157_25225_EA435_2013_1__2_1_CHAPTER_2 Inventory mangement (1)

8/18/2019 157_25225_EA435_2013_1__2_1_CHAPTER_2 Inventory mangement (1)

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11-1 Inventory Management

William J. Stevenson

Production planning and control

Chapter 2: Inventory management

9th edition


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Types of Inventories Types of Inventories

• Raw materials & purchased parts• Partially completed goods called

work-in-process (WIP)

• Finished-goods inventories • (manufacturing firms) or merchandise (retai stores)

• Replacement parts, tools, & supplies

• Goods-in-transit to warehouses or customers


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11-! Inventory Management

Functions of InventoryFunctions of Inventory

• To meet anticipated demand• To smooth production requirements

• To decouple operations

• To protect against stoc-outs

• To tae advantage o! order cycles

• To help hedge against price increases

• To permit operations

• To tae advantage o! quantity discounts


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11-" Inventory Management

Objective of Inventory ControlObjective of Inventory Control

• To achieve satis!actory levels o! customerservice while eeping inventory costs within

reasona"le "ounds

• #evel o! customer service

• $osts o! ordering and carrying inventory


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11-# Inventory Management

To "e e!!ective, management must have the !ollowing%• system to eep trac o! inventory on hand and on order

• relia"le !orecast o! demand

• 'nowledge o! lead times and its varia"ility

• Reasona"le estimates o!%

• nventory olding (carrying) costs

• *rdering costs

• +hortage costs

• classi!ication system !or inventory items

Eective Inventory ManagementEective Inventory Management


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11-$ Inventory Management

Inventory Counting SystemsInventory Counting Systems

• Periodic %ystemPhysical count o! items made at periodic

intervals

• Perpetua (continua) Inventory %ystem +ystem that eeps trac

o! removals !rom inventory

continuously, thus

monitoring

current levels o!

each item


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11-& Inventory Management

Inventory Counting Systems (Cont’!Inventory Counting Systems (Cont’!

Perpetual inventory system ranges betweenvery simple to very sophisticated such as:

• 'wo-in %ystem - Two containers o!

inventory reorder when the !irst is empty• niversa ar *ode (.$)- .ar code

printed on a la"el that has

in!ormation a"out the itemto which it is attached

0

214800 232087768


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11-+ Inventory Management

• Lead time: time interval "etween ordering and receiving the order • Holding (carrying) costs: cost to carry an item in inventory !or a

length o! time, usually a year (heat, light, rent, security,deterioration, spoilage, "reaage, depreciation, opportunity cost,/,etc0,)

• Ordering costs: costs o! ordering and receiving inventory (shippingcost, cost o! preparing how much is needed, preparing invoices, costo! inspecting goods upon arrival !or quality and quantity, moving thegoods to temporary storage)

• Shortage costs: costs when demand e1ceeds supply (the opportunitycost o! not maing a sale, loss o! customer goodwill, late charges,the cost o! lost o! production or downtime)

"ey Inventory Terms"ey Inventory Terms


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Classi#cation systemClassi#cation system

• n important aspect o! inventory management is thatitems held in inventory are not o! equal importance interms o! dollar invested, pro!it potential, sales or usagevolume, or stocout penalties0 For instance, a producer o!electrical equipment might have electric generators, coils

o! wire, and miscellaneous nuts and "olts among itemscarried in inventory0 t would "e unrealistic to devoteequal attention to each o! these items0 nstead, a morereasona"le approach would allocate control e!!orts

according to the relative importance o! various items ininventory0 This approach is called A-B-C classificationapproach


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11-1, Inventory Management

$%C Classi#cation System$%C Classi#cation System

$lassi!ying inventory according to some measureo! importance and allocating control e!!ortsaccordingly0

AA - very important

BB – moderate important

CC - least important

Figure 11.1

Annual$ value of items

AA

BB

CC

High

Low

Few Many

Number of Items


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$&%&C classi#cation approac'$&%&C classi#cation approac'• Example

