Operations Management Solution Manual (Chapter 12)
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Transcript of Operations Management Solution Manual (Chapter 12)
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164 CHAPTER 12MANAGING INVENTORY
C H A P T E R
Managing Inventory
DISCUSSION QUESTIONS1.Thefourtypesofinventoryare:
Rawmaterialitemsthataretobeconvertedintoproduct Workinprocess(WIP)itemsthatareintheprocessof
beingconverted Finishedgoodscompleteditemsforwhichtitlehasnot
beentransferred MRO(maintenance, repair, and operating supplies)
itemsthatarenecessarytokeepthetransformationprocessgoing
2.The advent of lowcost computing should not be seen asobviatingtheneedfortheABCinventoryclassificationscheme.Althoughthecostof computing hasdecreasedconsiderably,thecostof dataacquisition hasnotdecreasedinasimilarfashion.Businessorganizationsstillhavemanyitemsforwhichthecostofdata acquisition for a perpetual inventory system is stillconsiderablyhigherthanthecostoftheitem.
3.ThepurposeoftheABCsystemistoidentifythoseitemsthatrequiremoreattentionduetocostorvolume.
4.Types of costsholding cost: cost of capital invested andspacerequired; shortagecost:thecostoflostsalesorcustomerswhoneverreturn;thecostoflostgoodwill; orderingcost: thecosts associated with ordering, transporting, and receiving theitems;unitcost:theactualcostoftheitem.
5.AssumptionsofEOQmodel:demandisknownandconstantovertime;leadtimeisknownandconstant;receiptofinventoryisinstantaneous; quantity discounts are not possible; the onlyvariable costs are the costs of placing an order or setting upproductionandthecostofholdingorstoringinventoryovertimeandifordersareplacedattherighttime,stockoutsorshortagescanbecompletelyavoided.
6.TheEOQincreasesasdemandincreasesorasthesetupcostincreases;itdecreasesastheholdingcostincreases.ThechangesintheEOQareproportionaltothesquarerootofthechangesintheparameters.
7.PricetimesquantityisnotvariableintheEOQmodel,butisinthediscountmodel.Whenqualitydiscountsareavailable,theunitpurchasepriceoftheitemdependsontheorderquantity.
8.Advantagesofcyclecounting:1. Eliminatingtheshutdownandinterruptionofproduction
necessaryforannualphysicalinventories2. Eliminatingannualinventoryadjustments
3. Providing trained personnel to audit the accuracy ofinventory
4. Allowingthecauseoferrorstobeidentifiedandremedialactiontobetaken
5. Maintainingaccurateinventoryrecords9. A decrease in setup time decreases the cost per order,encouragesmoreandsmallerorders,andthusdecreasestheEOQ.
10.DiscountpointsbelowtheEOQhavehigherinventorycosts,andthepricesarenolowerthanattheEOQ.PointsabovetheEOQhavehigher inventorycosts than thecorrespondingpricebreakpointorEOQatpricesthatarenolowerthaneitherofthepricebreaksortheEOQ.(ItdependsonwhetherthereexistsadiscountpointabovetheEOQ.)
11.Servicelevelreferstothepercentofcustomerstowhomtheproductorserviceisdeliveredwhenandaspromised.
12.If the same costs hold, more will be ordered using aneconomicproductionquantity,becausetheaverageinventoryislessthanthecorrespondingEOQsystem.
13.Ina fixedquantity inventorysystem,whenthequantityonhandreachesthereorderpoint,anorderisplacedforthespecifiedquantity.Inafixedperiodinventorysystem,anorderisplacedattheendoftheperiod.Thequantityorderedisthatneededtobringonhandinventoryuptoaspecifiedlevel.
14.TheEOQmodelgivesquitegoodresultsunderinexactinputs;a10%errorinactualdemandalterstheEOQbylessthan5%.
15.Safety stock is inventory beyond average demandduringlead time, held to control the level of shortageswhendemandand/orleadtimearenotconstant;inventorycarriedtoassurethatthedesiredservicelevelisreached.
16.Thereorderpointisafunctionof:demandperunitoftime,leadtime,customerservicelevel,andstandarddeviationofdemand.
17.Mostretailstoreshaveacomputerizedcashregister(pointofsale) system. At the timeof purchase, thecomputer systemsimultaneouslyringsupthebillandreducestheinventorylevelinitsrecordsfortheproductssold.
18.Advantageofafixedperiodsystem:There isnophysicalcount of inventory when items are withdrawn. Disadvantage:Thereisapossibilityofstockoutduringthetimebetweenorders.
ETHICAL DILEMMASettingservicelevelstomeetinventorydemandisamanagersjob.Settingan85%servicelevelforwholebloodisanimportant
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165 CHAPTER 12MANAGING INVENTORY
judgmentcallonthepartofthehospitaladministrator.Anothermajordisastermeansacertainshortage,yetanyhigherlevelmaybehardtocostjustify.Manyhospitalsdodevelopjointorregionalgroupstosharesupplies.Thebasicissueishowtoputapricetagonlifesavingmedicines.Thisisnotaneasyquestiontoanswer,butitmakesforgooddiscussion.
ACTIVE MODEL EXERCISESACTIVEMODEL12.1:EconomicOrderQuantity(EOQ)Model1.WhatistheEOQandwhatisthelowesttotalcost?
EOQ200unitswithacostof$1002.WhatistheannualcostofcarryinginventoryattheEOQandtheannualcostoforderinginventoryattheEOQof200units?
$50forcarryingandalso$50forordering3.Fromthegraph,whatcanyouconcludeabouttherelationshipbetween the lowest total cost and the costs of ordering andcarryinginventory?
The lowest total cost occurs where the ordering andinventorycostsarethesame.4.Howmuchdoes the totalcost increase if thestoremanagerorders50morehypodermicsthantheEOQ?50fewerhypodermics?
Ordering more increases costs by $2.50 or 2.5%.Orderingfewerincreasescostsby$4.17or4.17%5.Whathappens to theEOQand total cost whendemand isdoubled?Whencarryingcostisdoubled?
