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Inventory control Inventory control
Chapter 4Chapter 4
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Lecture OutlineLecture Outline
Elements of Inventory Management
Inventory Control SystemsEconomic Order Quantity Models
Quantity Discounts
Reorder Point
Order Quantity for a Periodic InventorySystem
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What Is Inventory?What Is Inventory?
Stock of items kept to meet future
demandPurpose of inventory management
how many units to order
when to order
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Types of InventoryTypes of Inventory
Raw materials
Purchased parts and supplies
Work-in-process (partially completed)products (WIP)
Items being transportedSpare parts, Tools, and equipment
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Two Forms of DemandTwo Forms of Demand
IndependentIndependent Demand for items used by externalDemand for items used by external
customerscustomers
Cars, appliances, computers, andhouses are examples of independentdemand inventory
DependentDependent
Demand for items used to produceDemand for items used to producefinal productsfinal products
Tires stored at a plant are an exampleof a dependent demand item
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Inventory and Quality
Management
Customers usually perceive quality
service as availability of goods they wantwhen they want them
Inventory must be sufficient to provide
high-quality customer service in TQM
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Inventory ostsInventory osts
Carrying costCarrying cost cost of holding an item in inventorycost of holding an item in inventory
Ordering costOrdering cost cost of replenishing inventorycost of replenishing inventory
Shortage costShortage cost temporary or permanent loss of salestemporary or permanent loss of sales
when demand cannot be metwhen demand cannot be met
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Inventory ontrol !ystemsInventory ontrol !ystems
Continuous system (fixedContinuous system (fixed
order!uantity"order!uantity" constant amount orderedconstant amount ordered
when inventory declines towhen inventory declines topredetermined levelpredetermined level
#eriodic system (fixedtime#eriodic system (fixedtimeperiod"period"
order placed for variableorder placed for variableamount after fixed passage ofamount after fixed passage oftimetime
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"conomic Order Quantity
#"OQ$ Models
EOQ
optimal order quantity that willminimize total inventory costs
Basic EOQ model
Production quantity model
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%ssumptions of &asic%ssumptions of &asic
"OQ Model"OQ Model
Demand is $nown with certainty andDemand is $nown with certainty and
is constant over timeis constant over time %o shortages are allowed%o shortages are allowed &ead time (time from ordering to&ead time (time from ordering to
receipt" for the receipt of orders isreceipt" for the receipt of orders isconstantconstant Order !uantity is received all at onceOrder !uantity is received all at once
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Inventory Order ycleInventory Order ycle
DemandDemandraterate
TimeTimeLeadLeadtimetime
LeadLeadtimetime
OrderOrderplacedplaced
OrderOrderplacedplaced
OrderOrderreceiptreceipt
OrderOrderreceiptreceipt
I n v e n t o r y
L e v e l
I n v e n t o r y
L e v e l
Reorder point,Reorder point, R R
Order quantity,Order quantity, Q Q
00
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"OQ ost Model"OQ ost Model
A A cost of placing order cost of placing order DD annual demand annual demand
C C annual perunit carrying cost annual perunit carrying cost QQ order !uantity order !uantity
'nnual ordering cost 'nnual ordering cost
AD AD
'nnual carrying cost 'nnual carrying cost CQCQ