The annual dollar value o! 23 items has "een calculated "ased on annual demand and unit

cost0 The annual dollar values were then arrayed !rom highest to lowest to simpli!yclassi!ication o! items0 t is reasona"le to classi!y the !irst two items as , the ne1t threeitems as . and the remainder are $ items0

tem n!m"er Ann!al #eman# $nit cost %ollar &al!e classification

8 1000 4000 4'000'000 A

( 3)00 700 2'730'000 A

3 1)00 (00 )(0'000 B

6 1000 )1( )1('000 B

1 2(00 330 82('000 B

4 1(00 100 1(0'000 C

12 400 300 120'000 C

1 (00 200 100'000 C

) 8000 10 80'000 C

2 1000 70 70'000 C

7 200 210 42'000 C

10 )000 2 18'000 C

total 10'000'000

11 12 I M


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Cycle CountingCycle Counting

• nother application o! the -.-$ classi!ication approach is as aguide to cycle counting, which is a physical count o! items ininventory0 *he p!rpose of c+cle co!ntin, is to re#!ce#iscrepancies "eteen the amo!nts in#icate# "+ in&entor+recor#s an# the act!al .!antities of in&entor+ on han#/

• The ey questions concerning cycle counting !or management are%

• ow much accuracy is needed4

• 5hen should cycle counting "e per!ormed4

• 5ho should do it4

/B/

*he American ro#!ction an# n&entor+ Control ociet+ ACrecommen#s the folloin, ,!i#elines for in&entor+ recor# acc!rac+:5 0/2 percent for A items' 5 1 percent for B items' an# 5 ( percent for

C items/

11 1! I M


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11-1! Inventory Management

The question o! how much to order is !requently

determined "y using an 6conomic *rder 7uantity

(6*7) model0 6*7 models identi!y the optimal

order quantity "y minimi8ing the sum o! certain

annual costs that vary with order si8e0 Three ordersi8e models are descri"ed%

• The "asic economic order quantity model

• The economic production quantity model

• The quantity discount model

Economic Orer uantity MoelsEconomic Orer uantity Moels

11 1" I t M t


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11-1" Inventory Management

Ass!mptions of E o#el

20 *nly one product is involved

30 nnual demand requirements are nown

90 :emand is even throughout the year

;0 #ead time does not vary


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11-1# Inventory Management

EO Moel inventory cycleEO Moel inventory cycle

• The inventory cycle "egins with receipt o! an ordero! 7 units, which are withdrawn at a constant rateover time0 5hen the quantity on hand is >ustsu!!icient to satis!y demand during lead time, an

order !or 7 units is su"mitted to the supplier0.ecause it is assumed that "oth the usage rate andlead time don?t vary, the order will "e received atthe precise instant that the inventory on hand !alls

to 8ero0 Thus, orders are timed to avoid "othe1cess and stocouts (i0e0, running out o! stoc)0The !ollowing !igure illustrate this idea0

11 1$ I t M t


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11-1$ Inventory Management

T'e Inventory Cycle T'e Inventory CycleFigure 11.2

Profile of Inventory Level Over ime

!uantityon han"

!

#eeiveor"er

Plaeor"er

#eeive or"er

Plaeor"er

#eeive or"er

Lea" time

#eor"er %oint

&sagerate

ime

11 1& Inventory Management


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11-1& Inventory Management

Total Cost Total Cost

Annual

arryingost

Annual

or"eringostotal ost ' (

Q

2

H D

Q

S C ' (Where

Q !uantity to "e ordered

# holding cost per unit $carrying cost per unit%

& annual demand

S ordering $setup cost% per order

he total annual ost assoiate" with arrying an"

or"ering inventory when ! units are or"ere" eahtime is)

Note that * an"H must be in thesame units+ e,g,+

months+ years

11 1+ Inventory Management


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11-1+ Inventory Management

Cost Minimi)ation *oalCost Minimi)ation *oal

Or"er !uantity-!.

he otal/Cost Curve is &/0ha%e"

Or"ering Costs

!O

A n n u a l C o s t

-o%timal or"er 1uantity.