TheEOQrisesby82units(41%)andthetotalcostrisesby$41(41%)ineithercase.6.Scroll through lower setup cost values and describe thechangestothegraph.WhathappenstotheEOQ?
Thecurvesseemtodropandmovetotheleft.TheEOQdecreases.7.CommentonthesensitivityoftheEOQmodeltoerrorsindemandorcostestimates.
The total cost is not very sensitive to mistakes inforecastingdemandorplacingorders.
ACTIVEMODEL12.2:ProductionOrderQuantityModel1.Whatistheoptimalproductionrunsizeforhubcaps?
2832.HowdoesthiscomparetothecorrespondingEOQmodel?
TherunsizeislargerthanthecorrespondingEOQ.3.Whatistheminimalcost?
$70.714.HowdoesthiscomparetothecorrespondingEOQmodel?
ThetotalcostislessthanthecostfortheequivalentEOQmodel.
END-OF-CHAPTER PROBLEMS12.1AnABCsystemgenerallyclassifiesthetop70%ofdollarvolumeitemsasA,thenext20%asB,andtheremaining10%asC items. Similarly, A items generally constitute 20%of totalnumberofitems,Bitemsare30%;andCitemsare50%.
Item CodeNumber
AverageDollar Volume
Percent ofTotal $Volume
1289 400 3.75 = 1,500.00 44.0%2347 300 4.00 = 1,200.00 36.0%2349 120 2.50 = 300.00 9.0%2363 75 1.50 = 112.50 3.3%2394 60 1.75 = 105.00 3.1%2395 30 2.00 = 60.00 1.8%6782 20 1.15 = 23.00 0.7%7844 12 2.05 = 24.60 0.7%8210 8 1.80 = 14.40 0.4%8310 7 2.00 = 14.00 0.4%9111 6 3.00 = 18.00 0.5%
$3,371.50
100% (rounded
)Thecompanycanmakethefollowingclassifications:
A:1289,2347(18%ofitems;80%ofdollarvolume).B:2349,2363,2394,2395(36%ofitems;17.2%ofdollarvolume).C:6782,7844,8210,8310,9111(45%ofitems;2.7%ofdollarvolume).
12.2(a)Youdecidethatthetop20%ofthe10items,basedonacriterionofdemandtimescostperunit,shouldbeAitems.(Inthisexample,thetop20%constitutesonly58%ofthetotalinventoryvalue,butinlargersamplesthevaluewouldprobablyapproach70%to80%.)YouthereforerateitemsF3andG2asAitems.Thenext30%oftheitemsareA2,C7,andD1;theyrepresent23%ofthevalueandarecategorizedasBitems.Theremaining50%ofthe items(itemsB8,E9, H2,I5, andJ8)represent19%of thevalueandbecomeCitems.
Annual Item Demand Cost ($) Demand Cost Classificatio
n A2 3,000 50 150,000 B B8 4,000 12 48,000 C C7 1,500 45 67,500 B D1 6,000 10 60,000 B E9 1,000 20 20,000 C F3 500 500 250,000 A G2 300 1,500 450,000 A H2 600 20 12,000 C I5 1,750 10 17,500 C J8 2,500 5 12,500 C
(b)Borecki can use this information to manage his Aand Bitemsmorecloselyandtosaveorderingcostsonhisless importantCitemsbyorderingonlywhenAorBitemsarebeingorderedfromthesamesupplier.
(c)A2couldeasilymovetotheAcategorybasedonannualdollarvolume.Inasmallsample,30%oftheitemscanbeplacedintheAcategoryifdeemedappropriate.
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CHAPTER 12MANAGING INVENTORY 166
12.3
Inventory Item
$Valueper
Case
#Ordered
per Week
Total $ Value/Week
(52 Weeks) Total = ($*52) Rank
Percent of Inventory
Cumulative Percent of Inventory
Fish filets 143 10 $1,430 $74,360 1 17.54% 17.54%French fries 43 32 $1,376 $71,552 2 16.88% 34.43%Chickens 75 14 $1,050 $54,600 3 12.88% 47.31%Prime rib 166 6 $996 $51,792 4 12.22% 59.53%Lettuce (case) 35 24 $840 $43,680 5 10.31% 69.83%Lobster tail 245 3 $735 $38,220 6 9.02% 78.85%Rib eye steak 135 3 $405 $21,060 7 4.97% 83.82%Bacon 56 5 $280 $14,560 8 3.44% 87.25%Pasta 23 12 $276 $14,352 9 3.39% 90.64%Tomato sauce 23 11 $253 $13,156 10 3.10% 93.74%Tablecloths 32 5 $160 $8,320 11 1.96% 95.71%Eggs (case) 22 7 $154 $8,008 12 1.89% 97.60%Oil 28 2 $56 $2,912 13 0.69% 98.28%Trashcan liners 12 3 $36 $1,872 14 0.44% 98.72%Garlic powder 11 3 $33 $1,716 15 0.40% 99.13%Napkins 12 2 $24 $1,248 16 0.29% 99.42%Order pads 12 2 $24 $1,248 17 0.29% 99.72%Pepper 3 3 $9 $468 18 0.11% 99.83%Sugar 4 2 $8 $416 19 0.10% 99.93%Salt 3 2 $6 $312 20 0.07% 100.00%
$8,151 $423,852 100.00%(a)Fishfiletstotal$74,360.(b)Citemsareitems10through20intheabovelist(althoughthiscanbeoneortwoitemsmoreorless).(c)Totalannual$volume=$423,852.
12.47,0000.10700 700 20 35 35Aitemsperday7,0000.352,450 2450 60 40.83 41Bitemsperday7,0000.553,850 385012032 32Citemsperday
108items
12.5(a) 2(19,500)(25)EOQ = 493.71 494units4
Q
(b) Annualholdingscosts [Q/2]H[494/2](4)$988(c) Annualorderingcosts[D/Q]S[19500/494](25)$987
12.6 (a) 2(8,000)(45)EOQ 600units2
(b)IfHdoubles,from$2to$4/unit/month,
2 8,000 45EOQ = = 424.26units
4(c)IfHdropsinhalf,from$2to$1/unit/month,
2 8,000 45EOQ 848.53units
1
12.7(a)ThisproblemreversestheunknownofastandardEOQproblemtosolveforS.
