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12 - 1 2011 Pearson Education, Inc. publishing as Prentice Hall
12Inventory
Management
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12 - 2 2011 Pearson Education, Inc. publishing as Prentice Hall
Inventory ManagementInventory Management
The objective o inventor!The objective o inventor!
"anage"ent is to stri#e a balance"anage"ent is to stri#e a balancebet$een inventor! invest"ent andbet$een inventor! invest"ent and
custo"er servicecusto"er service
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Importance of InventoryImportance of Inventory
&ne o the "ost e'pensive assetso "an! co"panies representing as
"uch as (0) o total investedcapital
&perations "anagers "ust balance
inventor! invest"ent and custo"erservice
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12 - * 2011 Pearson Education, Inc. publishing as Prentice Hall
Types of InventoryTypes of Inventory
+a$ "aterial Purchased but not processed
or#-in-process
ndergone so"e change but not co"pleted unction o c!cle ti"e or a product
/aintenancerepairoperating /+&
3ecessar! to #eep "achiner! andprocesses productive
4inished goods
5o"pleted product a$aiting ship"ent
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12 - ( 2011 Pearson Education, Inc. publishing as Prentice Hall
The Material Flow CycleThe Material Flow Cycle
4igure 12.1
Input ait or ait to /ove ait in 6ueue 7etup +un &utputinspection be "oved ti"e or operator ti"e ti"e
5!cle ti"e
8() ()
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12 - 9 2011 Pearson Education, Inc. publishing as Prentice Hall
Managing InventoryManaging Inventory
1. Ho$ inventor! ite"s can beclassiied
2. Ho$ accurate inventor! recordscan be "aintained
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ABC AnalysisABC Analysis
;ivides inventor! into three classesbased on annual dollar volu"e
5lass - high annual dollar volu"e
5lass < - "ediu" annual dollarvolu"e
5lass 5 - lo$ annual dollar volu"e
sed to establish policies thatocus on the e$ critical parts andnot the "an! trivial ones
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12 - = 2011 Pearson Education, Inc. publishing as Prentice Hall
ABC AnalysisABC Analysis
Ite"7toc#
3u"ber
Percent o3u"ber o
Ite"s7toc#ed
nnual>olu"eunits '
nit5ost ?
nnual;ollar
>olu"e
Percent onnual;ollar
>olu"e 5lass
@102=9 20) 1,000 A 80.00 A 80,000 %=.=)
@11(29 (00 1(*.00 ::,000 %%.2)
@12:90 1,((0 1:.00 29,%(0 11.%) olu"eunits '
nit5ost ?
nnual;ollar
>olu"e
Percent onnual;ollar
>olu"e 5lass
@12(:2 900 A 1*.1: A =,(02 %.:) 5
@1*0:( 2,000 .90 1,200 .() 5
@010%9 (0) 100 =.(0 =(0 .*) 5
@01%0: 1,200 .*2 (0* .2) 5
@10(:2 2(0 .90 1(0 .1) 5
=,((0 A2%2,0(: 100.0)
()
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12 - 10 2011 Pearson Education, Inc. publishing as Prentice Hall
5 Ite"s
ABC AnalysisABC Analysis
Ite"s
< Ite"s
Perce
ntoannualdollarusage
=0 B
:0 B
90 B
(0 B
*0 B
%0 B
20 B
10 B0 B C C C C C C C C C C
10 20 %0 *0 (0 90 :0 =0 80 100
Percent o inventor! ite"s4igure 12.2
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12 - 11 2011 Pearson Education, Inc. publishing as Prentice Hall
ABC AnalysisABC Analysis
&ther criteria than annual dollarvolu"e "a! be used
nticipated engineering changes ;eliver! proble"s
Dualit! proble"s
High unit cost
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12 - 12 2011 Pearson Education, Inc. publishing as Prentice Hall
Holding, Ordering, andHolding, Ordering, and
Setp CostsSetp Costs Holding costsHolding costs- the costs o holding
or carr!ingF inventor! over ti"e
&rdering costs&rdering costs- the costs oplacing an order and receivinggoods
7etup costs7etup costs- cost to prepare a"achine or process or"anuacturing an order
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12 - 1% 2011 Pearson Education, Inc. publishing as Prentice Hall
Holding CostsHolding Costs
5ategor!