'* -

. /

-% = +

3

Figure 11.'C

Hol"ingost

11 19 Inventory Management


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+eriving t'e EO+eriving t'e EO

sing calculus, we tae the derivative o! thetotal cost !unction and set the derivative

(slope) equal to 8ero and solve !or 70

Q 2&S

#

2$(nnual &emand%$)rder or Setup Cost%

(nnual #olding Cost)P*

Number of or"er %er year' *2!3

Length of or"er yle ' !3 2 *

4here !3 ' !OP

11 2, Inventory Management


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11-2, Inventory Management

Minimum Total CostMinimum Total Cost

The total cost curve reaches its minimum where the

carrying and ordering costs are equal0 This minimum

cost can "e !ound "y su"stituting 7@ !or 7 in the Total

cost (T$) !ormula%

%

/ .

'*

@

@

3+=

11 21 Inventory Management


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EOEO

• 61ample

local distri"utor !or a national tire company e1pects to

sell appro1imately A=@@ steel-"elted radial tires o! a

certain si8e and tread design ne1t year0 nnual carrying

cost is B2= per tire, and ordering cost is BC


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EOEO

+olution

: E A=@@ tires per year

E B2= per unit per year

+ E BC< per order

a) 7@ E

") um"er o! order per year% :7@ E A=@@9@@ E 93 order c) #ength o! order cycle% 7@ : E 9@@A=@@ E293 o! a year ,

which is 293 (3DD days a year) E A wordays

9@@2=

C


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11 2! Inventory Management

EOEO

+olution (cont0)

d) Tc E $arrying cost H *rdering cost

E (7@3) H (:7@) +

E (9@@3) 2= H (A=@@9@@) C< E 3;@@ H 3;@@

E B;D@@

11-2" Inventory Management


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11 2" Inventory Management

• Production done in "atches or lots• $apacity to produce a part e1ceeds the part?s

usage or demand rate

• ssumptions o! 6P7 are similar to 6*7e1cept orders are received incrementally

during production

Economic ,rouction uantity (E,!Economic ,rouction uantity (E,!

11-2# Inventory Management


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11 2# Inventory Management

• *nly one item is involved• nnual demand is nown

• sage rate is constant

• sage occurs continually, "ut production occurs periodically

• Production rate is constant

• #ead time does not vary

• o quantity discounts

Economic ,rouction uantity $ssumptionsEconomic ,rouction uantity $ssumptions

11-2$ Inventory Management


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11 2$ Inventory Management

Economic -un Si)eEconomic -un Si)e

-

/%

.

p

p u@

3

= −

Where:

P production or delivery rate

+ usage rate

he 5onomi run si6e an be "etermine" by using the followingformula)

11-2& Inventory Management


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11 2& Inventory Management

Economic run si)eEconomic run si)e

The minimum total cost is determined as !ollows%

T$ min E carrying cost H setup cost E % - /

. I

+

@

ma1

3

)(@ma1 u P P - I −=

u

-cyce @=

P

- 0un @=

,a-imum inventory

cycle length

run length

11-2+ Inventory Management


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y g

E.ampleE.ample

• toy manu!acturer uses ;D@@@ ru""er wheels per year

!or its popular dump truc series0 The !irm maes itsown wheels, which it can produce at rate o! D@@ per

day0 The toy trucs are assem"led uni!ormly over the

entire year0 $arrying cost is B2 per wheel a year0 +etup

cost !or a production run o! wheels is B;


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y g

SolutionSolution

: E ;D@@@ wheels per year

+ E B;<

E B2 per wheel per year

P E D@@ wheels per day

E ;D@@@ wheels per 3;@ days, or 3@@ wheels per day

a0 7@ E

a0 T$ min E carrying cost H setup cost E

3;@@3@@D@@

D@@

2

;


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y g

Solution (cont/!Solution (cont/!

