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Optimal Level of Product Availability

Chapter 12 of Chopra

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Motivating News Article:Mattel, Inc. & Toys R s

Mattel !w"o intro#$ce# %ar ie in 1'(' an# r$n a stoc) o$t *orseveral years t"en on+ was "$rt last year y inventory c$t ac)s atToys R s, an# o**icials are also eager to avoi# a re eat o* t"e1''- T"an)sgiving wee)en#. Mattel "a# e ecte# to s"i a lot o*/erc"an#ise a*ter t"e wee)en#, $t retailers, wary o* e cessinventory , sto e# or#ering *ro/ Mattel. T"at le# t"e co/ any tore ort a 0( /illion sales s"ort*all in t"e last wee)s o* t"e year ...or t"e cr$cial "oli#ay selling season t"is year, Mattel sai# it willre $ire retailers to lace t"eir *$ll or#ers e*ore T"an)sgiving . An#,*or t"e *irst ti/e, t"e co/ any will no longer ta)e reor#ers in4ece/ er, Ms. %ara# sai#. T"is will ena le Mattel to tailor

ro#$ction /ore closely to #e/an# an# avoi# $il#ing inventory*or or#ers t"at #on5t co/e.

6 7all 8treet 9o$rnal, e . 1-, 1'''

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;ey =ow /$c" s"o$l# Mattel or#er>7ill Mattel?s action "el or "$rt ro*ita ility>7"at actions can i/ rove s$ ly c"ain ro*ita ility>

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Another !ample" Apparel #ndustry$o% much to order& Parkas at L'L' (ean

@ ecte# #e/an# is 1, 2 ar)as.

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Parkas at L'L' (ean

Bost er ar)a C c C 0 (8ale rice er ar)a C C 014isco$nt rice er ar)a C 0(=ol#ing an# trans ortation cost C 018alvage val$e er ar)a C s C ( 61 C0

Dro*it *ro/ selling ar)a C 6c C 1 6 ( C 0((Bost o* overstoc)ing C c6s C (6 C 0(

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Order uantity for a Single Order

C o = Cost of overstocking ) 34

C u = Cost of understocking ) 344

Q* ) Optimal order si,e

'1E.(((

((GF H =

+=

+=

ou

u

C C

C Q Demand P CSL

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Optimal Order uantity

5

5'2

5'6

5'7

5'8

1

1'2

6 4 7 9 8 : 15 11 12 1; 16 14 17 89

CumulativeProbability

Optimal Order Quantity = 13(00)

.'1E

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Parkas at L'L' (ean

@ ecte# #e/an# C 1 FK G ar)as@ ecte# ro*it *ro/ or#ering 1 FK G ar)as C 0 ''

A ro i/ate @ ecte# ro*it *ro/ or#ering 1FK G e tra ar)as i* 1 F? G are alrea#y or#ere#

C 1 '44 'P-D

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Parkas at L'L' (ean

A##itional1 s

@ ecte#Marginal %ene*it

@ ecte#Marginal Bost

@ ecte# MarginalBontri $tion

11 t" (( . ' C 2 '( ( .(1 C 2(( 2 '(62(( C 2

12 t" (( .2' C 1('( ( .E1 C 3(( 1('(63(( C 12

13 t" (( .1- C '' ( .-2 C 1 '' 6 1 C (-

1 t" (( . - C ( .'2 C 6 C 62

1( t" (( . C 22 ( .' C - 22 6 - C 62

1 t" (( . 2 C 11 ( .'- C ' 11 6 ' C 63-

1Et" (( . 1 C (( ( .'' C '( ((6 '( C 6

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Revisit . . %ean as a Newsven#or Dro le/Total cost y or#ering < $nits: BF

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Ordering >omen?s Designer (oots@nder Capacity Constraints

A$t$/n Ieaves R$**leRetail rice 01( 02 02(

D$rc"ase rice 0E( 0' 0118alvage rice 0 0( 0'

Mean 4e/an# 1 ( 2(8tan#. #eviation o* #e/an# 2( 1E( 12(

Available Store Capacity ) 1 455'

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Assuming Bo Capacity Constraints

Autumn Leaves +uffle

pi ! i 1( 6E(C0E( 2 6' C011 2( 611 C01:! i " i E(6: C03( ' 6 ( C 0: 11 6' C 02

Britical ractile E(M11 C .A- 11 M1( C .E3 1: M1A C .-E(Ni .:E .A1 1.1(< i 111- A E 3':

8torage ca acity is not s$**icient to )ee all /o#elsO

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Algorithm for Ordering@nder Capacity Constraints

#$nitiali%ation&orAll ro#$cts, Q i ") 5 . +emaining capacity") otal capacity .