5ost and rangeas a Percent oInventor! >alue
Housing costs building rent ordepreciation, operating costs, ta'es,
insurance
9) % - 10)
/aterial handling costs e6uip"ent lease ordepreciation, po$er, operating cost
%) 1 - %.()
Gabor cost %) % - ()
Invest"ent costs borro$ing costs, ta'es,and insurance on inventor! 11) 9 - 2*)
Pilerage, space, and obsolescence %) 2 - ()
&verall carr!ing cost 29)
Table 12.1
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12 - 1* 2011 Pearson Education, Inc. publishing as Prentice Hall
Holding CostsHolding Costs
5ategor!
5ost and rangeas a Percent oInventor! >alue
Housing costs building rent ordepreciation, operating costs, ta'es,
insurance
9) % - 10)
/aterial handling costs e6uip"ent lease ordepreciation, po$er, operating cost
%) 1 - %.()
Gabor cost %) % - ()
Invest"ent costs borro$ing costs, ta'es,and insurance on inventor! 11) 9 - 2*)
Pilerage, space, and obsolescence %) 2 - ()
&verall carr!ing cost 29)
Table 12.1
Holdingcostsvar!cons
iderabl!depending
onthebusiness,location,andinter
estrates.
enerall!greaterthan
1(),so"ehightech
ite"shaveholdingcos
tsgreaterthan*0).
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12 - 1( 2011 Pearson Education, Inc. publishing as Prentice Hall
Inventory ModelsInventory Models
1.
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12 - 19 2011 Pearson Education, Inc. publishing as Prentice Hall
Basic !O" ModelBasic !O" Model
1. ;e"and is #no$n, constant, andindependent
2. Gead ti"e is #no$n and constant
%. +eceipt o inventor! is instantaneous andco"plete
*. Duantit! discounts are not possible(. &nl! variable costs are setup and holding
9. 7toc#outs can be co"pletel! avoided
I"portant assu"ptions
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12 - 1: 2011 Pearson Education, Inc. publishing as Prentice Hall
Inventory #sage Over TimeInventory #sage Over Time
4igure 12.%
&rder6uantit! ? ""a'i"u"inventor!
level
sage rate verageinventor!on hand
"2
/ini"u"
inventor!
Inventor!level
Ti"e0
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12 - 1= 2011 Pearson Education, Inc. publishing as Prentice Hall
Minimi$ing CostsMinimi$ing Costs
&bjective is to "ini"ie total costs
Table 12.*c
.nn
ualcost
&rder 6uantit!