2D@@)3@@D@@(D@@

3;@@

)(

@

ma1 =−=−=

u P P

-

I

2D@@BA@@BA@@B;


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y g

uantity iscount moeluantity iscount moel

• 7uantity discounts are price reductions !or large orders

o!!ered to customers to induce them to "uy in largequantities0 n this case the price per unit decreases asorder quantity increases0

• ! the quantity discounts are o!!ered, the "uyer must

weigh the potential "ene!its o! reduced purchase price and!ewer orders that will result !rom "uying in largequantities against the increase in carrying cost caused "yhigher average inventories0

• The "uyer?s goal with quantity discounts is to select theorder quantity that will minimi8e the total cost, where thetotal cost is the sum o! carrying cost, ordering cost, and

purchasing (i0e0, product) cost0

11-!2 Inventory Management


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y g

Total Costs 0it' ,urc'asing Cost Total Costs 0it' ,urc'asing Cost

Annual

arryingost PurhasingostC ' (

Q

2

H D

Q

S C ' (

(

Annual

or"eringost

PD (

Where P is the unit price.

ecall that in the "asic /)Q model0 determination o order sie

doesn3t involve the purchasing cost. *he rationale or not

including unit price is that under the assumption o no !uantitydiscounts0 price per unit is the same or all order sie. *he

inclusion o the unit price in the total cost computation in that

case 4ould merely increase the total cost "y the amount P times

the demand $&%. See the ollo4ing graph.

11-!! Inventory Management


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Total Costs 0it' ,+ Total Costs 0it' ,+

C o s t

5O!

C with P*

C without P*

P*

0 !uantity

A""ing Purhasing ost"oesn7t hange 5O!

Figure 11.5

11-!" Inventory Management


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Total cost 0it' purc'asing cost Total cost 0it' purc'asing cost

• 5hen quantity discounts are o!!ered, there is a separate

-shaped total-cost curve !or each unit price0• .ecause the unit prices are all di!!erent, each curve is

raised "y a di!!erent amount% smaller unit price will raisethe total cost curve less than larger unit price0

• o one curve applies to the entire range o! quantitieseach curve applies to only a portion o! the curve0

• 6ach total cost curve has its own minimum0

• There are two general cases o! the quantity discountmodel%

20 the carrying cost is constant

30 the carrying cost is a percentage o! the purchase price0

11-!# Inventory Management


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CostsCosts

OC

5O! !uantity

o t

a l C o s t

Ca

C

Cb*ereasing

Prie

CC a+b+

Figure 11.6 In this ase there is asingle minimum %oint8 all

urves will have theirminimum %oint at thesame 1uantity

11-!$ Inventory Management


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Total Cost 0it' varying Carrying Costs Total Cost 0it' varying Carrying Costs

5hen carrying cost is e1pressed as a percentage o! the unit price, each curve will

have di!!erent minimum point0 *Ca*C"

*Cc

CCa

CC"

CCc

Cost

Quantity

)C

11-!& Inventory Management


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EO 0'en carrying cost is constantEO 0'en carrying cost is constant

• 9or carr+in, costs that are constant' the proce#!re

is as follos:20 $ompute the common minimum point "y using the

"asic economic order quantity model0

30 *nly one o! the unit prices will have the minimum

point in its !easi"le range since the ranges do notoverlap0 denti!y that range%

a0 i! the !easi"le minimum point is on the lowest pricerange, that is the optimal order quantity0

"0 i! the !easi"le minimum point is any other range,compute the total cost !or the minimum point and !orthe price "reas o! all lower unit cost0 $ompare thetotal costs the quantity that yields the lowest cost is theoptimal order quantity0

11-!+ Inventory Management


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E.ampleE.ample

the maintenance department o! a large hospital uses

a"out D2= cases o! liquid cleanser annually0

*rdering costs are B23, carrying costs are B; per

case a year, and the new price schedule indicates

that orders o! less than


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SolutionSolution

• : E D2= cases per year, + E B23

E B; per case per year0• The price schedule is%

20 $ompute the common 6*7

6*7 E

30 The C@ cases can "e "ought at B2D per case "ecause C@ !alls in the

range o!


