ch_2.3 inventory management

7/23/2019 Ch_2.3 Inventory Management

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Inventory Management

R. Dan Reid & Nada R. Sanders2nd Edition © Wiley 2005



Independent vs. DependentDemand

• Independent demand items are fnishedgoods or other items sold to someoneoutside the company

• Dependent demand items are materialscomponent parts used in the productiono another item (e.g. fnished product!



"ypes o Inventory

•#nticipation or seasonal inventory

• $aety stoc%& 'uer demand )uctuations

• *ot+si,e or cycle stoc%& ta%e advantage o-uantity discounts or purchasing eciencies

• /ipeline or transportation inventory• $peculative or hedge inventory protects

against some uture event e.g. la'or stri%e

• aintenance repair and operating (1!

inventories



'3ectives o Inventoryanagement

• /rovide accepta'le level o customerservice (on+time delivery!

• #llo4 cost+ecient operations• inimi,e inventory investment



1elevant Inventory ostsItem Cost Cost per item plus any other direct cos

associated with getting the item to theplant

HoldingCosts

Capital, storage, and ris cost typicallystated as a ! o" the unit value,

e.g. #$%$!

'rderingCost

(i)ed, constant dollar amount incurredeach order placed

ShortageCosts

*oss o" customer goodwill, +ac orderhandling, and lost sales



rder 6uantity $trategies

*ot%"or%lot rder e7actly 4hat is needed or thne7t period

(i)ed%orderuantity

rder a predetermined amount eactime an order is placed

Min%ma)system

When on+hand inventory alls 'elo4predetermined minimum level ordeenough to refll up to ma7imum leve

'rder n

periods

rder enough to satisy demand or

ne7t n periods



E7amples o rdering #pproache



"hree athematical odels

•

-conomic 'rder uantity /-' or System – #n optimi,ing method used or determining order -uan

and reorder points

– /art o continuous review system 4hich trac%s on+hand inventory each time a 4ithdra4al is made

• -conomic 1roduction uantity /-10 – # model that allo4s or incremental product delivery

• uantity Discount Model – odifes the E6 process to consider cases 4here

-uantity discounts are availa'le



Economic rder 6uantity

•

-' 2ssumptions3 – Demand is %no4n 8

constant + no saety stoc%is re-uired

– *ead time is %no4n 8constant

–

9o -uantity discounts areavaila'le

– rdering (or setup! costsare constant

– #ll demand is satisfed(no shortages!

– "he order -uantity arrivesin a single shipment



E6& "otal ost E-uation

costsetuporordering

costholdingannual

ordered beoquantity tdemandannual

costannualtotal

2

====

=

+

=

S

H

Q D

TC

Where

H QS Q DTC EOQ



"he E6 :ormula

•inimi,e the " 'y ordering the E6

H

DS EOQ

2=



E6 "otal osts• "otal annual costs ; annual ordering costs <

annual holding costs



"he 1eorder /oint

•Without saety stoc%&

• With saety stoc%

days/weeksintimelead

unitsindemandlydaily/week

unitsin pointreorder where

=

=

=

=

L

d

R

dL R

unitsinstocksafetywhere =+=

SS

SS dL R

E6 E l



E6 E7ample+ Wee%ly demand ; 2=0 units + 9o. o 4ee%s pe

year ; 52

+ rdering cost ; >50 + ?nit cost ; >@+ #nnual carrying charge ; 20A + *ead time ; 24ee%s

year units D /480,1224052 =×=

year per unit per H !152"0 =×=

units H DS Q #45$8"#44

50480,1222 ≅=××==

unitsdL R

H Q

S Q

DTC

4802240

!1,$4"$45"$#%44"$#%

2

#4550

#45

480,12

2

=×==

=+=

×+

×=

+

=



E/6 (Economic /roduction6uantity! #ssumptions

•$ame as the E6 e7cept& inventoryarrives in increments 8 is dra4n do4nas it arrives



E/6 E-uations

•

#d3usted total cost&

•

a7imum inventory&

•

#d3usted order -uantity&

+

= H I

S Q

DTC MAX

EPQ2

−= p

d Q I MAX 1

−

=

p

d H

DS EPQ

1

2

E/6 E7ample



E/6 E7ample• #nnual demand ; @B000 units /roduction rate ; 250

unitsCmonth

•

$etup cost ; >B00 #nnual holding cost ; >@B per unit• *ead time ; 5 days 9o. o operating days per month ;

monthunits pmonthunitsd /2500&/150012

000,18===

units

p

d

H

DS Q 2000

2500

1500118

800000,182

1

2=

−×

××=

−

=

units p

d Q I MAX 800

2500

1500120001 =

−×=

−=

400,14200,%200,%

182

800800

2000

000,18

2

=+=

×+

×=

+

= H

I S

Q

DTC MAX



•

"he reorder point&

• With saety stoc% o 200 units

unitsdL R %5520

1500=×==

unitsSS dL R 5%5200520

1500=+×=+=



6uantity Discount odel#ssumptions

•

$ame as the E6 e7cept& – ?nit price depends upon the -uantity

ordered

• #d3usted total cost e-uation& PD H QS

Q DTC QD +

+

=

2

6uantity Discount /rocedure



6uantity Discount /rocedure

• alculate the E6 at the lo4est price• Determine 4hether the E6 is easi'le at that pric