Total cost oholding andsetup order
Holding cost
7etup or ordercost
/ini"u"total cost
&pti"al order6uantit! "J
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12 - 18 2011 Pearson Education, Inc. publishing as Prentice Hall
An !O" !%ampleAn !O" !%ample
;eter"ine opti"al nu"ber o needles to order&? 1,000 unitsS? A10 per orderH? A.(0 per unit per !ear
"J ?2&S
H
"J ?21,00010
0.(0? *0,000 ? 200 units
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12 - 20 2011 Pearson Education, Inc. publishing as Prentice Hall
An !O" !%ampleAn !O" !%ample
;eter"ine opti"al nu"ber o needles to order&? 1,000 units "J ? 200 unitsS? A10 per orderH? A.(0 per unit per !ear
? '? ?E'pectednu"ber o
orders
;e"and
&rder 6uantit!&
"J
'? ? ( orders per !ear1,000200
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12 - 21 2011 Pearson Education, Inc. publishing as Prentice Hall
An !O" !%ampleAn !O" !%ample
;eter"ine opti"al nu"ber o needles to order&? 1,000 units "J ? 200 unitsS? A10 per order ' ? ( orders per !earH? A.(0 per unit per !ear
? T?E'pected
ti"e bet$eenorders
3u"ber o $or#ingda!s per !ear
'
T? ? (0 da!s bet$een orders2(0(
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12 - 22 2011 Pearson Education, Inc. publishing as Prentice Hall
An !O" !%ampleAn !O" !%ample
;eter"ine opti"al nu"ber o needles to order&? 1,000 units "J ? 200 unitsS? A10 per order ' ? ( orders per !earH? A.(0 per unit per !ear T ? (0 da!s
Total annual cost ? 7etup cost K Holding cost
TC? S K H&
"
"
2
TC? A10 K A.(01,000200
2002
TC? (A10 K 100A.(0 ? A(0 K A(0 ? A100
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12 - 2% 2011 Pearson Education, Inc. publishing as Prentice Hall
An !O" !%ampleAn !O" !%ample
/anage"ent underesti"ated de"and b! (0)&? 1,000 units "J ? 200 unitsS? A10 per order ' ? ( orders per !earH? A.(0 per unit per !ear T ? (0 da!s
TC? S K H&
"
"
2
TC? A10 K A.(0 ? A:( K A(0 ? A12(
1,(00
200
200
2
1,(00 units
Total annual cost increases b! onl! 2()
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12 - 2* 2011 Pearson Education, Inc. publishing as Prentice Hall
An !O" !%ampleAn !O" !%ample
ctual E&D or ne$ de"and is 2**.8 units&? 1,000 units "J ? 2**.8 unitsS? A10 per order ' ? ( orders per !earH? A.(0 per unit per !ear T ? (0 da!s
TC? S K H&
"
"
2
TC? A10 K A.(0
1,(00
2**.8
2**.8
2
1,(00 units
TC? A91.2* K A91.2* ? A122.*=
&nl! 2) lessthan the totalcost o A12(
$hen theorder 6uantit!
$as 200
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12 - 2( 2011 Pearson Education, Inc. publishing as Prentice Hall
(eorder )oints(eorder )oints
E&D ans$ers the ho$ "uchF 6uestion
The reorder point +&P tells $henF toorder
+&P ? Gead ti"e or ane$ order in da!s
;e"andper da!
? d' *
d?&
3u"ber o $or#ing da!s in a !ear
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12 - 29 2011 Pearson Education, Inc. publishing as Prentice Hall
(eorder )oint !%ample(eorder )oint !%ample
;e"and ? =,000 iPods per !ear2(0 $or#ing da! !earGead ti"e or orders is % $or#ing da!s
+&P ? d' *
d?&
3u"ber o $or#ing da!s in a !ear
? =,0002(0 ? %2 units
? %2 units per da! ' % da!s ? 89 units
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12 - 2: 2011 Pearson Education, Inc. publishing as Prentice Hall
"antity &iscont Models"antity &iscont Models
+educed prices are oten available $henlarger 6uantities are purchased
Trade-o is bet$een reduced product costand increased holding cost
Total cost ? 7etup cost K Holding cost K Product cost
TC? S K HK )&&
"
"
2
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12 - 2= 2011 Pearson Education, Inc. publishing as Prentice Hall
"antity &iscont Models"antity &iscont Models
;iscount3u"ber ;iscount Duantit! ;iscount ) ;iscountPrice )
1 0 to 888 no discount A(.00
2 1,000 to 1,888 * A*.=0
% 2,000 and over ( A*.:(
Table 12.2
t!pical 6uantit! discount schedule
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12 - 28 2011 Pearson Education, Inc. publishing as Prentice Hall
"antity &iscont Models"antity &iscont Models
1. 4or each discount, calculate "J
2. I "J or a discount doesnLt 6uali!,choose the s"allest possible order sieto get the discount
%. 5o"pute the total cost or each "J oradjusted value ro" 7tep 2
*. 7elect the "J that gives the lo$est totalcost
7teps in anal!ing a 6uantit! discount7teps in anal!ing a 6uantit! discount
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12 - %0 2011 Pearson Education, Inc. publishing as Prentice Hall
"antity &iscont Models"antity &iscont Models
1,000 2,000
TotalcostA
0
&rder 6uantit!
