssisgs sgs c 3r5) sg ggssgssssg s3sssss )3))) sgssisgsr

sr iisisss ssssssssss ssssss 1)

ssssssssss ssgssggsgs sysst sssss

� ssss sgysgssgy gsssss gss s ssgssggsgs gsyss� ssggssggs �ssgs s mmmmmmmmmmmmmmmmmmmmmmmmmmmmm ss gsss

� D gsgssg ssgsgs gssssyss sggsgg sss ssss ssgs

� s3gsssss ssgsgs gsg ggss ssgs

� �l)Q) gssssy3 sgssg s gs3ss )gsgsssy Q tssgsysg sss sgysgssgy ssyss sgsgs ss l

� �gsssssss sssgsssg ggssssggs �gss gssssssgssy sgssgss�3

� sssggsgs Q ggsg sss ssssggsgsssss gll gssss

� ssssss l ss sssssgy s ssgysss ssyss sg gsss L3 ssis sss ggs s ssssy ssss s ssssisgs tsss gss sssgg

P{Dc� l L

� sss sggssss ssss sssgs �sss �s s ssgssy ssssi

SSccclE E[D]

3 K p hQ

h p

++

Page 6: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

6

sr iisisss ssssssssss ssssss 11

sggss sssgs gsssg gsg D

� sgggsss ssss D sss sss gsggss ssssgs�gsssg �sss ssgs gssg � sgs ysgssgss s3

� ss gssgssg ssyss ssg sssg �s ssgggsss ss gssss�s

� ss gsgssg ysgss�ss Z sss sss sssgssgs gsggss ssssgs gsssg tsss gssg ) sgs ysgssgss 1

� ss yssgs sg K1EL ssg s gsggs ggsg sssgssgs gsggss ssssgs gsssg ss sss

1

1

1

{

L

L

L

D lP D l L P L

lP Z L

lK

l K

SS l K

m ms s

ms

msm s

m s

=

=

=

= =ü ü= + = = +ý ýþ þ=ü ü= +ý ý

þ þ=

+

+ +

+ = +

sr iisisss ssssssssss ssssss 13

sggss sssgs gsssg s ss

Page 7: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

3

sr iisisss ssssssssss ssssss 1

g3sggss

� ssgssssg sss gsgggsssggsgg sg sgssisgs gsg � ssssr ss ssss ss sgss ssss K 133)))3 c 1) gsg sgssisg3 h )r ) gsg sgssisg gsg gsgss sgs p 1r1) gsg sgssisg gsg gsgssr ssgs ss s ssss ssgs l 1 gsgssr sgggsss ssss sss ssgsgs gsg gsgss D ss gsgssg sgs ss sss sss gsggss ssssgs gsssg tsss gssg 3))) sgs sssgssgs ssysssssg 33)))r s gsgsgsis sss gssi sg sssgggssgg sss ggssgssssg ssgs3 gsgsgsgsgs tsgss ss ssys sgsggs ssgssy ssssi ss ssys sgssisgs syssss ss gsg L 35 sg sss ssgsr

33)3 )))3 33)311

33)311))))33(6 5r1)))3

5 )33 1r1

)r)1r1

)r)

)))313))))3 (33

1

+=+=+

+++++

++

++

+

=

msm

lSS

Kl

p

hp

h

KKQ

L

sr iisisss ssssssssss ssssss 1

l ssssssssss ssggssllsgsss sssss

� ssgssssg s gsgssss�ss ggssgss ssss ssg �s ssss sgsy sggsgg s sssssg sg gsgsss ssis gsstsgs3 ggsss gsss3 ssgsssgss sgsss3 sssssgss ggssssggs ssgss3 ggssgsss ssss sggsgg sssssgs ssy sg sssgssgss ssy3 gstsgsgsgs sgs gsgsssss gsgsisgss (gsts sy ggs ssg)

� Q sssssssg ysgss ss gsggsssgssgg sss sgssg )gsgsssy

� S sgysgssgy ssyss sgssg gssssysgg sss sgssg (S c Q)