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• .ecause lower cost ranges e1ist, each must "e checed

against the minimum total cost generated "y C@ cases atB2D each0 n order to "uy at B2C per case, at least D@ casesmust "e purchased0 The total cost at D@ cases will "e%

T$D@ E (D@3) ; H (D2=D@)23 H 2C(D2=) E B2;,2


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EO 0'en carrying cost is a percentage ofEO 0'en carrying cost is a percentage of

t'e unit pricet'e unit price• ;hen carr+in, cost are expresse# as a percenta,e of

price' #etermine the "est p!rchase .!antit+ ith thefolloin, proce#!re%

20 .eginning with the lowest unit price, compute theminimum points !or each price range until you !ind a

!easi"le minimum point (i0e0, until a minimum point !allsin the quantity range o! its price)0

30 ! the minimum point !or the lowest unit price is!easi"le, it is the optimal order quantity0 ! the minimum

point is not !easi"le in the lowest price range, comparethe total cost at the price "rea !or all lower prices withthe total cost o! the !easi"le minimum point0 Thequantity which yield the lowest total cost is the optimum

11-"2 Inventory Management


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E.ampleE.ample

• +urge 6lectric uses ;@@@ toggle +witches a year0

+witches are priced as !ollows% 2 to ;AA, A@ cents

each


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SolutionSolution

• : E ;@@@ switches per year, + E B9@ E @0; P

• Find the minimum point !or each price, starting with the lowest price, until you locate a!easi"le minimum point0

Iinimum point@0D@ E

Beca!se an or#er si


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• ow compute the total cost !or D;@, and compare it

to the total cost o! the minimum quantity necessary

to o"tain a price o! B@0D@ per switch

T$ E carrying cost H ordering cost H purchasing cost

E (73) H (:7)+ H P:T$D;@ E (D;@3) (@09;) H (;@@@D;@) (9@) H @0D


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1'en to -eorer 0it' EO Orering1'en to -eorer 0it' EO Orering

• The 6*7 models answer the equation o! how much to order , "ut

not the question o! when to order 0 The latter is the !unction o!models that identi!y the reorder point (R*P) in terms o! a quantity%the reorder point occurs when the quantity on hand drops to

predetermined amount0

• That amount generally includes e1pected demand during lead time

and perhaps an e1tra cushion o! stoc , which serves to reduce the pro"a"ility o! e1periencing a stocout during lead time0

• n order to now when the reorder point has "een reached, a perpetual inventory is required0

• The goal o! ordering is to place an order when the amount o!inventory on hand is su!!icient to satis!y demand during the time ittaes to receive that order (i0e0, lead time)

11-"$ Inventory Management

' i ' i1' - i ' EO O i


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1'en to -eorer 0it' EO Orering1'en to -eorer 0it' EO Orering

• Reorder Point - 5hen the quantity on hand o!an item drops to this amount, the item is

reordered

• Safety Stoc - +toc that is held in e1cess o!e1pected demand due to varia"le demand rate

andor lead time0

• Service Level - Pro"a"ility that demand will note1ceed supply during lead time0

11-"& Inventory Management

i f ' i+ t i t f t' - , i t


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+eterminants of t'e -eorer ,oint+eterminants of t'e -eorer ,oint

•The rate o! demand (usually "ased on a !orecast)• The lead time

• :emand andor lead time varia"ility• +tocout ris (sa!ety stoc)

f the #eman# an# lea# time are "oth constant' thereor#er point is simpl+:

R*P E d 2 3T

1'ere4

5 eman rate (units per ay or 0ee6!3T 5 lea time in ays or 0ee6sNote that demand and lead time must beexpressed in the same time units.

11-"+ Inventory Management

1' 1' t


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1'en to reorer1'en to reorer

• 5hen varia"ility is present in demand or lead time,

it creates the possi"ility that actual demand will

e1ceed e1pected demand0 $onsequently, it "ecomes

necessary to carry additional inventory, called

Jsa!ety stocK, to reduce the ris o! running out o!stoc during lead time0 The reorder point then

increases "y the amount o! the sa!ety stoc%

R*P E e1pected demand during lead time H sa!ety stoc*he folloin, ,raph shos ho safet+ stoc@ can re#!ce

the ris@ of stoc@ o!t #!rin, lea# time

11-"9 Inventory Management

S f t St 6S f t St 6


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Safety Stoc6Safety Stoc6

L ime

59%ete" "eman""uring lea" time

Ma9imum %robable "eman""uring lea" time

#OP

! u a n t i t y

0afety sto:

