managerial economics ch 8
TRANSCRIPT
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Dr. Karim Kobeissi
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Chapter 8: Inventory
Management
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Inventory - Defnition
Any stored resource used to
satisfy a current or future need
(raw materials, work-in-process,
nished goods, etc.).
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What Type o Businesses ee! to Manage Inventory "
Maintaining inventories is necessary for any
company dealing with physical products,
including manufacturers, wholesalers, and
retailers.
- Manufacturers
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Wholesalers and Retailers
Inventories of RawMaterials
Inventories of Finished Products AwaitingShipment
Inventories of oods Availa!le for Purchase !y"ustomers
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Why Do We ee! to Manage Inventory"
#a$es %ro&th# right inventory at the right place at
the right time Avoiding Stoc$outs % &o 'ost (eal #
)Sorry we are out of that item*.
Cost 'e!u(tion# less money tied up in inventory
+represents as much as - of invested capitol at
some companies/, inventory management,
o!solescence.
0igher Pro1t
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T : Tri$$ion
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0edge against uncertain demand
0edge against uncertain supply
2conomi3e on ordering costs
Smoothing
4ene1ts of Inventory
We !uild and $eep inventory in order tomatch supply and demand in the mostcost e5ective way.
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Inventory Planning and "ontrol
For maintaining the right !alance !etweenhigh and low inventory to minimi3e cost
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Inventory "ontrol (ecisions
6!7ective# Minimi3e 8otal Inventory"ost
(ecisions#
0ow much to order9
When to order9 0ow much stoc$ to $eep9
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Basi( *(onomi( +r!er ,uantity *+,:(etermining 0ow Much to 6rder
6ne of the oldest and most well $nown
inventory control techni:ues
2asy to use
4ased on a num!er of assumptions
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Assumptions of the 26; Model
-- units ? day @ --- units ?
month.
. 8he lead time +the delay !etween the initiation of an order
and the completion of its ful1lment/ is $nown and
constant.
>. 8he order :uantity to replenish inventory arrives all at
once 7ust when desired.
B. Purchase cost per unit is constant +no :uantity discount/.
. Planned shortages +inventory C -/ are not allowed.
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*(onomi( +r!er ,uantity/ormu$a
*+, 0 !ai$y !eman! 1 $ea! time 0 'eor!er 2oint
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Applied 2=ample on 26;'et )Atlantic "ost 8ire % A"8* !e a 1rm that sell tires with#
Dearly demand C E--- units
'ead time C days
8he num!er of wor$ing days per year or 34CT5C - days
%"ompute the 26; for )A"8*
(aily (emand C yearly demand ?num!er of wor$ing days per
year
C E---?- C B tires sold per day
26; C !ai$y !eman! 1 $ea! time 0 67 1 0 69 tires
*a(h time the inventory $eve$ !rops !o&n to having 69
tires remaining; 4CT a
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69
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Inventory Manager Software
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The Optimal Inentory !olicy "or the #asic $O%
To fn! an optima$ inventory po$i(y;
managers o(us on Minimi=ing the
Tota$ >ariab$e Inventory Cost per
?ear /in!ing the +ptima$ +r!er
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Finding the 6ptimal 6rder ;uantity +;G/
Parameters#;G C 6ptimal order :uantity +the26;/
( C Annual demand"oC 6rdering cost per order
"hC 0olding +or carrying /cost per unit
per year
P C Purchase cost per unit
C t th T t $ > i b$
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Components o the Tota$ >ariab$eInventory Cost
Annual setup cost C +&um!er of orders per year/ = +6rdering cost per order/
C +(?;/ = "o
Annual holding cost C +Average inventory/ = +0olding cost per unit per year/
C +;?/ = "h
08ota l Har ia!le Inventory "ost per Dear
&ote#
,A6 is the average inventory $eve$
2ur(hase (ost !oes not !epen! on ,
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8wo Methods for "arrying "ost
"arry cost +"h/ can !e e=pressed either#
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*+, Mo!e$ Tota$ Cost
At optimal order :uantity +;G/#
"arrying cost C 6rdering cost
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Finding the 6ptimal 6rder ;uantity+con/
8here is a simple square root formula that
gives the optimal order :uantity +;G/ that
minimi3es the total varia!le inventory
cost per year for any application of the
!asic 26; model.