– Will the vendor sell that -uantity at that price• I yes stop i no continue• hec% the easi'ility o E6 at the ne7t higher pric• ontinue until you identiy a easi'le E6• alculate the total costs (including total item cost!

the easi'le E6 model• alculate the total costs o 'uying at the minimum

-uantity re-uired or each o the cheaper unit price• Compare the total cost o" each option & choo

the lowest cost alternative• 2ny other issues to consider4



E7ample

• #nnual Demand ; 5000 units

•rdering cost ; >=F

• #nnual carrying charge ; 20A

• ?nit price schedule&

Quantity Unit Price0 to 999 $5.00

1000 to 1999 $4.80

2000 and over $4.75



$olution• $tep @

( ) feasi!enot Q P %18%5"42"0

4$000,52%5"4! =

×××==

( ) feasi!enot Q P %1480"42"0

4$000,5280"4! =

×××

==

( ) feasi!eQ P %0000"52"0

4$000,5200"5! =

×××

==



• $tep 2

%0,25!500000"500"52"0

2

%004$

%00

000,5%00 =×+××+×==QTC

%2,24!500080"480"42"02

10004$

1000

000,51000 =×+××+×==QTC

82,24!5000%5"4%5"42"02

20004$

2000

000,52000 =×+××+×==QTC



What i Demand is ?ncertain



$aety $toc% and $ervice *ev

• rder+cycle service level is the pro'a'ilitythat demand during lead time 4onGt e7ce

on+hand inventory.• 1is% o a stoc%out ; @ (service level!

• ore saety stoc% means greater servicelevel and smaller ris% o stoc%out



$aety $toc% and 1eorder /oi

•

Without saety stoc%&

• With saety stoc%&

daysintimelead

unitsindemanddaily

unitsin pointreorder where

==

==

L

d

R

dL R

unitsinstocksafetywhere =+=

SS

SS dL R



1eorder /oint Determination

1 ; reorder point

d ; average daily demand* ; lead time in days, ; num'er o standard deviations associated 4i

desired service level

σ ; standard deviation o demand during lead tim

dL

dL

" dL R

" SS

σ

σ

+=

=i"e",



$aety $toc% E7ample

•

Daily demand ; 20 units• *ead time ; @0 days

• $.D. o lead time demand ; 50 units

• $ervice level ; F0A

Determine&

@. $aety stoc%

2. 1eorder point



$olution

$tep @ determine ,:rom ta'le& , ; @.2B

$tep 2 determine saety stoc%

$tep H determine reorder point

units#45028"1 =×=SS

units2#4#41020 =+×=+= SS dL R



# Inventory lassifcation

• 25C classi6cation is a method or determining leo control and re-uency o revie4 o inventory item

• # /areto analysis can 'e done to segment items invalue categories depending on annual dollar volum

• 2 Items typically 20A o the items accounting o

B0A o the inventory value+use 6 system• 5 Items typically an additional H0A o the items

accounting or @5A o the inventory value+use 6 o

• C Items "ypically the remaining 50A o the itemaccounting or only 5A o the inventory value+use



25C -)ample

•

"he ta'le 'elo4 sho4s a solution to an #analysis. "he inormation that is re-uired tdo the analysis is& Item J ?nit > Kalue a#nnual ?nit ?sage. "he analysis re-uires a

calculation o #nnual ?sage > and sortingthat column rom highest to lo4est > valuecalculating the cumulative annual > volum

and grouping into typical # classifcatio



Item Annua U!a"e #$ Percenta"e o% &ota $ 'umuative Percenta"e o% &ota $ Item 'a!!i%ica

10( 1()500 *4.4 *4.4 A

110 12)500 2(.1 (0.5 A

115 4500 9.4 (9.9 +

105 *200 (.7 7(.( +

111 2250 4.7 81.* +

104 2000 4.2 85.5 +

114 1200 2.5 88 '

107 1000 2.1 90.1 '

101 9(0 2 92.1 '

11* 875 1.8 9*.9 '

10* 750 1.( 95.5 '108 (00 1.* 9(.8 '

112 (00 1.* 98.1 '

102 500 1 99.1 '

109 500 1 100.1 '



Inventory 1ecord #ccuracy

• Inaccurate inventory records can cause3 – *ost sales – Disrupted operations – /oor customer service – *o4er productivity – /lanning errors and e7pediting

• 7wo methods are availa+le "or checing record accura – /eriodic counting+physical inventory – ycle counting+daily counting o pre+specifed items provid

the ollo4ing advantages&• "imely detection and correction o inaccurate records• Elimination o lost production time due to une7pected

stoc% outs• $tructured approach using employees trained in cycle

counting

ch_2.3 inventory management

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