"J or discount 2 is belo$ the allo$able range at point a
and "ust be adjusted up$ard to 1,000 units at point +
a
+
1st pricebrea#
2nd pricebrea#
Total costcurve or
discount 1
Total cost curve or discount 2
Total cost curve or discount %
4igure 12.:
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12 - %1 2011 Pearson Education, Inc. publishing as Prentice Hall
"antity &iscont !%ample"antity &iscont !%ample
5alculate "J or ever! discount " -2&SI)
"1J ? ? :00 carsorder2(,000*8
.2(.00
"2J ? ? :1* carsorder2(,000*8
.2*.=0
"%J ? ? :1= carsorder2(,000*8
.2*.:(
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12 - %2 2011 Pearson Education, Inc. publishing as Prentice Hall
"antity &iscont !%ample"antity &iscont !%ample
5alculate "J or ever! discount " -2&SI)
"1J ? ? :00 carsorder2(,000*8
.2(.00
"2J ? ? :1* carsorder2(,000*8
.2*.=0
"%J ? ? :1= carsorder2(,000*8
.2*.:(
1,000 M adjusted
2,000 M adjusted
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12 - %% 2011 Pearson Education, Inc. publishing as Prentice Hall
"antity &iscont !%ample"antity &iscont !%ample
;iscount3u"ber
nitPrice
&rderDuantit!
nnualProduct
5ost
nnual&rdering
5ost
nnualHolding
5ost Total
1 A(.00 :00 A2(,000 A%(0 A%(0 A2(,:00
2 A*.=0 1,000 A2*,000 A2*( A*=0 A2*,:2(
% A*.:( 2,000 A2%.:(0 A122.(0 A8(0 A2*,=22.(0
Table 12.%
5hoose the price and 6uantit! that givesthe lo$est total cost
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12 - %* 2011 Pearson Education, Inc. publishing as Prentice Hall
)ro+a+ilistic Models and)ro+a+ilistic Models and
Safety Stoc.Safety Stoc. sed $hen de"and is not constant
or certain
se saet! stoc# to achieve a desiredservice level and avoid stoc#outs
+&P ? d' *K ss
nnual stoc#out costs ? the su" o the units short' the probabilit! ' the stoc#out costunit
' the nu"ber o orders per !ear
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12 - %( 2011 Pearson Education, Inc. publishing as Prentice Hall
Safety Stoc. !%ampleSafety Stoc. !%ample
3u"ber o nits Probabilit!%0 .2
*0 .2
+&P (0 .%
90 .2
:0 .1
1.0
+&P ? (0 units 7toc#out cost ? A*0 per ra"e&rders per !ear ? 9 5arr!ing cost ? A( per ra"e per !ear
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12 - %9 2011 Pearson Education, Inc. publishing as Prentice Hall
Safety Stoc. !%ampleSafety Stoc. !%ample
+&P ? (0 units 7toc#out cost ? A*0 per ra"e&rders per !ear ? 9 5arr!ing cost ? A( per ra"e per !ear
7aet!
