Ch 5 Inventory management slides iijfsjfksjkf

inventory

1. Production and Operations
Management Systems
Chapter 5: Inventory Management
SushilK. Gupta
Martin K. Starr
2014
1

2. After reading this chapter, you should
be able to:
Explain what inventory management entails.
Describe the difference between static and dynamic inventory
models.
Discuss demand distribution effects on inventory situations.
Differentiate inventory costs by process types.
Describe all costs relevant to inventory models.
2

3. After reading this chapter, you should
be able to (continued):
Discuss the use of economic order quantity (EOQ) models.
Discuss the use of economic production quantity (EPQ)
models.
Describe the discount model and explain how it indicates when
a discount should be taken.
Perform ABC classification of materials.
3

4. After reading this chapter, you should
be able to (continued):
Discuss lead-time effects on inventory situations.
Explain order point policies (OPP) and when they are used.
Explain the operation of the periodic inventory model.
Explain the operation of the perpetual inventory model.
Discuss reorder points.
Discuss and calculate safety stocks.
Describe a two-bin system.
4

5. Types of Inventory Situations
oOrder repetition—static versus dynamic situations.
oDemand distribution—certainty, risk, and uncertainty.
oStability of demand distribution—fixed or varying.
oDemand continuity—smoothly continuous or sporadic and
occurring as lumpy demand; independent.
oLead-timedistributions—fixedorvarying.
oDependentorindependentdemand.
5

6. 6
Functions of Inventory
Considerthreesubsystemsofanorganizationrepresentingthe
supplier,manufacturerandthemarket.
Thesethreesubsystemsarerigidlyconnectedwitheachother,
withoutanyinventories,asshownbelow.
Inventoriesreducedependencyofonesubsystemovertheother
inasupplychain.
Suppliers Manufacturer Market

7. Functions of Inventory (continued)
Production Planning –level production.
Take advantage of quantity (price) discounts.
Protect against anticipated increase in prices.
Protect against anticipated shortages.
7

8. Inventory Related Costs
oCostsofordering
oCostsofsetupsandchangeovers
oCostsofcarryinginventory
oCostsofdiscounts
oOut-of-stockcosts
oCostsofrunningtheinventorysystem
8

9. 9
Data for Inventory Problems
•D: Annual Demand (units per year)
•C: Unit Price (purchase price of the item)
•S: Ordering or Setup Cost per Order
•H: Inventory Holding (Carrying) Cost/unit per year
•i: H may be given as i percent of C
•TC: Total Annual Cost
•TVC: Total Annual Variable Cost
•Q: Order Quantity
•EOQ: Economic Order Quantity (optimal value of Q)

10. 10
Economic Order Quantity
(EOQ) Model

11. 11
Inventory Level Variations
Suppose Annual Demand
D= 1200
Suppose Qunits are purchased
at a time, where,
Q= 600
Q = 400 etc.
The figures on the RHS show
inventory variations for
different values of Qassuming
a constant and continuous
demand of 100 units per
month.
Order Size, Q= 600
Order Size, Q= 400

12. Average Inventory and Number of Orders
Average inventory = Q/2.
Number of orders = D/Q.
If Q= 400
Average Inventory
= 400/2 = 200
# Orders = 1200/400 = 3
12
Average Inventory during the first four months
is (400+0)/2 = 200.
For the next four months it is again (400+0)/2
= 200
Similarly for the last four months, the average
inventory is (400+0)/2 = 200
This means that the average inventory through
out the year is 200.
Order Size, Q= 400

13. 13
TC and TVC Formulae
Total Annual Cost (TC) = Annual Ordering Cost (D/Q)S +
Annual Holding Cost (Q/2)H+ Annual Purchase Cost (DC)
Total Annual Variable Cost (TVC) = Annual Ordering Cost +
Annual Holding Cost
Note: Annual purchase cost is not included in TVC. H
Q
S
Q
D
TVC
2
 DCH
Q
S
Q
D
TC 
2

14. 14
EOQ Formula
In the equations for TCand TVC, the values of D, H, S and Care known.
The only unknown variable is Q. Our objective is to minimize TC.
TCis minimized at that value of Q, where, Annual Ordering Cost = Annual Holding
Cost. See the equation below.
Solving the above equation for Q, gives the value of EOQ(Q
O) as shown below. H
Q
S
Q
D
2
 H
DS
EOQ
2


15. EOQ Example
SupposeD=1,200units,S=$5.00,H=$1.20andC=$12.00.
EOQ(Q
O)forthisproblemisgivenbelow.
15Qo =
2∗1200∗5
1.2
= 100

16. Graphs of Various Costs
The figure on RHS shows the
graphs of various costs as the
order quantity Qis changed.
The graphs for Annual
Ordering Cost and Annual
Inventory Cost intersect at
EOQ(=100).
16