� c ggss ssss gsg gggsssssgg sg ggssgssgg ssss ggss

� h sssssgg ssss gsg ggss gsgssgsgg ss sss sgs sg sss gsgsss (sgssgsss sssgsgs ssss gsggs sssysgs yssgs)

� p sssgssgs ssss gsg ggss sg ggsssssgsss ssgsgs (sgssgsss ssss gsysggs sgs ssss sg sgsssgsg gssstsss)

� D gsgssg ssgsgs sggsgg sss gsgsss( ) { (ssg)

{ ( ) (gsg)

x x P D x

P D xx x

x

+ =

=+

Page 8: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

sr iisisss ssssssssss ssssss 15

ssssssg sssss

)

( 3 ) gs3{)3 gs3{)3

( ) [ ( 3 )] ( ) ( ) ( ) ( )S

S

D D S cS p D S h S D

D S E D D S cS p x S x x x h S x x x x

+ + = + =

+ + + = + =ò ò

gggssssgrssgys3 s ss )(

))()()(

{)(

{ ){1(

{ {

)()()(

3

3

)

SD

Sxhp S

SD

SDPhppc

SDhPSDPpc

SDhPSDpPc

xxxh xxxpc S

S D

S

S

³++

=++=+

=+===+

=+>=+

+=+ ò ò+¥

sr iisisss ssssssssss ssssss 16

lgssgss sssgsssg

* * ggssg

ggssg sysg

lgssgsissssg ggs ssg3 gsg ( )

( )) ( ) {

( ) ( )

S D S

D D S p c p cx S P D S

S p h p c c h D D

= =+ = + = + + +

+ = + + +

Page 9: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

3

sr iisisss ssssssssss ssssss 13

g3sggss

� � �ssssssss ssssgs�gssg sg �ssyssss ss ssysgg sgsg�ss sg gsgsgsgg sss sgysgssgy sg sg sss gssssr ss gsgggsssggsg sss gsssgssy sggsggss sss ssssgs gssg ssss ssss gssss ss ssgg sssssgssggssr s sssg ssssg sgs sss ssssi3 sss gsgggsssggsg ss sggsgsgg s sgsssss ssss ggsss sg sgsy 3) gsg ssysssr ss ssssgs gssg gssss ssss ssss sggsg tsss gsis ss gssss ss ss gsis s gsgss gsggs sg sssss sggsgg sss ssgsssgss sssssg gsg sgsy 5 gsg ssysss gsg s ggsgss sg 5 l 3) 35 gsg ssysssr lgy ssysss gss ssss sggsgg sss sssssg ssg s sssgssss sg ss s sssysgs yssgs sg 1)3 sssgsgsgs gsssysgsgg sssg sg sss ssssr ssgssssgsgg sss ssss sg ssgssss ssss gg sg sgysgssgy sgs ssssg sssgsgs sssss3 ssss sgysgssgy ssss ss ss ssssgssss ss s 1 gsg ssysss gsgssgsgg sg sgysgssgy sgssg ssgsssgssr sgs3 ssgssssgsgg sss sssysgs yssgs sg 1) ss tsss3 sss ggss sssssgg ssss ss l 3 gsg ssysss ssgs ss sss sgsr ss ssgsgs sggsgg sss sssssg ss ssssgssss ss s s3gsgsgsssssy ssssgs gsss tsss gssg 1)3)))r ss ssssgs gssg tsgss ss ssssggsgs sst gsgy ssyssss sssgss s gggssssssr

sr iisisss ssssssssss ssssss 1

sssgsssg

� �gsg sss ssss gsysg3 c 3)3 p 5 sgs h l3

) ) ) )

*

*

*

* *

21)3)))

21)3)))

21)3)))

*

*

*

5 3)( ) { )r63

5 3

1 )r63

1 )r63 )r )556

sg sg )r )556

1r1 561)3)))