7toc#
dditional
Holding 5ost 7toc#out 5ost
Total
5ost20 20A( ? A100 A0 A100
10 10A( ? A (0 10.1A*09 ? A2*0 A280
0 A 0 10.2A*09 K 20.1A*09 ? A890 A890
saet! stoc# o 20 ra"es gives the lo$est total cost
+&P ? (0 K 20 ? :0 ra"es
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12 - %: 2011 Pearson Education, Inc. publishing as Prentice Hall
7aet! stoc# 19.( units
+&P
Place
order
)ro+a+ilistic &emand)ro+a+ilistic &emand
Inventor!level
Ti"e0
/ini"u" de"and during lead ti"e
/a'i"u" de"and during lead ti"e
/ean de"and during lead ti"e
3or"al distribution probabilit! ode"and during lead ti"e
E'pected de"and during lead ti"e %(0 #its
+&P ? %(0 K saet! stoc# o 19.( ? %99.(
+eceive
order
Geadti"e
4igure 12.=
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12 - %= 2011 Pearson Education, Inc. publishing as Prentice Hall
)ro+a+ilistic &emand)ro+a+ilistic &emand
se prescribed service levels to set saet!stoc# $hen the cost o stoc#outs cannot bedeter"ined
+&P ? de"and during lead ti"e K /d*T
$here /? nu"ber o standarddeviations
d*T? standard deviation o
de"and during lead ti"e
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12 - %8 2011 Pearson Education, Inc. publishing as Prentice Hall
)ro+a+ilistic &emand)ro+a+ilistic &emand
7aet!stoc#
Probabilit! o
no stoc#out8() o the ti"e
/ean
de"and%(0
+&P ? N #its Duantit!
3u"ber ostandard deviations
0
+is# o a stoc#out() o area onor"al curve
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12 - *0 2011 Pearson Education, Inc. publishing as Prentice Hall
)ro+a+ilistic !%ample)ro+a+ilistic !%ample
verage de"and ? ? %(0 #its7tandard deviation o de"and during lead ti"e ? d*T? 10 #its
() stoc#out polic! service level ? 8()
sing ppendi' I, or an area under the curveo 8(), the /? 1.9(
7aet! stoc# ? /d*T? 1.9(10 ? 19.( #its
+eorder point ? e'pected de"and during leadti"e K saet! stoc#
? %(0 #its K 19.( #its o saet!stoc#
? %99.( or %9: #its
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12 - *1 2011 Pearson Education, Inc. publishing as Prentice Hall
Other )ro+a+ilistic ModelsOther )ro+a+ilistic Models
1. hen de"and is variable and leadti"e is constant
2. hen lead ti"e is variable and
de"and is constant%. hen both de"and and lead ti"e
are variable
hen data on de"and during lead ti"e isnot available, there are other "odelsavailable
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12 - *2 2011 Pearson Education, Inc. publishing as Prentice Hall
Other )ro+a+ilistic ModelsOther )ro+a+ilistic Models
;e"and is variable and lead ti"e is constant
+&P ? average dail! de"and
' lead ti"e in da!s K /d*T
$here d ? standard deviation o de"and per da!
d*T ? d lead ti"e
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12 - *% 2011 Pearson Education, Inc. publishing as Prentice Hall
)ro+a+ilistic !%ample)ro+a+ilistic !%ample
verage dail! de"and nor"all! distributed ? 1(7tandard deviation ? (Gead ti"e is constant at 2 da!s80) service level desired
/or 80) ? 1.2=4ro" ppendi' I
+&P ? 1( units ' 2 da!s K /d*T
? %0 K 1.2=( 2
? %0 K 8.02 ? %8.02 O %8
7aet! stoc# is about 8 iPods
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12 - ** 2011 Pearson Education, Inc. publishing as Prentice Hall
Other )ro+a+ilistic ModelsOther )ro+a+ilistic Models
Gead ti"e is variable and de"and is constant
+&P ? dail! de"and '
average lead ti"e in da!s? /' dail! de"and ' *T
$here *T ? standard deviation o lead ti"e in da!s
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12 - *( 2011 Pearson Education, Inc. publishing as Prentice Hall
)ro+a+ilistic !%ample)ro+a+ilistic !%ample
;ail! de"and constant ? 10verage lead ti"e ? 9 da!s7tandard deviation o lead ti"e ?