2 240 48060 ;or60 , or
.4 10 4
3,60060 120 , sosolvingfor resultsin $30.
12
S S
S S S
(b)IfSwere$30,thentheEOQwouldbe60.Ifthetrue orderingcostturnsouttobemuchgreaterthan$30,thenthefirmsorderpolicyisorderingtoolittleatatime.
12.8(a) EconomicOrderQuantity(Holdingcost $5peryear):
whereDannualdemand,Ssetuporordercost,Hholdingcost
(b) EconomicOrderQuantity(Holdingcost $6peryear):
2 2 400 4073units
6DS
QH
where Dannualdemand, S setuporordercost, Hholdingcost
12.9 D15,000,H$25/unit/year,S$75
(a)2 2 15,000 75
EOQ 300units25
DSH
(b) Annualholdingcosts (Q/2)H(300/2)25$3,750
(c) Annualorderingcosts (D/Q)S(15,000/300)75$3,750
(d)15,000units
ROP = 2days 100units300days
d L
2 2 400 4080units
5DS
QH
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167 CHAPTER 12MANAGING INVENTORY
12.10 (a)ReorderpointDemandduringleadtime100units/day21days2,100units
(b)Ifdemandduringleadtimedoublesto200units/day,ROP=200units/day21days=4,200units.
(c)Ifdemandduringleadtimedropsto50units/day,ROP=50units/day21days=1,050units.
12.11(a)D10,000Numberofbusinessdays300Leadtime5daysROP[Demand/Day](Leadtime)[10,000/300](5)
166.67167units.(b)ThisnumberisimportantbecauseithelpsDuncankeep
enoughinventorytopreventstockoutswhileshewaitsforthenewordertoarrive.
12.12 (a) 2 2(6,000)(30)= = = 189.74units10
DSEOQ
H
(b)Averageinventory=94.87(c)Optimalnumberoforders/year=31.62
(d)Optimaldaysbetweenorders=
(e) C ostofinventorymanagement,excludingcostofgoods=(31.6230)+(94.8710)=$1,897.30
(f)Totalannualinventorycost=$601,897.30(includingthe$600,000costofgoods)
Note:Roundingoccursinanswers.
12.13(a)2 2(2500)18.75
1.50250bracketsperorder
DSQ
H
(b) 250Averageinventory 125units2 2Q
Annualholdingcost 125(1.50) $187.502QH
(c) 2500Numberoforders 10orders/y ear250
DQ
Annualordercost 10(18.75) $187.50DS
Q
(d) TC 187.50 187.50 $375/ year2Q DH S
Q
(e)
WorkingdaysTimebetweenorders
( / )250
25days10
D Q
(f)ROP dL 10(2) 20 units (where 10 daily
demand)2500
10250
d
12.14(a) Totalcost Ordercost + Holdingcost2
DS QHQ
1,200 25 25 24For 25: $1,500
25 21,200 25 40 24
For 40: $1,23040 2
1,200 25 50 24For 50: $1,200
50 21,200 25 60 24
For 60: $1,22060 2
1,200 25 100 24For 100: $1,500
100 2
Q
Q
Q
Q
Q
(b) EconomicOrderQuantity:
2 2 1,200 2550units
24DS
QH
where D annualdemand, S setuporordercost,HholdingcostAsexpected, small variations inorderquantitywillnothaveasignificanteffectontotalcosts.Ifweordertwice as many (e.g., Q goes from 25 to 50), TCincreasesbyonly$300(seeparta).
12.15(a) TheEOQassumptionsaremet,sotheoptimalorderquantityis
2 2(250)20EOQ 100units
1DSH
(b) Numberofordersperyear D/Q 250/100 2.5ordersperyear.
Notethatthiswouldmeaninoneyearthecompanyplaces3orders andin thenext it wouldonlyneed2orderssincesomeinventorywouldbecarriedoverfromthepreviousyear.Itaverages2.5ordersperyear.
(c) Averageinventory Q/2100/250units(d) Givenanannualdemandof250,acarryingcostof
$1, and an order quantity of 150, PattersonElectronics must determine what the ordering costwouldhavetobefortheorderpolicyof150unitstobeoptimal.Tofindtheanswertothisproblem,wemust solve the traditional economic order quantityequationfortheorderingcost.Asyoucanseeinthecalculations thatfollow,anorderingcostof$45isneededfortheorderquantityof150unitstobeoptimal.
DSQ
HH
S QD
2
2
2
2
(150) (1)=
2(250)22,500
= $45500
250 7.9131.62
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CHAPTER 12MANAGING INVENTORY 168
12.16D=12,500/year,sod=(12,500/250)=50/day,p=300/day,S=$30/order,H=$2/unit/year
(a)
(b)
(c)
(d)Days of demand satisfied by each production run
Daysinproductionforeachorder=
Totaltime=13.42dayspercycle.Thus,percentoftimeinproduction
(e)
12.17ProductionOrderQuantity,noninstantaneousdelivery.(a) D12,000/yr
H$.10/lightyrS$50/setupP$1.00/lightp100/day
12,000/yr
40/d ay300days/yr
d
2 2(12,000)50
40.10 11100
DSQ
dH p
4,472lightsperrun
(b)Averageholdingcost/ y ear 1
2
4,472 $26,832401 (.10) $134.162 100 200
Q d Hp
(c)12,000Averagesetupcost/y ear 504,472
$134.16
DS
Q
(d) Totalcost(includingcostofgoods)PD$134.16$134.16($112,000)$134.16$134.16$12,268.32/year
12.18(a) ProductionOrderQuantity,noninstantaneousdelivery:2 2 10,000 40
5010.601 500
1217.2, or1,217units
DSQ
dH p
where D annual demand, S setup cost, H holdingcost, d dailydemandrate, p dailyproductionrate
(b) maxInventory 1,0951d
Qp
(c) 10,000 8.221,217DQ
(d)
12.19AttheEconomicOrderQuantity,wehave:
EOQ (2 36,000 25) / 0.45 2,000units.