113 56

g gsgsgss3 sg

S

S

S

p cx S P D S

p h

e

e

e

S

S

c hS

p hl

=

=

=

= =+ = + + +

+ =

= +

+ = +

+

= + =

+

ö ö++ = ÷ ÷+ø ø

Page 10: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

1)

sr iisisss ssssssssss ssssss 13

sssss tsss gsssss ssssi

� sgggsss ssss sssgs ss sgsssss ssssi c

� ss S gsggsssgs sss ssyss sg sgysgssgy sgssg sss sgssg ss gssssyss (sgssglgglss ssyss3 sss ssssi)

gsg ( )S c D S cc³+ =

)

gsg ( ) ( ) ( ) ( ) ( )S

S c

S

c S c p x S x x x h S x x x x

³

ü üï ï= + = + =ý ý

ï ïþ þò ò

* *

*

sgssg sg lgssgss sgssgsgg gssssy ( sss ssssi gssssy)

ss gss sgssg sg

S cE c c S

c S

ü <= ý

³þ

*( )p c

x Sp h

=+

+

sr iisisss ssssssssss ssssss 3)

sssss tsss sssgg ssss

� sgggsss gs� ssss sssgs ss s gs3ss ssss K gsg sg sgssg

{ }{ }{ }{ }

* *

*

gsg ( ) 3gsg ( )

gsg ( )3gsg ( )

sgssg sg lgssgss sgssgsgg gssssy (( ) gssssy)

ss gss sgssg sg

S c

S c

D c cc K D S cc

D c K D S cc

S cE c c ss)S

c s

>

>

= + =

+ + =

ü <= ý

³þ

*

* *

( )

( ) ( )

p cx S

p h

D s K D S

=+

+

+ +

Page 11: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

11

sr iisisss ssssssssss ssssss 31

g3sggss� g sss �ssysss s3sggss3 sgggsss ssss K )) tsss c 3)3 p 5 sgs h l3r

s gsggs ssgsssg ssss S* 113 56r*

*

*

* * 21)3))) * 21)3)))

)

113 5621)3))) 21)3)))

113 56 )

* 21)3))) *

1 13) 5 ( ) 3 ( )

1)3))) 1)3)))

1 1 )) 3)(113 56) 5 ( 113 56) 3 (113 56 )

1)3))) 1)3)))

3) 5(1)3)))) 3 1)3))

s

x x

s

x x

s

s x s e x s x e x

x e x x e x

s e s

+¥= =

+¥= =

=

+ = = =

+ + + = = =

ß

+ = =

ò ò

ò ò

*

*

21)3)))

*

* *

*

* *

)(1 ) 1333)

1)363

113 56 1)363 131 3

1sg

g gsgsgss3 g3gsgsgssss( )1 1

( ) ( ) ( ) ( )

s

s

e

s

S s

h pS

h cD

c h s h p e K c h S c ha

aa

a a

=

=

ù ù= +û û

ß

+

= + = + = +

ü +ö ö+ ÷ ÷ïï +ø øÞ = ýï + + + + + + + +ïþ

sr iisisss ssssssssss ssssss 33

lsssg ssgss

� sgsssggssgss sgysgssgy sysssgs

� ��s ssssssgssssssg

� sgsssssssssg sgysgssgy sysssgs

� sgggsy ssssg gsgsgsgsgs

Page 12: ssssssssss ssssss - home.ku.edu.trhome.ku.edu.tr/~indr343/files/Chapter 18 (Inventory Theory).pdf · ssssssssss ssssss sgsgsgsgs sg gsgssgsss gggsgssgsgg ysy ygsysgsssy 8888888888

13

sr iisisss ssssssssss ssssss 3

5sgstsgi 5

� �sgs�sgi 5 � 1 r �3� 1 r �1 � 1 r6�3� 1 r3� � 1 r3�11

� syss� g3sgsssss � 1 r � � 1 r �5� 1 r � � 1 r6�5� 1 r3