13-1 Inventory Management

CHAPTER13

Inventory Management

Homework problems # 3,4,8, 14,15,17, 24,26,36,37 on pp. 589-595.

13-2 Inventory Management

Inventory• Inventory• Astockorstoreofgoods

• Independentdemanditems• Itemsthatarereadytobesoldorused

13-3 Inventory Management

Independent vs. Dependent DemandIndependentDemand

lWhenitem’sdemandisinfluencedbymarketconditionsandisnotrelatedto(i.e.,is“independent”of)productiondecisionforanyotheritem.

l Wholesaleandretailmerchandise(finishedgoods),serviceindustryinventory,end-itemandreplacement-partinventories,spare-parts,MRO(maintenance,repair,andoperating)supplies.

l Demandmustbeforecasted.

DependentDemandlWhenitem’sdemandderivesfrom(i.e.,“depend”on)theproductiondecisionsforitsparents.

lAllintermediateandpurchaseditemsinmanufacturing.lDemandmustbederived.

13-4 Inventory Management

Independent Demand

A

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand

Inventory: a stock or store of goods

13-5 Inventory Management

Types of Inventories

• Rawmaterialsandpurchasedparts• Work-in-process• Finishedgoodsinventoriesormerchandise• Maintenanceandrepairs(MRO)inventory,toolsandsupplies

• Goods-in-transittowarehousesorcustomers(pipelineinventory)e.g.,DeLL

13-6 Inventory Management

Functions of Inventory• Inventoriesserveanumberoffunctionssuchas:

1. Tomeetanticipatedcustomerdemand2. Tosmoothproductionrequirements3. Todecoupleoperations4. Toprotectagainststockouts5. Totakeadvantageofordercycles6. Tohedgeagainstpriceincreases7. Topermitoperations8. Totakeadvantageofquantitydiscounts

13-7 Inventory Management

Inventory Management• Managementhastwobasicfunctionsconcerninginventory:1. Establishasystemfortracking itemsininventory2. Makedecisionsabout

• Howmuchtoorder?• Whentoorder?

13-8 Inventory Management

• Asystemtokeeptrackofinventory• Areliableforecastofdemand• Knowledgeofleadtimes• Reasonableestimatesof

• Holdingcosts• Orderingcosts• Shortagecosts

• Aclassificationsystem

Effective Inventory Management

13-9 Inventory Management

InventoryTracking/Reviewing/CountingSystems

• PeriodicSystem• Physicalcountofitemsininventorymadeatperiodicintervals

• Perpetual(continuous)InventorySystem• Systemthatkeepstrackofremovalsfrominventorycontinuously,thusmonitoringcurrentlevelsofeachitem• Two-binsystem

• Twocontainersofinventory;reorderwhenthefirstisempty

13-10 Inventory Management

Demand Forecast and Lead Time• Forecasts

• Inventoriesarenecessarytosatisfycustomerdemands,soitisimportanttohaveareliableestimatesoftheamount andtiming ofdemand

• Leadtime• Timeintervalbetweenorderingandreceivingtheorder

• Point-of-sale(POS)systems• Asystemthatelectronicallyrecordsactualsales• Suchdemandinformationisveryusefulforenhancingforecastingandinventorymanagement

13-11 Inventory Management

ABC Classification System

Annual$valueofitems

AB

C

High

LowFew Many

VolumeofItems

• A-B-Capproach• Classifyinginventoryaccordingtosomemeasureofimportance,andallocatingcontroleffortsaccordingly

• Aitems(veryimportant)

• 10to20percentofthenumberofitemsininventoryandabout60to70percentoftheannualdollarvalue

• Bitems(moderatelyimportant)

• Citems(leastimportant)• 50to60percentofthenumberofitemsininventorybutonlyabout10to15percentoftheannualdollarvalue

13-12 Inventory Management

Cycle Counting• Cyclecounting

• Aphysicalcountofitemsininventory• Cyclecountingmanagement

• Howmuchaccuracyisneeded?• Aitems:± 0.2percent• Bitems:± 1percent• Citems:± 5percent

• Whenshouldcyclecountingbeperformed?• Whoshoulddoit?