Thetotalcostsatthisquantityare:
HoldingcostQ/2H1,000.45$450OrderingcostD/QS36,000/2,00025$450PurchasecostDP36,0000.85$30,600Totalcost$900$30,600$31,500
Atthequantitydiscount,wehave:
HoldingcostQ/2H3,000.45$1,350OrderingcostD/QS36,000/6,00025$150PurchasecostDP36,0000.82$29,520Totalcost$1,500$29,520$31,020
Thequantitydiscountwillsave$480onthisitem.Thecompanyshouldalsoconsidersomequalitativeaspectsofthedecision,suchasavailablespace,theriskofobsolescenceofdisks,andtheriskof deterioration of the storage medium over time, as 6,000representsonesixthoftheyearsneeds.
12.20D (Annual demand)=400 12=4,800, P (Purchaseprice/Unit)=$350/unit, H (Holdingcost/Unit)=$35/unit/year, S(Orderingcost/Order)=$120/order.So,
(a)
DSQ
dH p
2 2 12,500 30= = = 671
502 11 300
D
NQ
12,500Numberofproductionruns( ) = = =18.63
671
50Maximuminventorylevel 1 = 671 1
300
1= 671 1 = 559
6
dQ
p
250 =13.42days18.63
671= = 2.24300
Qp
Costofinventory,excludinggoods
559(18.63 30) 2 $1,117.90
2
2.24= = 16.7%13.42
DSQH
2 2 4,800120= =35
= 181.42 = 181units(rounded).
Thus, (Totalcost)= + +2
35181 120 4,800= (4,800 325)+ +
2 181
= $1,560,000 + 3,168 + 3,182 = $1,566,350,
wherePrice=$325/unit.
HQ SDTC PD
Q
maxInventory2
328.50 328.80 $657.30
DTC H SQ
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169 CHAPTER 12MANAGING INVENTORY
However,ifBellComputersorders200units,whichisoptionalwiththediscountmodel,then
Bell Computers should order 200 units for aminimumtotalcostof$1,446,380.
(b)
181 units would not be bought at $350. 196 unitscannot be bought at $300, hence that isnt possibleeither.So,EOQ=188units.
The minimum order quantity is 200 units yet againbecausetheoverallcostof$1,445,880islessthanordering188units,whichhasanoverallcostof$1,566,119.
12.21The solution to any quantity discount model involvesdeterminingthetotalcostofeachalternativeafterquantitieshavebeencomputedandadjustedfor theoriginal problemandeverydiscount.
Westarttheanalysiswithnodiscount:
2(1,400)(25)EOQ(nodiscount) =0.2(400)
= 29.6units
Totalcost(nodiscount) = Costofgoods + Orderingcost+ Carryingcost
1,400(25) $400(1,400)29.6
29.6($400)(0.2)2
$560,000 $1,183 $1,183
$562,366
Thenextstepistocomputethetotalcostforthediscount:
2(1,400)(25)EOQ(withdiscount) =0.2($380)
= 30.3unitsEOQ(adjusted) = 300units
Becausethislasteconomicorderquantityisbelowthediscountedprice,wemustadjusttheorderquantityto300units.TheadjustedEOQfor300unitsisusedtocomputetotalcost.
Totalcost(withdiscount) = Costofgoods+ Orderingcost+ Carryingcost
1,400(25)= $380(1,400) +300
300($380)(0.2)2
$532,000 $117 $11,400$543,517
The optimal strategy is to order 300 units at a total cost of$543,517.
12.22 = 45,000, = $200, = 5%ofunitprice,D S I H = IPBestoptionmustbedeterminedfirst.SinceallsolutionsyieldQvaluesgreaterthan10,000,thebestoptionisthe$1.25price.
(a)
(b)
(c) D 45,000
Annualorderingcost = S 200Q 16,971
$530.33
(d) Unitcosts= PD=($1.25)(45,000)=$56,250(e)Totalcost=$530.33+$530.33+56,250.00=$57,310.66
12.23(a)D20,000/yrI20percentofpurchasepriceperyearinholdingcosts,
whereHIPS$40/orderP$20/tireiffewerthan500areordered;
$18/tireifbetween500and999areordered;and$17/tireif1,000ormoreareordered
35 200 120 4,800= (4,800 325) + +2 200
=1,440,000 + 3,500 + 2,880 = $1,446,380.
TC
DSQ
H
DSQ
H
DSQ
H
1
2
3
2 2 4,800120= = =181units
35
2 2 4,800120= = =188units
32.5
2 2 4,800 120= = =196units
30
Thus, (188units)= ++2
32.5 188 120 4,800 += (325 4,800)+
2 188
=1,560,000+3,055+ 3,064=$1,566,119
HQ SDTC PDQ
( )2
16,971Annualholdingcost= = (.05)(1.25)2
=$530.33
Q IP
( 45,000Annualorderingcost= ) = (200)16,971
=$530.33
D SQ
DSQ
IP* 2= =16,970.56
(200units)= + +2
30 200 120 4,800= (300 4,800)+ +2 200
=1,440,000+3,000+ 2,880=$1,445,880
HQ SDTC PDQ
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CHAPTER 12MANAGING INVENTORY 170
20
18
17
2 /
= (2 20,000 40) /(.2 20)
= 632.5(notvalid)Over500,$18discountwouldapply.
2 /
= (2 20,000 40) /(.2 18)
= 666.7(valid) 667
2 /
= (2 20,000 40) /(.2 17)
Q DS H
Q DS H
Q DS H
= 686(notvalid)
Cannotbuy686at$17.
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171 CHAPTER 12MANAGING INVENTORY
(b)Wecomparethecostofordering667withthecostof ordering1,000:
667 /2 /
= $18 20,000 (.2 $18 667)/2($40 20,000)/667
= $360,000 + $1,200 + $1,200= $362,400peryear
TC PD HQ SD Q
1,000 /2 /
= $17 20,000 (.2 $17 1,000)/2($40 20,000) /1,000
= $340,000 + $1,700 + $800= $342,500peryear
TC PD HQ SD Q
RockyMountainshouldorder1,000tireseachtime.