17. Costs for Various Order Quantities
Order Size (Q)
AnnualOrdering
Cost
Annual
Inventory
Costs
Total Annual
Variable Cost
(TVC)
50 $120 $30 $150
75 $80 $45 $125
100 $60 $60 $120
125 $48 $75 $123
150 $40 $90 $130
175 $34 $105 $139
200 $30 $120 $150
225 $27 $135 $162
250 $24 $150 $174
275 $22 $165 $187
300 $20 $180 $200
Note that minimum cost is
for Q= 100 (EOQ).
Ordering Cost = Inventory
Cost = 60 for Q= 100.
TCcan be calculated as
TC = TVC + DC.
DCis a constant term and
is independent of Q.
17

18. 18
Economic Production (EPQ)
Model

19. 19
Economic Production Quantity
The economic production quantity (EPQ) model is used in
manufacturing situations where inventory is replenished at a
finite rate given by the production rate of the item under
consideration.
We define two more variables:
p: Production rate per day (daily production)
d: Demand rate per day (daily demand)
Note: pand dmust be defined in the same time unit. For example
these could be weekly instead of daily rates.

20. 20
Economic Production Quantity continued
Suppose
p= 50 units/day
d= 10 units/day
EPQ= 500 (production quantity, Q); Note: the optimal value of
Qis EPQor Q
P
In this case we will need 10 days to produce 500 units
(EPQ/p= 500/50).

21. Economic Production Quantity continued
During these ten days, we produce 50 units per day but also use
10 units per day.
Therefore, we are building up inventory at the rate of 40 (p-d
=50-10) units per day.
At the end of 10 days, the total number of units in inventory is
400 (40 * 10). This is the maximum inventory level, I
max.
After 50 days, the next batch consisting of EPQ units is
scheduled for production. This is how the cycles continue.
21

22. Economic Production Quantity continued
At the end of the 10
th
day, we stop producing this item and then
continue to meet the demand from the inventory. The inventory
will last for 40 days (400/10) because we have 400 units in stock
and the demand rate is 10 units/day.
The production cycle thus consists of 50 days. For the first 10
days we produce and use the item. For the next 40 days, there is
no production and there is only the usage of the item.
22

23. 23
Economic Production Quantity continued
The maximum inventory level as explained
earlier is I
max = Q (1-d/p) = 400.
Average Inventory = (I
max)/2
Annual Setup Cost = (D/Q)S
Annual Holding Cost =
EPQis obtained by equating the annual setup
cost with annual holding cost and then solving for
Q. The expression for EPQis given on the RHS.









p
d
H
DS
EPQ
1
2 



















p
dQ
HH
ax
1
22
Im 














p
dQ
HS
Q
D
TVC 1
2

24. Example: EPQ
AnnualDemand(D)=50,000units,SetupCost(S)=$25.00per
setup,InventoryHoldingCost(H)=$5.00perunitperyear.
Productionrate(p)=500unitsperday.
Numberofworkingdays=250.Demandoccursonlyduringthe
workingdays.Therefore,(d)=50,000/250=200.
EPQ(Q
P)=912.87=
I
max=548.
24

25. 25
Quantity (Price) Discount
Model

26. 26
Quantity (Price) Discount Model
Quantity discount model is used when the vendor (supplier)
offers a discount for buying in large quantities.
For example, the supplier may quote a price of $ 10.00 per unit
for order size 1 to 999 and $ 9.50 for order size of 1,000 or more.
This scenario is also called a “price break” at quantity 1,000.
There could be several price breaks.

27. Example: Quantity (Price) Discounts
Theannualdemand(D)foranitemis240,000units.Theorderingcostperorder(S)is
$30.00.Theinventorycarryingcostperunitperyear(H)is30%ofthecost(price)of
theitem,thatis,H=30%ofC.
Thevendorhasquotedthefollowingcosts(prices).
Price1:$2.80fororderquantitylessthanorequalto29,999.
Price2:$2.77fororderquantity30,000andabove.
FindtheEconomicOrderquantity.
27

28. Example: Quantity (Price) Discounts
(continued)
Tosolvethisproblemwewillcomparethetotalcostsforboth
prices.AsintheEOQmodel,theeconomicorderquantityis
givenbythefollowingequation,
Q
O=
and,thetotalcost(TC)isgivenbythefollowingequation:
TC=(D/Q)*S+(Q/2)*H+D*C
28