13-13 Inventory Management

• Economicorderquantitymodel

• Economicproductionmodel

•Quantitydiscountmodel

How Much to Order: EOQ Models

Skip

13-14 Inventory Management

Basic EOQ Model• ThebasicEOQmodelisusedtofindafixedorderquantitythatwillminimizetotalannualinventorycosts

• Assumptions• Onlyoneproductisinvolved(atatime)• Annualdemandrequirementsareknown• Demandiseventhroughouttheyear• Leadtimedoesnotvary• Eachorderisreceivedinasingledelivery(nopartialdelivery)• Therearenoquantitydiscounts

13-15 Inventory Management

Key Inventory Terms• Leadtime:timeintervalbetweenorderingandreceivingtheorder

• Holding(carrying)costs:costtocarryanitemininventoryforalengthoftime,usuallyayear

• Orderingcosts:costsoforderingandreceivinginventory

• Shortagecosts:costswhendemandexceedssupply

13-16 Inventory Management

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receiveorder

Placeorder

Receiveorder

Lead time

Reorderpoint

Usagerate

Time

The Inventory Cycle

WhenorderquantityisQ ,howmuchisaverageinventory?

13-17 Inventory Management

Large vs. Small orders13-18 Inventory Management

Total CostAnnualcarryingcost

Annualorderingcost

Total cost = +

Q2 H

DQ STC = +

13-19 Inventory Management

Cost Minimization Goal

OrderQuantity(Q)

TheTotal-CostCurveisU-Shaped

OrderingCosts

QO

Ann

ual C

ost

(optimal order quantity)

Howtofindtheoptimalorderquantity?

HQ2

SQD

13-20 Inventory Management

Deriving the EOQ

Usingcalculus,wetakethederivativeofthetotalcostfunctionandsetthederivative(slope)equaltozeroandsolveforQ.

Cost Holding AnnualCost) Setupor der Demand)(Or 2(Annual =

H2DS = QOPT

13-21 Inventory Management

Minimum Total Cost

Thetotalcostcurvereachesitsminimumwherethecarryingandorderingcostsareequal.

13-22 Inventory Management

EOQ Sensitivity• Whathappenstooptimalorderquantity(andcycleinventory)ifthedemandrateincrease?

• Whathappenstolotsizesifsetup/orderingcostsdecrease?

• Whathappensifinterestratesdrop?• HowcriticalareerrorsinestimatingD,H,andS?

• Conclusion:EOQisrobust,insensitivetoparameterestimationerrors!

13-23 Inventory Management

EOQ Sensitivity13-24 Inventory Management

• Productiondoneinbatchesorlots• Capacitytoproduceapartexceedsthepart’susageordemandrate

• AssumptionsofEPQaresimilartoEOQexceptordersarereceivedincrementallyduringproduction

Economic Production Quantity (EPQ)

13-25 Inventory Management

EOQ with Quantity Discounts• Objectives:

• Considertradeoffsbetweendiscountbenefitsandincreasesinholdingcosts

• Theintroductionofquantitydiscountswillcausetheoptimumorderquantitytobeunchangedorgreater.

• TypesofDiscounts:• All-units:• Increment:

13-26 Inventory Management

Total Costs with Quantity Discounts

Annualcarryingcost

PurchasingcostTC = +

Q2 H

DQSTC = +

+Annualorderingcost

PD+

13-27 Inventory Management

Total Costs with constant PD

constant

13-28 Inventory Management

Total Costs with Variable PD

13-29 Inventory Management

EOQ with Quantity Discounts• Two-StepProcedure

• Step1.Beginningwith lowestprice,calculatetheEOQforeachpriceleveluntilafeasibleEOQisfound.Itisfeasibleifitliesintherangecorrespondingtoitsprice.

• Step2.IfthefirstfeasibleEOQfoundisforthelowestpricelevel,thisquantityisbest.Otherwise,calculatethetotalcostforthefirstfeasibleEOQandforthepricebreakquantityateach lowerpricelevel.Thequantitywiththelowesttotalcostisoptimal.

13-30 Inventory Management

Quantity Discounts ExampleExample.Assumethatthefollowingquantitydiscountscheduleisprovidedbyasupplier:

Ordersize Discount Unitcost0~49 0% $30.0050~99 5% $28.50100ormore 10% $27.00

Ifannualdemandis120units,orderingcostis$20perorder,andannualunitinventoryholdingcostis25%,whatorderquantitywouldminimizetotalinventorycosts?

13-31 Inventory Management

When to Reorder with EOQ Ordering• ReorderPoint- Whenthequantityonhandofanitemdropstothisamount,theitemisreordered

• SafetyStock- Stockthatisheldinexcessofexpecteddemandduetovariabledemandrateand/orleadtime.

• ServiceLevel- Probabilitythatdemandwillnotexceedsupplyduringleadtime.