12.24D700128,400,H5,S50
Allen 1499 $16.00 500999 $15.50 1,000 $15.00
Baker 1399 $16.10 400799 $15.60 800 $15.10
(a)
(b,c) Vendor:Allen
Vendor:Baker
VendorAllenbestatQ=1,000,TC=$128,920.
410 8,400at410, (5) (50) 8,400(16) $136,449.36
2 410
500 8,400at500, (5) (50) 8,400(15.5) $132,290
2 500
TC
TC
1,000 8,400at1,000, (5) (50) 8,400(15)
2 1,000$128,920BEST
TC
410 8,400at410, (5) (50) 8,400(15.60) $133,089.39
2 410800 8,400
at800, (5) (50) 8,400(15.10) $129,3652 800
TC
TC
2 2(8,400)50 409.88 4105
DSQH
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CHAPTER 12MANAGING INVENTORY 172
12.25S10,H3.33,D2,400
12.26CalculationforEOQ:S$50,I=50%,H50%ofP, D9,600
EOQ120withslightroundingCosts
Qty Price Holding Ordering Purchase Total 120 $33.55 $199.80 $200.00 $80,520.00 $80,919.80 Vendor A 150 $32.35 $249.75 $160.00 $77,640.00 $78,049.75 300 $31.15 $499.50 $80.00 $74,760.00 $75,339.50 500 $30.75 $832.50 $48.00 $73,800.00 $74,680.50 120 $34.00 $199.80 $200.00 $81,600.00 $81,999.80 Vendor B 150 $32.80 $249.75 $160.00 $78,720.00 $79,129.75 300 $31.60 $499.50 $80.00 $75,840.00 $76,419.50 500 $30.50 $832.50 $48.00 $73,200.00 $74,080.50 BEST 120 $33.75 $199.80 $200.00 $81,000.00 $81,399.80 Vendor C 200 $32.50 $333.00 $120.00 $78,000.00 $78,453.00 400 $31.10 $666.00 $60.00 $74,640.00 $75,366.00 120 $34.25 $199.80 $200.00 $82,200.00 $82,599.80 Vendor D 200 $33.00 $333.00 $120.00 $79,200.00 $79,653.00 400 $31.00 $666.00 $60.00 $74,400.00 $75,126.00
(a) Price EOQ Vendor $17.00 336.0672 feasible 1 $16.75 338.5659 not feasible $16.50 341.1211 not feasible $17.10 335.0831 feasible 2 $16.85 337.5598 not feasible $16.60 340.0921 not feasible
(b,c) CostsQty Price Holding Ordering Purchase Total 336 $17.00 $1,428.00 $1,428.57 $163,200.00 $166,056.57 Vendor 1 500 $16.75 $2,093.75 $960.00 $160,800.00 $163,853.751000 $16.50 $4,125.00 $480.00 $158,400.00 $163,005.00 335 $17.10 $1,432.13 $1,432.84 $164,160.00 $167,024.97 Vendor 2 400 $16.85 $1,685.00 $1,200.00 $161,760.00 $164,645.00 800 $16.60 $3,320.00 $600.00 $159,360.00 $163,280.001200 $16.25 $4,875.00 $400.00 $156,000.00 $161,275.00 BEST
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173 CHAPTER 12MANAGING INVENTORY
(d) Otherconsiderationsincludetheperishabilityofthechemical and whether there is adequate space in thecontrolledenvironmenttohandle1,200poundsofthechemicalatonetime.
12.27(a)60;7Safetystockfor90%servicelevelZ(at0.90)71.288.969
(b)ROP60969BX5bandages.12.28(a)Z1.88
(b) Safetystock Z1.88(5)9.4drives(c) ROP 509.459.4drives
12.29
12.30
Incremental CostsSafety Stock Carrying Cost Stockout Cost Total Cost
0 0 70(100 0.4 + 200 0.2) = 5,600 $5,600
100100 15 =
1,500 (100 0.2) (70) = 1,400 $2,900
200200 15 =
3,000 0 $3,000 Thesafetystockwhichminimizestotalincrementalcostis100kilos.Thereorderpointthenis200kilos+100kilos,or300kilos.
12.31
12.32Only demand is variable in this problemso Equation (1215)applies
(a)ROP(AveragedailydemandLeadtimeindays)ZdLT
d(1,000 2) (2.055)( ) Leadtime 2,000 2.055(100) 2
2,0002912,291towels(b)Safetystock291towels
12.33Only leadtimeisvariableinthisproblem,soEquation (1216)isused.
1.88for97%servicelevel
ROP(DailydemandAverageleadtimeindays)DailydemandLT
Incremental CostsSafety Stock Carrying
CostStockout Cost Total Cost
0 0 (100 0.2 200 0.2) 70 4,200 $4,200100 100 30
3,000(100 0.2) 70 1,400 4,400
200 200 30 6,000
0 6,000
Safety Stock
Additional Carrying Cost Stockout Cost
Total Cost
0 0 10 0.2 50 7 20 0.2 50 7 30 0.1 50 7 3,150 3,150 10 10 5 50 50 7(10 0.2 20 0.1) 1,400 1,450 20 20 5 100 10 0.1 50 7 350 450 30 30 5 150 0 150
TheBB1setshouldthereforehaveasafetystockof30units;ROP90units.
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CHAPTER 12MANAGING INVENTORY 174
ROP(12,5004)(1.88)(12,500)(1)50,00023,50073,500pages
12.34(a)Bothleadtimeanddemandarevariables,soEquation(1217)applies,inweeks.1.28for90%service.
ROP(2006)1.28dLTwheredLT 2 2 2(6 25 ) (200 2 )
(6 625) (40,000 4) 3,750 160,000
163,750 405SoROP1,200(1.28)(405)1,2005181,718cigars(b)For95%servicelevel,Z=1.65
SoROP=(2006)+1.65(405)1,200+668=1,868cigars.(c)Ahigherservicelevelmeansalowerprobabilityofstocking
out.Hence,theROPincreasesfrom1,718to1,868whentheservicelevelchangefrompart(a)topart(b).