))
Total cost *Total cost *
AD AD
CQCQ
))
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"OQ ost Model"OQ ost Model
TC = + AD
Q
CQ
2
= - + AD
Q 2C
2
TC
Q
0 = - + AD
Q 2
C
2
Q opt =2 AD
C
Deriving Q opt roving equality o!co"t" at optimal point
= ADQ CQ 2
Q 2 =2 AD
C
Q opt =2 AD
C
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"OQ ost Model #cont'$"OQ ost Model #cont'$
Order +uantity,Order +uantity, QQ
'nnual 'nnualcost ("cost (" Total CostTotal Cost
Carrying Cost Carrying Cost
CQCQ
))
Slope -Slope -
.inimum.inimumtotal costtotal cost
Optimal order Optimal order QQoptopt
Ordering Cost Ordering Cost AD AD
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"OQ "(ample"OQ "(ample
C C -/01 per yard -/01 per yard A A 21- 21- DD 2-,--- yards 2-,--- yards
QQoptopt ))C C
ooDD
C C cc
QQoptopt )(21-"(2-,---")(21-"(2-,---"
(-/01"(-/01"
QQoptopt ),--- yards ),--- yards
TC TC minmin * * AD AD
CQCQ
))
TC TC minmin * *(21-"(2-,---"(21-"(2-,---"
),---),---
(-/01"(),---"(-/01"(),---"
))
TC TC minmin 01- * 01- 2,1-- 01- * 01- 2,1--
Orders per year Orders per year DD33QQoptopt
2-,---3),---2-,---3),---
1 orders3year 1 orders3year
Order cycle time Order cycle time 422 days3(422 days3(DD33QQoptopt""
4223142231
5)/) store days5)/) store days
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)eorder *oint)eorder *oint
Level of inventory at which a new orderLevel of inventory at which a new order
is placedis placed
R R dLdL
wherewhere
d d demand rate per period demand rate per periodLL lead time lead time
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)eorder *oint+ "(ample)eorder *oint+ "(ample
Demand 2-,--- yards3year Demand 2-,--- yards3year
Store open 422 days3year Store open 422 days3year Daily demand 2-,--- 3 422 4)/216Daily demand 2-,--- 3 422 4)/216
yards3dayyards3day
&ead time & 2- days&ead time & 2- days
7 d& (4)/216"(2-" 4)2/16 yards7 d& (4)/216"(2-" 4)2/16 yards
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Production Quantity
Model
An inventory system in which an order isreceived gradually, as inventory is
simultaneously being depleted
Non-instantaneous receipt model assumption thatQis received all at once is relaxed
p -daily rate at which an order is received overtime, production rate
d -daily rate at which inventory is demanded
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*roduction Quantity Model*roduction Quantity Model
#cont'$#cont'$
QQ(2(2d/pd/p""
InventoryInventorylevellevel
(2(2d/pd/p""QQ
2 2
TimeTime--
Order Order receipt periodreceipt period
8egin8egin
order order receiptreceipt
9nd9nd
order order receiptreceipt
.aximum.aximum
inventoryinventorylevellevel
'verage 'verageinventoryinventorylevellevel
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*roduction Quantity Model*roduction Quantity Model
#cont'$#cont'$ p p = production rate= production rate d d = demand rate= demand rate
#a$imum inventory level =#a$imum inventory level = Q Q -- d d
== Q Q % -% -
Q Q
p p
d d
p p
&verage inventory level =&verage inventory level = % -% -
Q Q
22d d
p p
TC TC = + % -= + % -d d
p p
AD AD
Q Q
CQ CQ
22
Q Q optopt ==22 AD AD
C C
% -% -
d d
p p
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*roduction Quantity Model+*roduction Quantity Model+
"(ample"(ampleC C -/01 per yard -/01 per yard A A 21- 21- DD 2-,--- yards 2-,--- yards
d d 2-,---3422 4)/) yards per day 2-,---3422 4)/) yards per day p p 21- yards per day 21- yards per day
Q Q optopt = = = 2,2'()* yard"= = = 2,2'()* yard"22 AD AD
C C % -% - d d
p p
2%'0%0,0002%'0%0,000
0)' % -0)' % -.2)2.2)2
%'0%'0
TC TC = + % - = /%,.2= + % - = /%,.2d d p p
AD AD
Q Q CQ CQ
22
roduction run = = = %')0' day" per order roduction run = = = %')0' day" per order QQ
p p
),)15/:),)15/:
21-21-
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Production Quantity Model:Production Quantity Model:
Example (cont.)Example (cont.)