*T? %
8=) service level desired
/or 8=) ? 2.0((4ro" ppendi' I
+&P ? 10 units ' 9 da!s K 2.0((10 units%
? 90 K 91.9( ? 121.9(
+eorder point is about 122 ca"eras
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12 - *9 2011 Pearson Education, Inc. publishing as Prentice Hall
Other )ro+a+ilistic ModelsOther )ro+a+ilistic Models
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12 - *: 2011 Pearson Education, Inc. publishing as Prentice Hall
)ro+a+ilistic !%ample)ro+a+ilistic !%ample
verage dail! de"and nor"all! distributed ? 1(07tandard deviation ?
d? 19
verage lead ti"e ( da!s nor"all! distributed7tandard deviation ?
*T? 1 da!
8() service level desired /or 8() ? 1.9(4ro" ppendi' I
+&P ? 1(0 pac#s ' ( da!s K 1.9(d*T
? 1(0 ' ( K 1.9( ( da!s ' 192 K 1(02' 12? :(0 K 1.9(1(* ? 1,00* pac#s
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12 - *= 2011 Pearson Education, Inc. publishing as Prentice Hall
Single )eriod ModelSingle )eriod Model
&nl! one order is placed or a product
nits have little or no value at the end othe sales period
Cs? 5ost o shortage ? 7ales priceunit B 5ostunit
Co? 5ost o overage ? 5ostunit B 7alvage value
7ervice level ?Cs
CsK Co
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12 - *8 2011 Pearson Education, Inc. publishing as Prentice Hall
Single )eriod !%ampleSingle )eriod !%ample
verage de"and ? ? 120 papersda!
7tandard deviation ? ? 1( papers
Cs? cost o shortage ? A1.2( - A.:0 ? A.((
Co? cost o overage ? A.:0 - A.%0 ? A.*0
7ervice level ?Cs
CsK Co.((
.(( K .*0
.((
.8(
?
? ? .(:=
7ervicelevel
(:.=)
&pti"al stoc#ing level
? 120
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12 - (0 2011 Pearson Education, Inc. publishing as Prentice Hall
Single )eriod !%ampleSingle )eriod !%ample
4ro" ppendi' I, or the area .(:=, / .20
The opti"al stoc#ing level
? 120 copies K .20? 120 K .201( ? 120 K % ? 12% papers
The stoc#out ris# ? 1 B service level
? 1 B .(:= ? .*22 ? *2.2)
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12 - (1 2011 Pearson Education, Inc. publishing as Prentice Hall
Fi%ed0)eriod 1)2 SystemsFi%ed0)eriod 1)2 Systems
&rders placed at the end o a i'ed period
Inventor! counted onl! at end o period
&rder brings inventor! up to target level
&nl! relevant costs are ordering and holding
Gead ti"es are #no$n and constant
Ite"s are independent ro" one another
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12 - (2 2011 Pearson Education, Inc. publishing as Prentice Hall
Fi%ed0)eriod 1)2 SystemsFi%ed0)eriod 1)2 Systems
&
n-handinvento
r!
Ti"e
"1
"2
Target 6uantit! T
)
"%
"*
)
)
4igure 12.8
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12 - (% 2011 Pearson Education, Inc. publishing as Prentice Hall
Fi%ed0)eriod 1)2 !%ampleFi%ed0)eriod 1)2 !%ample
&rder a"ount " ? Target T - &n-hand inventor! - Earlier orders not !et
received K
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Fi%ed0)eriod SystemsFi%ed0)eriod Systems
Inventor! is onl! counted at eachrevie$ period
/a! be scheduled at convenient ti"es ppropriate in routine situations
/a! result in stoc#outs bet$een
periods /a! re6uire increased saet! stoc#
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