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175 CHAPTER 12MANAGING INVENTORY
12.35
Note: Items of new product development, advertising, and researcharenotpartofholdingororderingcost.
$34,300Costperorder $171.50
200$17,530
Holdingcostperunit $1.75310,000
(2)(1000)(171.5)Therefore,EOQ 442.34units.
1.753
12.36 = $9 $5 = $4= $5 $2 = $3
s
o
C
C
4 4 .57144 3 7
Servicelevel s
s o
CC C
Z.18,=100,=15Optimalstockinglevel=100+.18(15)=102.7,or103poundsofoysters.
12.37 = $1 0 $6 = $4
= $6 $5 = $1s
o
C
C
4 4Servicelevel .80
4 1 5
s
s o
CC C
SoZ=.84,=25,=4Optimalstockinglevel=25+.84(4)=28.36,or28cakes.
12.38 23 90,000 60,000programs, =5,000
s
o
s
s o
CC
CC C
(a) = $4 $1 =$3 = costofunderestimatingprogram demand
b = $1 $.10 = $.90 = costofoverage
3 3c Servicelevel = = = = .7692
+ 3+.90 3.90
So Z .735(abouthalfwayinAppendixIbetween.73and.74)Optimalnumberofprogramstoorderpergame
=60,000+.735(5,000)=60,000+3,675=63,675
(d)Stockoutrisk=1Servicelevel=1.7692=.2308,or23.1%
12.39Annualdemand,D8,000Dailyproductionrate,p200Setupcost,S120Holdingcost,H50Productionquantity,Q400
(a) Dailydemand, dD/2508,000/25032(b) Numberofdaysinproductionrun Q/p400/2002
(c) Numberofproductionrunsperyear D/Q8,000/40020Annualsetupcost20($120)$2,400
(d) Maximuminventorylevel Q(1d/p)400(132/200)336
AverageinventoryMaximum/2336/2168(e) Totalholdingcost Totalsetupcost(168)5020(120)
$8,400$2,400$10,800
(f)2 2(8,000)120
213.813211 50 200
DSQ
dH
p
TotalholdingcostTotalsetupcost4,4904,490$8,980Savings$10,800$8,980$1,820
12.40 ( a)d75lbs/day200daysperyearD15,000lb/yearH$3/lb/yearS$16/order
Q400lbofbeans2(15,000)(16)
3(b) Totalannualholdingcost= =(200)($3)=$600
2Q
H
(c) Totalannualordercost= =(37.5)(16)=$600D
SQ
(d)LT4dayswith15 Stockoutrisk 1%
2.33ROPLeadtimedemandSS
whereSS( )(dLT)andleadtimedemand(d)(LT)
dLT (15) 4 (15) 30LT ROP369.99 whereROP(d)(LT)SS
(e)SS69.99frompart(d)(f) Annualsafetystockholdingcost $209.97(g) 2%stockoutlevelZ=2.054
SS(Z)(dLT)61.61Thelowerwemakeourtargetservicelevel,thelessSSweneed.
ADDITIONAL HOMEWORK PROBLEMSHerearesolutionstoadditionalhomeworkproblems12.4112.53which are found on our Web site,www.pearsonglobaleditions.com/myomlab.
12.41
AnnualSKU Demand Cost ($) Demand Cost Classificati
on A 100 300 30,000 A B 75 100 7,500 B C 50 50 2,500 C D 200 100 20,000 A E 150 75 11,250 B
HoldingCost
Ordering Cost
$2,000 1,500 600 500 750 800 280 30,000 12,800 500 800 1,000 300 $34,300
$17,53
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CHAPTER 12MANAGING INVENTORY 176
Obviously,withsofewitems,thebreakdownsintoA,B,andCcannotfollowtheguidelinesexactly.
12.42
Annual Demand
Item Demand Cost($)
Cost Classification
E102 800 4.00 3,200 CD23 1,200 8.00 9,600 A 27%D27 700 3.00 2,100 CR02 1,000 2.00 2,000 CR19 200 8.00 1,600 CS107 500 6.00 3,000 CS123 1,200 1.00 1,200 CU11 800 7.00 5,600 B 16%U23 1,500 1.00 1,500 C 33%V75 1,500 4.00 6,000 B 17%
12.43 2(1000)62.50 500units0.50
EOQ
12.442(8,000)45 720,000
300 90,000
720,000$8
90,000
H H
H
12.45 ( a) EconomicOrderQuantity:2 2 1,500 150
100units45
DSQ
H
where: Dannualdemand, Ssetuporordercost,Hholdingcost
(b)100 45
Holdingcost $2,250.002 2
QH
(c)1500 150
Ordercost $2,250.00100
DSQ
(d) Reorderpoint:Reorderpoint = demandduringleadtime
1,500units/d ay 6days
30030units
12.46Reorderpointdemandduringleadtime
500units/day14days7,000units
12.47(a) EconomicOrderQuantity:2 2 5,000 30
77.46or78units50
DSQ
H
where: Dannualdemand, Ssetuporordercost,Hholdingcost
(b) Averageinventory 78 392
units
(c) NumberofordersperyearDemand 5,000
78EOQ
64.1or64orders
(d) Assuming250business days per year, the optimalnumberofbusinessdaysbetweenordersisgivenby:
250Optimalnumberofdays 3.91days
64
(e)
Totalcost ordercost holdingcost5,000 30 78 50
2 78 21,923.02 1,950 $3,873.08
DS QHQ
Note:OrderandcarryingcostsarenotequalduetoroundingoftheEOQtoawholenumber.IfanEOQof77.46isused,theorderand carrying costs calculate to $1,936.49 for a total cost of$3,872.98.
(f) Reorderpoint:Reorderpoint = demandduringleadtime
5,000units10days 200units
250days
Thisisnottosaythatwereorderwhenthereare200unitsonhand(asthereneverare).TheROPindicatesthat orders are placedseveral cycles prior to their actualdemand.
