Download - 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

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


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


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

+ ++ + + +

+ = + + = +

+ +

+ + + +


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

+ + + +

+

+ +

+ + + + +


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)


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

= ++

++

5


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

++

6


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=

+

+ +

+ = +


sggss sssgs gsssg s ss

3


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


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

+ =

=+


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+¥


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

= =+ = + = + + +

+ = + + +

3


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


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

1)


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

=+

+

+ +

11


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


lsssg ssgss

� sgsssggssgss sgysgssgy sysssgs

� ��s ssssssgssssssg

� sgsssssssssg sgysgssgy sysssgs

� sgggsy ssssg gsgsgsgsgs

13


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