29. Example: Quantity (Price) Discounts
(continued)
StartcalculationsbyfindingEOQatthelowerprice($2.77).
Theinventorycarryingcostforthispriceis$0.83(=30%of$2.77)perunit
peryearandtheeconomicorderquantityforthispriceis4,163.
However,wecannotbuy4,163unitsatthepriceof$2.77becausethe
minimumquantityspecifiedbythevendoratthispriceis30,000.
Therefore,wehavetobuyatleast30,000unitstoobtainthispricediscount.
WecalculatethetotalcostTC(at30,000).UsingtheTCequation,
TC(at30,000)=(240,000/30,000)*30+(30,000/2)*0.83+240,000*2.77=$677,505.00
29

30. Example: Quantity (Price) Discounts
(continued)
NowcalculatetheEOQforthehigherprice$2.80.
ThevalueofHforthispriceis$0.84(30%of$2.80).
Theeconomicorderquantityis4,140.
Thisquantityisfeasiblebecausewecanbyupto29,999unitsat$2.80per
unit.
Thetotalcost,TC(at4,140)willbe:
TC(at4,140)==(240,000/4,140)*30+(4,140/2)*0.84+240,000*2.80=$675,477.93.
Theorderquantityforthisexampleis4,140
sinceTC(at4,140)<TC(at30,000).
30

31. 31
ABC Analysis

32. ABC Analysis
Somematerialsaremoreimportantthanothers.
Importancecanbeestablishedinthefollowingtwo
ways:
oMaterialCriticality
oAnnualDollarVolumeofMaterials
32

33. Material Criticality
Therearevariousdefinitionsof‘‘critical’’thatfitdifferent
situations.Forexample,apartiscriticalwhen:
oApartfailurecausesproductorprocessfailure.
oPartfailurecanhaveaprobability(notacertainty)ofstopping
theprocessorproduct.
oPartfailurereducesproductionoutputbyasignificantamount.
oDangerinvolvedinusingmaterials.Flammability,
explosiveness,andtoxicityoffumesarecrucialsafetyfactors
formaterialsmanagement.
33

34. Material Criticality (continued)
Whicheverdefinitionofcriticalityisused,theprocedureistolistfirstthe
mostcriticalparts.
Next,systematicallyrank-orderpartsaccordingtotheirrelativecriticality.
The concept of criticality should reflect the costs of failures, including safety
dangers, loss of life, and losses in production output.
CurvessimilartothefigureonRHS
canbecreatedforsuchsituations.
34

35. Annual Dollar Volume of Materials
ABCcategoriesarebasedonsortingmaterialsbytheirannualdollarvolume.
Dollarvolumeisthesurrogateforpotentialsavingsthatcanbemadeby
improvingtheinventorymanagementofspecificmaterials.
Accordingly,allparts,components,andothermaterialsusedbyacompany
shouldbelistedandthenrankorderedbytheirannualdollarvolume.
Startwiththoseitemsthathavethehighestlevelsofdollarvolumeandrank
orderthemfromthehighesttothelowestlevels.
oThetop25percentofthesematerialsarecalledA-typeitems.
oThenext25percentarecalledB-typeitems.
oThebottom50percentarecalledC-typeitems.
35

36. Annual Dollar Volume of Materials
(continued)
However,thereisnofixedconventionthatA,B,andCclassbreaksmust
occurat25and50percent.
Companiesdifferwithrespecttowhatpercentofallitemsstockedaccountfor
75percentoftheirtotalannualdollarvolume.
ThefigureonRHSportraysatypical
casewhere20to30percentofall
itemscarriedaccountforasmuchas
70to80percentofthecompany’s
totaldollarvolume.
36

37. Annual Dollar Volume of Materials -
Example
Item Stock
Number
Annual
Volume
(Units)
Unit Cost
Annual Dollar
Volume
Percentage of
Annual Dollar
Volume
Cumulative % of
Annual Dollar
Volume
Percentage
of Number
of Items
Stocked
Cumulative % of
Number of Items
Stocked
Category
P 1250 $92.00 $115,000.00 40.17% 40.17% 10.00% 10.00% A
Q 530 $168.00 $89,040.00 31.10% 71.26% 10.00% 20.00% A
R 1970 $18.75 $36,937.50 12.90% 84.17% 10.00% 30.00% B
S 430 $42.20 $18,146.00 6.34% 90.50% 10.00% 40.00% B
T 990 $13.80 $13,662.00 4.77% 95.27% 10.00% 50.00% B
U 680 $12.50 $8,500.00 2.97% 98.24% 10.00% 60.00% C
V 2150 $0.98 $2,107.00 0.74% 98.98% 10.00% 70.00% C
W 210 $9.80 $2,058.00 0.72% 99.70% 10.00% 80.00% C
X 1250 $0.52 $650.00 0.23% 99.93% 10.00% 90.00% C
Y 335 $0.64 $214.40 0.07% 100.00% 10.00% 100.00% C
Total $286,314.90
37