12.48(a) Totalcost ordercostholdingcost2
DS QHQ
ForQ50:600 60 50 20
720 500 $1,22050 2
(b) EconomicOrderQuantity:
2 2 600 6060units
20DS
QH
where: Dannualdemand, S setuporordercost,HholdingcostForQ60:600 60 60 20
600 600 $1,20060 2
(c) Reorderpoint:Reorderpointdemandduringleadtime
600units10days 24units
250days
12.49EconomicOrderQuantity,noninstantaneousdelivery:
2 2 8,000 100
1,651.4or1,651units400.80 11150
DSQ
dH p
where:Dannualdemand,Ssetuporordercost,Hholdingcost,ddailydemandrate,pdailyproductionrate12.50EconomicOrderQuantity:
2DSQ
H
where:Dannualdemand,Dsetuporordercost,Hholdingcost,pprice/unit
(a) EconomicOrderQuantity,standardprice:
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177 CHAPTER 12MANAGING INVENTORY
2 2,000 10200units
1Q
Totalcost ordercost holdingcost purchasecost
22,000 10 200 1
(2,000 1)200 2
100 100 2,000$2,200
DS QHPD
Q
(b) QuantityDiscount:Totalcost ordercost holdingcost purchasecost
22,000 10 2,000 12,000 2(2,000 0.75)
10 1,000 1,500 $2,510
DS QHPD
Q
Note:No,EOQwith200unitsandatotalcostof$2,200isbetter.
12.51Underpresentpriceof$7.00perunit, EconomicOrderQuantity:
2
2 6,000 20478.1or478units
0.15 7
DSQ
H
Q
where:Dannualdemand,Ssetuporordercost,Hholdingcost,pprice/unitTotalcost ordercost holdingcost purchasecost
26,000 20 478 0.15 7
(7 6,000)478 2
251.05 250.95 42,000$42,502.00
DS QHPD
Q
Note:OrderandcarryingcostsarenotequalduetoroundingoftheEOQtoawholenumber.Underthequantitydiscountpriceof$6.65perunit:Totalcost ordercost holdingcost purchasecost
26,000 20 3,000 0.15 6.65
(6,000 6.65)3,000 2
40.00 1,496.25 39,900 $41,436.25
DS QHPD
Q
Therefore, the newpolicy, with a total cost of $41,436.25, ispreferable.
12.52EconomicOrderQuantity:2DS
QH
where:Dannualdemand,Ssetuporordercost,Hholdingcost,Pprice/unit
(a) Orderquantity9sheetsorless,unitprice $18.00
2 100 4550units
0.20 18Q
Totalcost ordercost holdingcost purchasecost
2100 45 50 0.20 18
(18 100)50 2
90 90 1,800$1,980 (seenoteatendofproblemregardingactualprice)
DS QHPD
Q
(b) Orderquantity10to50sheets:unitprice $17.50
2 100 4550.7unitsor51units
0.20 17.50Q
Totalcost ordercost holdingcost purchasecost
2100 45 51 0.20 17.50
51 2(17.50 100)
88.23 89.25 1,750.00 1,927.48
DS QHPD
Q
Note:OrderandcarryingcostsarenotequalduetoroundingtheEOQtoawholenumber.Seenoteatendofproblemregardingprice.
(c) Order quantity more than 50 sheets: unit price $17.25
2 100 4551.1unitsor51units
0.20 17.25Q
Totalcost ordercost holdingcost purchasecost
2100 45 51 0.20 17.25
51 2(17.25 100)
88.24 87.98 1,725.00 $1,901.22
DS QHPD
Q
Therefore,order51units.Note:Orderandcarryingcostsarenotequaldueto
roundingoftheEOQtoawholenumber.ImportantNote:Studentswilllikelycompleteall
threesetsofcalculations,includingthecalculationsoftotalcosts.Theyshouldbepromptedtorealizethatcalculationsoftotalcostunder(a)and(b)areactuallyinappropriatebecausetheoriginalassumptionsastolotsizewouldnotbesatisfiedbythecalculatedEOQs.
12.53Z1.28for90%servicelevelSafetystock(1.28)(15)19.2or19Reorderpoint361955TVs
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1
2
CHAPTER 12MANAGING INVENTORY 178
CASE STUDIESHERRERSBICYCLESHOP,TILBURG,THENETHERLANDS
1. Giventhedata,canyouprovideadvicetoJoontheorderquantityandreorderpoint?
Theforecasteddemandforallthe12monthsof2010is888bicycles.Hencetheaveragedemandpermonth=888/12=74bicycles.Thestandarddeviationofthemonthlydemand=57.78bicycles.Otherparametersoftheproblemaregivenbelow.
Ordercost=$100/orderCostperbicycle=$200Holdingcost=($200)(18%)=$36peryearperbicycle
UsingthesimpleEOQmodel,theeconomicorderquantity(Q*)iscalculatedasfollows.
Servicelevel=95%,withcorrespondingZvalueof1.645Leadtime=1month(4weeks)
Thereorderpoint(ROP)iscalculatedbythefollowingrelation:
ROP=Averagedemandduringtheleadtime()+Z(Standarddeviationofthedemandduringtheleadtime()
Therefore,ROP=74+1.645(57.78)=169.01bicycles(roundedupto170).
2.IfJowantedtoincreaseserviceto99%,whatwouldthenewreorderpointbe?Howmuchadditionalholdingcostswouldresult?
For99%servicelevel,Zvalueis2.326.Hencethenewreorderpointis,
ROP=74+2.326(57.78)=208.39bicycles(roundedupto209)
Thus,withthenewservicelevel,thereorderpointis209units.Thisrepresents39additionalunitsofsafetystock,oranadditional$1404inholdingcostperannum.
3.Whatcriticalassumptionisnotmetintheanalysisabove?Whatimprovementsonthepolicycanyouimagine?
TheEOQmodelassumesaconstantdemandwhichisnotthecasehere.Thatsaid,theEOQmodelisnotoriouslyrobust.MorecriticalisbasingtheROPonaveragemonthlydemandand
standarddeviations.Thiswillleadtoanincreasedchanceofastockoutduringthepeakdemand months.Abetterpolicywouldbetocalculateareorderpointwhichchangesbasedonthemonth.