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Finding the 6ptimal 6rder ;uantity +;G/
Recall that at the optimal order :uantity +;G/#
"arrying cost C 6rdering cost +(?;G/ = "oC +;G?/
= "h
Rearranging to solve for ;G#
;G C
Where,( C Annual demand
"oC 6rdering cost per order
"hC 0olding cost per unit per year
)/2( hCDCo
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2=ample# Sumco Pump "o.Sumco Pump "o. !uys pump housing from a manufacturer and
sells to retailers
( C Annual demand C
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26; With Planned Shortages6ne of the !anes of any inventory manager is the
occurrence of an inventory shortage. 8his causesa variety of headaches, including dealing with
unhappy customers and having e=tra record
$eeping to arrange for 1lling the demand later
+ba(or!ers/ when the inventory can !e
replenished. 4y assuming that planned shortages
are not allowed, the !asic 26; model satis1es the
common desire of managers to avoid shortages
as much as possi!le.
26; Wi h Pl d Sh
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26; With Planned Shortages0owever, there are situations where permitting
limited planned shortages ma$es sense from amanagerial perspective. 8he most important
re:uirement is that the customers generally are
a!le and willing to accept a reasona!le delay in
1lling their orders if need !e. If the cost of holding
inventory is high relative to these shortage costs,
then lowering the average inventory level !y
permitting occasional !rief shortages may !e a
sound !usiness decision.
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26; with Planned Shortages
4ssumptions (emand occurs at a constant rate of D items?year.
6rdering cost# Jkper order.
0olding cost# Jhper item in inventory per year.
4ac$order cost# Jp unit shortage cost+!ac$ordered/ per year.
Purchase cost per unit is constant +no :uantitydiscount/.
Set%up time +lead time/ is constant. Planned shortages are permitted +!ac$ordered
demand units are withdrawn from a replenishmentorder when it is delivered/.
nder these assumptions the I l l
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nder these assumptions, the
pattern of inventory levels over
time has the appearance
shown !eside. &ow theinventory levels e=tend down
to negative values that reNect
the num!er of units of the
product that are !ac$ordered.
'etting the inventory level is
allowed to go down to +%S/, at
which point an order :uantity
+;/ is placed. +S/ units out of
the +;/ are used to 1ll the
!ac$orders, so the ma=imum
inventory level is +; % S/.
Q- S
Q- S
0
- S
Time
Inventory level
Q
S
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The +bEe(tive o the Mo!e$
8his model has two decision varia!les the
order :uantity +Q) and the ma=imum shortage+S).8he o!7ective in choosing +Q)and +S)is to#
Minimi3e 8H" C total varia!le inventory cost
per year
8his 8H" needs to include the same $inds of costsas for the !asic 26; model plus the cost of
incurring the shortages. 8hus,8H"C Annual setup cost Annual holding cost Annual
shortage cost
26; ith Pl d Sh t
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26; with Planned Shortages
/ormu$as 6ptimal order :uantity#
Q G C KD?h +h+ p/?p
Ma=imum num!er of !ac$orders#
S G C Q GQh?+h p/- Ma=imum inventory level C QG % SG
- Reorder Point C % SG +daily demand/ +lead time/
&um!er of orders per year# D?Q G
8ime !etween orders +cycle time/# Q G?Dyears
8otal annual cost#
Qh +Q G%S G/?Q G QDk?Q G QS Gp?Q G
+holding ordering !ac$ordering/
Application to the A"8 "ase Study
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Application to the A"8 "ase Study DC J