1umer o! production run" = = = 3)3. run"4year DQ
%0,0002,2'()*
#a$imum inventory level = 5 % - = 2,2'()* % -
= %,2 yard"
d
p.2)2%'0
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,' Quantity Discounts Model,' Quantity Discounts Model
#rice per unit decreases as order#rice per unit decreases as order
!uantity increases!uantity increases
TC TC * * * * PDPD AD AD
CQCQ
))
wherewhere
P P per unit price of the item per unit price of the itemDD annual demand annual demand
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Cont;Cont;
The goal < is to reduce price (#" for an item when it is purchased inThe goal < is to reduce price (#" for an item when it is purchased inlarger !uantitieslarger !uantities
Di"count 1umer Di"count 5uantity Di"count 6 Di"count rice
2 - to === no discount 1/--
) 2,--- to 2,=== 6 6/:-
4 ),--- and over 1 6/01
Total Cost Setup cost(order cost" * >olding cost * #roduct costTotal Cost Setup cost(order cost" * >olding cost * #roduct cost
TC DS3+ * +>3) * #DTC DS3+ * +>3) * #D
+ < +uantity ordered+ < +uantity ordered
D < 'nnual demand in unitsD < 'nnual demand in units
S < Ordering or setup cost per order per setupS < Ordering or setup cost per order per setup
# < #rice per unit# < #rice per unit
> < >olding cost per unit per year > < >olding cost per unit per year
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The Steps to determine Optimum +uantity order olding cost (I" as percentage of unit price (#">olding cost (I" as percentage of unit price (#"
)/)/ If order !uantity is too low, ad@ust the order !ty upward to the lowestIf order !uantity is too low, ad@ust the order !ty upward to the lowest!ty that will !ualify for the discount!ty that will !ualify for the discount
4/4/ Compute Total cost for eachCompute Total cost for each
6/6/ Select +? with the lowest total costSelect +? with the lowest total cost
9xample < The store stoc$s toy race cars/ 7ecently, the store has9xample < The store stoc$s toy race cars/ 7ecently, the store hasbeen given a !uantity discount schedule for these cars/ The normalbeen given a !uantity discount schedule for these cars/ The normalcost for the race car is 1/--/ Aor orders between 2,--- and 2,===cost for the race car is 1/--/ Aor orders between 2,--- and 2,===units, the unit cost drops to 6/:-B for orders ),--- or more units, theunits, the unit cost drops to 6/:-B for orders ),--- or more units, theunit cost is only6/01/ Aurthermore, ordering cost is 6=/-- per order,unit cost is only6/01/ Aurthermore, ordering cost is 6=/-- per order,annual demand is 1,--- race cars and inventory carrying charge as aannual demand is 1,--- race cars and inventory carrying charge as a
percent of cost is )-/ hat order !uantity will minimiEe the totalpercent of cost is )-/ hat order !uantity will minimiEe the totalinventory costFinventory costF
2/2/ +2? )DS3I# )(1,---"(6="3()-"(1/--" 0-- cars order +2? )DS3I# )(1,---"(6="3()-"(1/--" 0-- cars order
+)? )DS3I# )(1,---"(6="3()-"(6/:-" 026 cars order +)? )DS3I# )(1,---"(6="3()-"(6/:-" 026 cars order
+4? )DS3I# )(1,---"(6="3()-"(6/01" 02: cars order +4? )DS3I# )(1,---"(6="3()-"(6/01" 02: cars order
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)/)/
+2? 0--+2? 0--
+)? 2,--- ad@usted+)? 2,--- ad@usted
+4? ),--- ad@usted+4? ),--- ad@usted
4/ Calculate Total Cost each discount4/ Calculate Total Cost each discount
TC DS3+ * +>3) * #DTC DS3+ * +>3) * #D
'nnual #roduct Cost #D 'nnual #roduct Cost #D 'nnual ordering cost DS3+ 'nnual ordering cost DS3+
'nnual >olding cost +>3) +I#3) 'nnual >olding cost +>3) +I#3)
6/ Select Order +uantity at the lowest cost 2,--- units6/ Select Order +uantity at the lowest cost 2,--- units
Di"count1um2er 7nit rice +, Order 5uantity &nnual roductCo"t &nnualOrdering Co"t &nnual8olding Co"t TotalCo"t