#$terati'e "tep&7"ile +emaining capacity P #o

orAll ro#$cts,Compute t"e marginal contribution o* increasing Q i y 1I* all marginal contributions QC , 8T D

#Order "i%e" are already "uffi!iently lar e for all produ!t"&else Eind t"e ro#$ct wit" t"e largest marginal contribution , call it F#Priority i'en to t e mo"t profita*le produ!t&Q j ") Q j 1 an# +emaining capacity)+emaining capacity.1 #Order more of t e mo"t profita*le produ!t&

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Garginal Contribution)-p.c/P-D< /.-c.s/P-D= / Order uantity Garginal Contribution

+emaining Capacity Autumn Leaves +uffle Autumn Leaves +uffle1455 5 5 5 96'::9 15:'79: 1;7';7516:5 5 5 15 96'::9 15:'79: 1;4'711

1;75 5 5 165 96'::9 15:'79: 15:'7:11;45 5 5 145 96'::9 15:'79: 157'15;1;65 5 15 145 96'::9 15:'719 157'15;1;;5 5 25 145 96'::9 15:'46; 157'15;1;25 5 ;5 145 96'::9 15:'649 157'15;1;15 5 65 145 96'::9 15:';49 157'15;

8:5 5 ;85 2;5 96'::9 9;'5;; 95'195

885 15 ;85 2;5 96'::7 9;'5;; 95'195895 25 ;85 2;5 96'::4 9;'5;; 95'195

2:5 485 655 2;5 7:'889 79'622 95'195285 485 655 265 7:'889 79'622 74'151

1 988 667 274 4;'1:7 4;'197 42';4:5 98: 667 274 4;'59; 4;'197 42';4:

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Optimal Safety #nventory and Order Levels"-+OP / ordering model

ea# Ti/es

ti/e

inventory

8"ortage

An inventory cycle

R D

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Dost one/ent is a c"ea er way o* rovi#ing ro#$ct variety

4ell #elivers c$sto/i e# DB in a *ew #ays@lectronic ro#$cts are c$sto/i e# accor#ing to t"eir #istri $tion c"annelsToyota is ro/ising to $il# cars to c$sto/er s eci*ications an# #elivert"e/ in a *ew #ays

Increase# ro#$ct variety /a)es *orecasts *or in#ivi#$al ro#$cts inacc$rate ee an# %illington F1'' G re orts [ *orecast errors *or "ig" tec"nology ro#$cts

4e/an# s$ ly /is/atc" is a ro le/U =$ge en#6o*6t"e season inventory write6o**s. 9o"nson an# An#erson F2 G esti/ates

t"e cost o* inventory "ol#ing in DB $siness ( [ er year.

Not rovi#ing ro#$ct *le i ility lea#s to /ar)et loss. An A/erican tool /an$*act$rer *aile# to rovi#e ro#$ct variety an# lost

/ar)et s"are to a 9a anese co/ etitor. 4etails in McB$tc"eon et. al. F1'' G.Dost one/ent: 4elaying t"e co//it/ent o* t"e wor)6in6 rocess inventoryto a artic$lar ro#$ct , a.).a. en# o* line con*ig$ration, late oint#i**erentiation, #elaye# ro#$ct #i**erentiation.

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Dost one/ent

Dost one/ent is #elaying c$sto/i ation ste as /$c" as ossi le Nee#:

In#isting$is"a le ro#$cts e*ore c$sto/i ation B$sto/i ation ste is "ig" val$e a##e# n re#icta le #e/an# Negatively correlate# ro#$ct #e/an#s le i le 8B to allow *or any c"oice o* c$sto/i ation ste

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or/s o* Dost one/ent y \inn an# %owerso F1'--G

a eling ost one/ent: 8tan#ar# ro#$ct is la ele##i**erently ase# on t"e reali e# #e/an#. =D rinter #ivision laces la els in a ro riate lang$age on to rinters a*ter t"e

#e/an# is o serve#.

Dac)aging ost one/ent: Dac)aging er*or/e# at t"e#istri $tion center. In electronics /an$*act$ring, se/i6*inis"e# goo#s are trans orte# *ro/ 8@ Asia to

Nort" A/erica an# @$ro e w"ere t"ey are locali e# accor#ing to local lang$age an#

ower s$ ly

Asse/ ly an# /an$*act$ring ost one/ent: Asse/ lyor /an$*act$ring is #one a*ter o serving t"e #e/an#. Mc4onal#s asse/ les /eal /en$s a*ter c$sto/er or#er.

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@ a/ les o* Dost one/ent=D 4es)9et Drinters Drinters locali e# wit" ower s$ ly /o#$le, ower cor# ter/inators, /an$als

Asse/ ly o* I%M R8 8erver ( 6E( en# ro#$cts #i**erentiate# y 1 *eat$res or co/ onents. Asse/ ly $se# to start *ro/

scratc" a*ter c$sto/er or#er. Ta)es too long. Instea# I%M stoc)s se/i *inis"e# R8 calle# vanilla o es. Wanilla o es are c$sto/i e#

accor#ing to c$sto/er s eci*ication.Vilin Integrate# Birc$its 8e/i6*inis"e# ro#$cts, calle# #ies , are "el# in t"e inventory. or easily *ast c$sto/i a le

ro#$cts, c$sto/i ation starts *ro/ #ies an# no *inis"e# goo#s inventory is "el#. or /oreco/ licate# ro#$cts *inis"e# goo#s inventory is "el# an# is s$ lie# *ro/ t"e #ies inventory.