13-32 Inventory Management

Determinants of the Reorder Point• Therateofdemand• Theleadtime• Demandand/orleadtimevariability• Stockoutrisk(safetystock)

Example:

13-33 Inventory Management

Safety StockFigure13.12

13-34 Inventory Management

Reorder PointFigure13.13 TheROPisbasedonaNormal

distributionofleadtimedemand

13-35 Inventory Management

Reorder Point Figure13.1413-36 Inventory Management

uVariable demand and constant lead time

uConstant demand and variable lead time

uVariable demand and variable lead time

Reorder Point Models

ROP= 𝑑• 𝐿𝑇 + Z• 𝐿𝑇 • 𝜎𝑑& +𝑑&• 𝜎𝐿𝑇&

�

ROP = 𝑑• 𝐿𝑇 + Z • d • 𝜎LT

ROP = 𝑑• LT + Z • 𝜎d • 𝐿𝑇�

13-37 Inventory Management

Reorder Point ExampleTheinjectionmoldingdepartmentofacompanyuses40pondsofapowderaday.Inventoryisreorderedwhentheamountonhandis240pounds.Leadtimeaveragesfivedays.Itisnormallydistributedandhasastandarddeviationoftwodays.

a).Whatistheprobabilityofastockoutduringleadtime?

b).Whatreorderpointwouldprovidea5%stockout?

13-38 Inventory Management

Fixed-order-interval (FOI) model

• Ordersareplacedatfixedtimeintervals• ReasonsforusingtheFOImodel:

• Supplier’spolicymayencourageitsuse• Mayrequireonlyperiodicchecksofinventorylevele.g.,grocerystores,smallshops

• Groupingordersfromthesamesuppliercanproducesavingsinshippingcosts

• Somecircumstancesdonotlendthemselvestocontinuouslymonitoringinventoryposition

13-39 Inventory Management

• Tightcontrolofinventoryitems• Itemsfromsamesuppliercanbecombinedandmayyieldsavingsin:• Ordering• Packing• Shippingcosts

• Maybepracticalwheninventoriescannotbecloselymonitored

• Note:

Fixed-Interval Benefits13-40 Inventory Management

Fixed-order-interval Model (Figure 13-15)

13-41 Inventory Management

Fixed-order-interval Model• ComparePandQsystemsintermsoforderquantity,reorderpoint,orderinterval(timebetweenorder)

• Whenbothdemandandleadtimeareconstant,PandQsystemsfunctionidentically.

orderquantity reorderpoint orderinterval

Q system

P system

13-42 Inventory Management

• Tightcontrolofinventoryitems• Itemsfromsamesuppliermayyieldsavingsin:

• Ordering• Packing• Shippingcosts

• Maybepracticalwheninventoriescannotbecloselymonitored

Fixed-Interval Benefits

13-43 Inventory Management

• Requiresalargersafetystock• Increasescarryingcost• Costsofperiodicreviews?

Fixed-Interval Disadvantages13-44 Inventory Management

Fixed-order-interval order quantityAmount to order (target Inventory) =

Where

OI = order (review) interval

A = inventory on hand at reorder time

13-45 Inventory Management

FOI Example13-46 Inventory Management

• Singleperiodmodel:modelfororderingofperishablesandotheritemswithlimitedusefullives

• Shortagecost:generallytheunrealizedprofitsperunitCs =

• Excesscost:differencebetweenpurchasecostandsalvagevalueofitemsleftoverattheendofaperiod

Ce=

Single Period Model

13-47 Inventory Management

Stocking Levels

Service level

SoBalance Point

Quantity

Ce Cs

So =OptimumStocking Quantity

unitper cost excess unitper cost shortage

where

level Service

==

+=

e

s

es

s

CC

CCC

So

Optimal stocking point =

13-48 Inventory Management

Single Period Model Example• GreatFarmer’sMarketbuysorganicmixedsaladfor$2.00perpoundandsellsitfor$4.20perpound.Attheendofeachweek,anyremainingmixedsaladissoldtoaproducerofcannedsoupfor$0.6perpound.Weeklydemandcanbeapproximatelybyanormaldistributionwithameanof100poundsandastandarddeviationof10pounds.Whatistheoptimalstockinglevel?

13-49 Inventory Management

Areasunderthestandardnormalcurve,from-∞to+z-∞ 0

13-50 Inventory Management

• Toomuchinventory• Tendstohideproblems• Easiertolivewithproblemsthantoeliminatethem

• Costlytomaintain• Wisestrategy

• Reducelotsizes• Reducesafetystock

Operations Strategy