38. Lead-Times
Leadtime(LT)istheintervalthatelapsesbetweentherecognitionthatan
ordershouldbeplacedandthedeliveryofthatorder.SeeFigurebelow.
Thediminishingstocklevelreachesathreshold(orlimen)calledQ
RP-the
stocklevelofthereorderpoint.
Thethresholdtriggerstheorderforreplenishment.
Thestocklevelatthereorderpoint,RP,isenoughtomeetordersuntilthe
replenishmentsupplyarrivesandisreadytobeused.
38

39. Lead-Times (continued)
Eightlead-time(LT)considerationsthatapplytoEOQorEPQor
both:
Theamountoftimerequiredtorecognizetheneedtoreorder.
Theintervalfordoingwhateverclericalworkisneededto
preparetheorder.
Mail,e-mail,EDI,ortelephoneintervalstocommunicatewith
thesupplier(orsuppliers)andtoplacetheorder(s).
Timethattakesthesupplier’sorganizationtoreacttothe
placementofanorder?
39

40. Lead-Times (continued)
Deliverytimeincludingloading,transit,andunloading.
Processingofdelivereditemsbythereceivingdepartment.
Inspectiontobesureitemsmatchspecifications.
TimedelaysinupdatingrecordsTheeffectofsuchdelayson
theproductionschedulemustbeconsidered.
Theeightlead-timecomponentsareaddedtogettheleadtime.
Leadtimesareusuallyvariable.
Safetystocksmaybeincreasedtodealwithvariableleadtimes.
40

41. Order Point Policies (OPP)
Orderpointpolicies(OPP)definethestocklevelatwhichan
orderwillbeplaced.Thereorderpoint(RP),triggersanorderfor
morestock.
OPPsystemsspecifythenumberofunitstoorderandwhento
order.
Wewilldiscussthefollowingtwosystems
Periodic,alsoknownasfixedtime,inventorysystems.
Perpetual,alsoknownasfixedquantity,inventorysystems.
41

42. Periodic (Fixed Time) Inventory
Systems
Theintervalbetweenordersisfixedwhiletheorderedamountvaries.
Theordersizeisdeterminedbytheamountofstockon-handwhentherecord
isread.
Itisthedatethattriggersthereviewandtheorderbeingplaced.
SeethefigureonRHS.
42

43. Perpetual (Fixed Quantity) Inventory
Systems
Perpetual,alsoknownasfixedquantity,inventorysystemscontinuously
recordinventoryreceivedfromsuppliersandwithdrawnbyemployees.
Anorderisplacedwhenreorderpointisreached.
Theamountorderedissame(generallyEOQorEPQ)ineachcycle.
Theintervalbetweenplacingordersisdifferentineachcyclebecauseof
demandvariability.
SeethefigureonRHS.
43

44. Reorder Point and Safety (Buffer) Stock
Shortagesoccurwheneveractualdemandinthelead-timeperiodexceedsQ
RP.
Thelikelihoodofashortagewillbedecreasedbyincreasingthevalueof
safety(buffer)stock.
Determiningsafety(buffer)stocklevelrequiresaneconomicbalancing
situationbetweenthecostofgoingoutofstockversusthecostofcarrying
moreinventory.
Thelargebufferstockmeansthatthecarryingcostofstockishightomake
surethattheactualcostofstock-outagesissmall.
Thestocklevelofthereorderpoint(Q
RP)isequaltotheexpected(average)
demandduringtheleadtimeperiodplusthesafetystock(SS)quantity.
Thus,
44QRP = LT + SS

45. Expected Demand During Lead Time
Theexpecteddemandduringleadtimeisafunctionofaveragedemandper
day(d)andthemagnitudeofleadtime(LT)andisdeterminedas
Itmaybenotedthatcalculationofdemandduringleadtimebecomescomplex
ifleadtimealsovaries.
45

46. Safety Stock Calculations
ThevalueofSSdependsonthevariabilityofdemandandtheservicelevel.
Theservicelevelisameasureofthestock-outsituationsallowed.For
example,a95%servicelevelmeansthattherewillbenoout-of-stocksituation
95%ofthetimeduringleadtime.
AssumingthatthedemandfollowsanormaldistributionthevalueofSScanbe
determinedas
SS=zσ
LT
where,σ
LTisthestandarddeviationofdemandduringleadtimeandzisa
measureoftheservicelevelthatwewanttoprovide.ziscalledstandard
normalrandomvariableandcanbefoundfromitsstatisticaltable.Forthe
95%servicelevelthevalueofz=1.65.
46

47. Two-Bin Perpetual Invenory Control
System
Thetwo-binsystemisasmartwayofcontinuouslymonitoring
theorderpoint.
Itisasimpleself-operatingperpetualinventorysystem.
Seethefigurebelow.
47

48. 48
Thank you