2 1/-- 0-- )1,---/-- 41- 41- )1,0--
) 6/:- 2,--- )6,---/-- )61 6:- )6,0)1
4 6/01 ),--- )4,01-/-- 2)),1 =1- )6,:)4
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Quantity Discount+ "(ampleQuantity Discount+ "(ample
+G'%TITH+G'%TITH #7IC9#7IC9
2 6=2 6= 2,6--2,6--
1- :=1- := 2,2--2,2--
=-*=-* =--=--
A A ),1--),1--
C C 2=- per computer2=- per computer
DD )--)--
QQoptopt 0)/1 #Cs 0)/1 #Cs))C C
ooDD
C C cc
)()1--"()--")()1--"()--"
2=-2=-
TC TC * * * * PDPD )44,0:6 )44,0:6
AD AD
QQoptopt
CQCQoptopt
))
AorAor QQ 0)/1 0)/1
TC TC * * * * PDPD 2=6,2-1 2=6,2-1 AD AD
CQCQ
))
AorAor QQ =- =-
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!afety !toc-s!afety !toc-s
Safety stoc$Safety stoc$ buffer added to on hand inventory during leadbuffer added to on hand inventory during lead
timetime Stoc$outStoc$out
an inventory shortagean inventory shortage
Service levelService level probability that the inventory available duringprobability that the inventory available during
lead time will meet demandlead time will meet demand
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)eorder *oint with)eorder *oint with
a !afety !toc- a !afety !toc-
Reorder Reorder
point,point, R R
Q Q
LTLT
TimeTime
LTLT
I n v e n t o r y
l e v e l
I n v e n t o r y
l e v e l
00
9a!ety 9toc:
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)eorder *oint With)eorder *oint With
.aria/le Demand
.aria/le Demand
R R == dLdL ++ z z d d L L
wherewhere
d d average daily demandaverage daily demand
LL lead timelead time
σσd d the standard deviation of daily demandthe standard deviation of daily demand
z z number of standard deviationsnumber of standard deviations
corresponding to the service levelcorresponding to the service level
probabilityprobability (service factor"(service factor"
z z σσd d L L safety stoc$safety stoc$
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)eorder *oint for)eorder *oint for
a !ervice Levela !ervice Levelroaility o!roaility o!
meeting demand duringmeeting demand during
lead time = "ervice levellead time = "ervice level
roaility o!roaility o!
a "toc:outa "toc:out
RR
9a!ety "toc:9a!ety "toc:
d d LL
DemandDemand
z z d d L L
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Service factor values for CS&Service factor values for CS&
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)eorder *oint for)eorder *oint for
.aria/le Demand.aria/le DemandThe carpet store wants a reorder point with a =1The carpet store wants a reorder point with a =1
service level and a 1 stoc$out probabilityservice level and a 1 stoc$out probability
d d 4- 4- mm per dayper day LL 2- days 2- days
σσd d 1 1 mm per dayper day
Aor a =1 service level,Aor a =1 service level, z z 2/5 2/566
R R dLdL ** z z σσd d L L
4-(2-" * (2/5 4-(2-" * (2/566"(1"( 2-""(1"( 2-"
4) 4)1/=1/= mm
Safety stoc$Safety stoc$ z z σσd d L L
(2/5 (2/566"(1"( 2-""(1"( 2-"
) )11//== mm
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%& lassification%& lassification
The items on hand are classified intoThe items on hand are classified intoA, B,A, B, andandCC typestypes
on the basis of theon the basis of thevalue in terms of capital or annualvalue in terms of capital or annual
dollar usage (i.e., dollar value per unit multiplied bydollar usage (i.e., dollar value per unit multiplied byannual usage rateannual usage rate), and then allocates control efforts), and then allocates control efforts
accordingly.accordingly.
Thus, the items withThus, the items withhigh valuehigh valueandandlow volumelow volumeare keptare kept
inin A-type A-type, items with, items withlow valuelow valueandandhigh volumehigh volumeare keptare kept
inin C-typeC-type, and the items, and the items withwith moderate valuemoderate value andand
moderate volumesmoderate volumesbelong to the B-type.belong to the B-type.