New rogra//a le logic #evices w"ic" can e c$sto/i e# y t"e c$sto/er $sing a s eci*ic

so*tware.Motorola cell "ones 4istri $tion centers "ave t"e cell "ones, "one service rovi#er logos an# service rovi#er

literat$re. T"e ro#$ct is c$sto/i e# *or #i**erent service rovi#ers a*ter #e/an# is/ateriali e#.

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Dost one/ent

8aves Inventory "ol#ing cost y re#$cing sa*ety stoc) Inventory ooling Resol$tion o* $ncertainty

8aves solescence costIncreases 8ales8tretc"es t"e 8$ ly B"ain

8$ liers Dro#$ction *acilities, re#esigns *or co/ onent co//onality 7are"o$ses

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Wal$e o* Dost one/ent: %enetton case

Eor each color 25 %eeks in advance forecasts Gean demand) 1 555* Standard Deviation) 455

Eor each garment

Sale price ) 345 Salvage value ) 315 Production cost using option 1 -long lead time/ ) 325

U Dye the thread and then knit the garment

Production cost using option 2 -short lead time/ ) 322U Mnit the garment and then dye the garment

7"at is t"e val$e o* ost one/ent> C( J sC1 J cC2 or cC22

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Wal$e o* Dost one/ent: %enetton case

B8 CF 6cG F 6cLc6sGC3 C .E(

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A ly o tion 2 to all ro#$cts: %enetton case

B8 CF 6cG F 6cLc6sGC2- C .E4e/an# is nor/al wit" /ean 1 an# st.#ev s rtF G (

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Dost one/ent 4ownsi#e

%y ost oning all t"ree gar/ent ty es, ro#$ction costo* eac" ro#$ct goes $7"en t"is increase is s$ stantial or a single ro#$ct?s#e/an# #o/inates all ot"er?s Fca$sing li/ite#$ncertainty re#$ction via aggregation G, a artial

ost one/ent sc"e/e is re*era le to *$ll ost one/ent.

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Dartial Dost one/ent: 4o/inating 4e/an#Color %ith dominant demand" Gean ) ; 155 SD ) 855Other three colors" Gean ) ;55 SD ) 255

@ ecte# ro*it wit"o$t ost one/ent C 01 2,2 (@ ecte# ro*it wit" ost one/ent C 0'',-E2

Are t"ese cases co/ ara le> Total e ecte# #e/an# is t"e sa/eC

Total variance originally C H2( , C1, , Total variance nowC- H- L3F2 H2 GC , L12 , CE ,

4o/inating #e/an# yiel#s less ro*it even wit" less total variance.Dost one/ent can not e any etter wit" /ore variance.

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Dartial Dost one/ent: %enetton case

or eac" ro#$ct a art o* t"e #e/an# is aggregate#, t"e rest is notDro#$ce Q1 $nits *or eac" color $sing tion 1 an# Q $nitsFaggregateG $sing tion 2, res$lts *ro/ si/$lation:

< 1 *or eac" < A Dro*it

133E 0' ,(E

(2 0'-, '2

11 (( 0'',1-

1 -( 01 ,312

- 1(( 01 , 3

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Tailore# F4$alG 8o$rcing

Tailore# so$rcing #oes not /ean $ying *ro/ two ar itrary so$rces.T"ese two so$rces /$st e co/ le/entary: Dri/ary so$rce: ow cost, long lea# ti/e s$ lier

U Bost C 02 (, ea# ti/e C ' wee)s

Bo/ le/entary so$rce: =ig" cost, s"ort lea# ti/e s$ lier U Bost C 02( , ea# ti/e C 1 wee)

An e a/ le B7D FBra*te# 7it" Dri#eG o* a arel in#$stry ringingo$t co/ etitive a#vantages o* $ying *ro/ #o/estic s$ liers vsinternational s$ liers.Anot"er e a/ le is %enetton?s ractice o* $sing internationals$ liers as ri/ary an# #o/estic FItalianG s$ liers asco/ le/entary so$rces.

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Tailore# 8o$rcing: M$lti le 8o$rcing 8ites

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4$al 8o$rcing 8trategies *ro/ t"e8e/icon#$ctor In#$stry

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Learning ObFectives

Optimal order Nuantities are obtained bytrading off cost of lost sales and cost of e!cessstock

Levers for improving profitability #ncrease salvage value and decrease cost of stockout #mproved forecasting uick response %ith multiple orders

Postponement ailored sourcing