Figure 11.12

Saety stoc7 reduces ris7 o

stoc7out during lead time

11-#, Inventory Management

S f t t 6S f t t 6


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Safety stoc6Safety stoc6

• .ecause it cost money to hold sa!ety stoc, a manager must

care!ully weigh the cost o! carrying sa!ety stoc against thereduction in stocout ris it provides0

• The customer service level increases as the ris o! stocoutdecreases0

• The order cycle Jservice levelK can "e de!ined as the pro"a"ilitythat demand will not e1ceed supply during lead time0 This means aservice level A


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-eorer point moels-eorer point moels

• There are many models that can "e used in cases when varia"ility

is present0 These models are%1/ *he expecte# #eman# #!rin, lea# time an# its stan#ar#

#e&iation are a&aila"le/ n this case the form!la is:

R*P E e1pected demand during lead time H Mσd#T5here%

M E num"er o! standard deviationsσd#T E the standard deviation o! lead time demand E sa!ety stoc

• This model assume that any varia"ility in demand rate or lead timecan "e adequately descri"ed "y a normal distri"ution, this is not astrict requirements the model provide appro1imate reorder pointseven where actual distri"utions depart !rom a normal distri"ution0

11-#2 Inventory Management

- , i t-eorer ,oint


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-eorer ,oint-eorer ,oint

#is: of a sto:out

0ervie level

Probability of no sto:out

59%ete"

"eman" 0afetysto:

3 z

!uantity

6/sale

Figure 11.18

*he )P "ased on a normal

&istri"ution o lead time demand

11-#! Inventory Management

E lE l


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E.ampleE.ample

• +uppose the manager o! a construction supply house

determined !rom historical records that demand !or sandduring lead time averages


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solutionsolution

The e1pected lead time demand E


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-O, Moels-O, Moels

30 ! only demand is varia"le, then σd#TE

and the reorder point is%

R*P E

5here%

d Eaverage daily or weely demand

σd E standard deviation o! demand per day or wee #T E lead time in days or wees

90 ! only lead time is varia"le, then σd#T Edσ#T, and then the reorder point is%

R*P E

5here%

d E daily or weely demand

#T E average lead time in days or wees

σ#T E standard deviation o! lead time in days or wees

σ d 1'

d 1' 2 1' d σ +×

1' 2d 1' d σ +×

11-#$ Inventory Management

-O, l-O, moels


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-O, moels-O, moels

;0 ! "oth demand and lead time are varia"le, then

nd the reorder point is%

ote% each o! these models assume that demand and lead

time are independent

333

1' d d1' d 1' σ σ σ +=

333

' d d 1' 2 1' d 03P σ σ ++×=

11-#& Inventory Management

E.ampleE.ample


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E.ampleE.ample

• restaurant uses an average o! ars o! a special

sauce each wee0 5eely usage o! sauce has a standarddeviation o! 9 >ars0 The manager is willing to accept no

more than a 2@ percent ris o! stocout during lead

time, which is two wees0 ssume the distri"ution o!

usage is normal0

a0 5hich o! the a"ove !ormulas is appropriate !or this

situation4 5hy4

"0 :etermine the value o! 84c0 :etermine the R*P4

11-#+ Inventory Management

SolutionSolution


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SolutionSolution

d E arswee, #T E 3 wees, σd E 9 >arswee

ccepta"le ris E 2@ percent, so service level is @0A@

a0 .ecause only demand is varia"le ( i0e0, has a standard

deviation) the second model is appropriate0

"0 From appendi1 ., ta"le ., using a service level o! @0A@, you

o"tain 8 E 203D0

c0 R*P E

E


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CommentComment

• The logic o! the last three !ormulas !or the reorder

point is as !ollows%

20 The !irst part o! each !ormula is the e1pected

demand, which is the product o! daily (or weely)

demand and the num"er o! days (or wees) o! leadtime0

30 The second part o! the !ormula is 8 times the

standard deviation o! lead time demand, i0e0, thesa!ety stoc0

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157_25225_EA435_2013_1__2_1_CHAPTER_2 Inventory mangement (1)