A ---- very important, B ---- moderately important, A ---- very important, B ---- moderately important,
and C-- least importantand C-- least important
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Class AClass A
5 – 15 % of units5 – 15 % of units
70 – 80 % of value70 – 80 % of value
Class BClass B
30 % of units30 % of units
15 % of value15 % of value
Class CClass C 50 – 60 % of units50 – 60 % of units
5 – 10 % of value5 – 10 % of value
The actual number of categories varies fromThe actual number of categories varies fromorganiEation to organiEation, depending on the extentorganiEation to organiEation, depending on the extent
to which a firm wants to differentiate the control efforts/to which a firm wants to differentiate the control efforts/
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%& lassification+ "(ample%& lassification+ "(ample
%% / (0/ (0 00
22 .'0.'0 3030
.. .0.0 %.0%.033 *0*0 (0(0
'' .0.0 %00%00
(( 2020 %*0%*0
%0%0
%0%0
** .20.20 '0'0
'%0'%0 (0(0
%0%0 2020 %20%20
&RT&RT 71IT CO9T71IT CO9T &117&L 79&;
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%& lassification+%& lassification+
"(ample #cont'$"(ample #cont'$
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%& lassification+%& lassification+
"(ample #cont'$"(ample #cont'$
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*urchasing*urchasing
Purchasing is an important function ofPurchasing is an important function of
materials management.materials management.
In any industry purchase means buyingIn any industry purchase means buying
of equipments, materials, tools, parts etc.of equipments, materials, tools, parts etc.
required for industry.required for industry.
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O/0ectives of *urchasingO/0ectives of *urchasing
The basic objective of the purchasingThe basic objective of the purchasing
function is to ensure continuity of supplyfunction is to ensure continuity of supply
of raw materials, sub-contracted itemsof raw materials, sub-contracted items
and spare parts and to reduce theand spare parts and to reduce theultimate cost of the finished goods.ultimate cost of the finished goods.
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*arameters of *urchasing*arameters of *urchasing
The success of any manufacturing activity isThe success of any manufacturing activity is
largely dependent on the procurement of rawlargely dependent on the procurement of raw
materials of right quality, in the right quantities,materials of right quality, in the right quantities,
from right source, at the right time and at rightfrom right source, at the right time and at right
price popularly known asprice popularly known asten ‘R’s’ten ‘R’s’of the art ofof the art of
efficient purchasing.efficient purchasing.
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*urchase parameters*urchase parameters
RIGHT PRICERIGHT PRICE
RIGHT QUALITYRIGHT QUALITY
RIGHT TIMERIGHT TIME RIGHT SOURCERIGHT SOURCE
RIGHT QUANTITYRIGHT QUANTITY
RIGHT ATTITUDERIGHT ATTITUDE
7I>T CO%T7'CT7I>T CO%T7'CT
7I>T .'T97I'&7I>T .'T97I'&
7I>T T7'%S#O7T'TIO%7I>T T7'%S#O7T'TIO%
7I>T #&'C9 OA7I>T #&'C9 OA
D9&IJ97HD9&IJ97H
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*urchasing *rocedure*urchasing *rocedure
RECOGNITION OF THE NEEDRECOGNITION OF THE NEED
THE SELECTION OF THE SUPPLIERTHE SELECTION OF THE SUPPLIER
PLACING THEORDERPLACING THEORDER FOLLOW-UP OF THEORDERFOLLOW-UP OF THEORDER
RECEIVING AND INSPECTION OF THE MATERIALSRECEIVING AND INSPECTION OF THE MATERIALS
PAYMENT OF THEINVOICEPAYMENT OF THEINVOICE
MAINTENANCE OF THE RECORDSMAINTENANCE OF THE RECORDS
MAINTENANCE OF VENDORRELATIONSMAINTENANCE OF VENDORRELATIONS
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"(ercise"(ercise
The XYZ Ltd. carries a wide assortment of items for itsThe XYZ Ltd. carries a wide assortment of items for its
customers.customers.
One of its popular items has annual demand of 8000 units.One of its popular items has annual demand of 8000 units.
Ordering cost per order is found to be Rs. 12.5. The carrying costOrdering cost per order is found to be Rs. 12.5. The carrying cost
of average inventory is 20% per year and the cost per unit is Rs.of average inventory is 20% per year and the cost per unit is Rs.
1.00. Determine the optimal economic quantity and make your1.00. Determine the optimal economic quantity and make yourrecommendations.recommendations.
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