Data
2008 2009 2010Forecast
Jan 12 14 16
Feb 23 26 30
Mar 43 51 59
Apr 83 97 113
May 162 193 225
Jun 83 97 113
Jul 62 73 85
Aug 33 39 45
Sep 21 25 29
Oct 22 25 29
Nov 42 51 59
Dec 61 73 85
STURDIVANTSOUNDSYSTEMS1.Computetheoptimalorderquantity.First,determinethecostunderthepresentpolicy:
Numberoforders/year52weeks4weeks13ordersAverageordersize5,000/13384.6or385unitsTotalcostordercostholdingcostpurchasecostPurchasecost5000units60/unit 300,000Ordercost$20/order13orders 260
Note:Didnotround384.6above.Next, develop an Economic Order Quantity and determine thetotalcosts:
whereDannualdemand, Ssetuporordercost, Hholdingcost.
2. Determinetheappropriatereorderpoint(inunits).ReorderpointDemandduringleadtime205100
3.Computethecostsavingsthatthecompanywillrealizeifitimplementstheoptimalinventoryprocurementdecision.
2 2 5,000 20 182.5,or183units6
DSQH
384.6units/Order $6 / unit 1154Carryingcost2 Totalcost = $301,414
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1
1
2
179 CHAPTER 12MANAGING INVENTORY
Totalcost Ordercost Holdingcost Purchasecost
2
5,000 20 183 6 5,000 60183 2
546.45 549.00 300,000.00$301,095.45
QHDS PDQ
Note:OrderandcarryingcostsarenotequalduetoroundingoftheEOQtoawholenumber.
ThecostsavingsundertheEOQorderingpolicywouldthenbe:Costunderpresentpolicy: $301,414.00CostunderEOQpolicy: 301,095.45
$318.55whichisaverysmallsavings.
4.The typical costs associated with procurement of materialsinclude costs of preparing requisitions, writing purchase orders,receivingmerchandise,inspectinggoods,storage,updatinginventoryrecords,andsoforth.Thesecostsareusuallyfixed,regardlessofthesizeoftheorder.Alargeordermayrequiremoreprocessingtime(ininspection,forexample),buttheincreaseinprocurementcostsistypically minimal. As lot size increases, the number of ordersdecreases (assuminga constant requirement level). Consequently,procurementcoststypicallydecreasewithanincreaseinlotsize.
VIDEO CASE STUDIESMANAGINGINVENTORYATFRITOLAY
Thisvideo,filmedspecificallyforourtext,isavailablefromPrenticeHallandisdesignedtosupplementthiscase.
1.Aprocessfocusedfacilitywillhavesubstantialrawmaterialfortheunexpectedorder,substantialWIPbecauseofimbalanceinthesystem,fewfinishedgoodsbecausemostitemsaremadetoorder,andlessMRObecauseofoptionalroutingsintheplant.
2.ThemajorinventoryitemsatFritoLayarepotatoes,corn,cornmeal,seasonings,andoil.Theymovequicklythroughtheprocess,usuallyinhours.AttheFloridaplant,forexample,potatoesarriveby the truckload from nearby farms, and 50,000 pounds (10truckloads)areconsumedinoneshift. Onlyabout7 hoursofpotatoesareheldinthestoragearea.
3.Fourtypesofinventory:(a)Rawmaterials:potatoes,corn,seasonings,andoil(b)Workinprocess:potatoesbeingcleaned,seasoned,
cooked,andbagged(c)Finishedgoods:bagsandcartonsofchipsorotherproducts(d)MRO:motors,gears,andswitchesthatkeeptheplantrunning
4.Dollarinvestmentsineachoftheabovefourtypesofinventory:(a)Least:WIPThereisvirtuallynoWIPonlyoneshiftworththatismovingrapidlythroughtheplant.(b)Nexttoleast:Rawmaterialwithfrequentdeliverywillhavelowvolumeonhandatanyonetime.(c)Nexttomost:FinishedgoodsSeveraldaysofinventorybutwithanaverageof1.4days,toensurethatpropermixisavailablefordelivery.Thisismorecostlyasithasboththerawmaterialcostandtheprocessingcostincluded.
(d)Most:MRO(maintenancerepairandoperatingsupplies)Thisinventoryistypicallyhighinprocessindustriesbecausereplacementpartsmustbeavailabletokeepthehighcapitalinvestmentprocessrunning.Good/highutilizationrequiresthis.
5. Inventory flowsquicklybecause theplant is automatedandefficient, and it suffers minimal breakdowns. It has to moverapidly because the basic corn and potato ingredients areperishableuntiltheyareprocessedandsealedinbags.
6.ThefirmhasplantsthroughouttheUnitedStatesandCanada(30ofthem)becausetheproductmustmovetomarketquicklytokeepitfresh.Sothemanufacturingprocessneedstobeneartheconsumerandmarkets.
7. FritoLay does not make all 41 products at each plant.Equipment to handle specialty products that have (relatively)smaller sales is expensive. So some plants make only a fewproductsanddistributethemmorebroadly.Itsacostissue.
INVENTORYCONTROLATWHEELEDCOACH
The7minutevideo,filmedspecificallyforthistext,isavailablefromPearsonEducationanddesignedtosupplementthiscase.1.WheeledCoachimplementsABCanalysisbyidentifyingtheannualuseofthosehighdollaritemsandclassifyingthemasA.They represent some 15% of the total inventory items, but70%80%of the totalcost. Bitemsarethoseitemsthatareofmediumvaluethatrepresent30%oftheitemsand15%25%ofthevalue.ThelowdollaritemsareclassCitems,whichrepresents5%oftheannualdollarvolume,butabout55%ofthetotalitems.2.TheinventorycontrolmanageratWheeledCoachwouldwantto not only have ABC analysis but implement tight physicalcontrol of the stockroom. He would also implement a cyclecountingsystem,andensurethatissuesrequireengineeringchangenoticesforthoseitemsnotinitiallyincludedonthebillofmaterial.Totheextentfeasible,stockroomswouldbeconsolidated.3.Theinventorycontrolmanagerwouldimplementthesechangesthrougheffectiveleadership,hiringandtrainingofcyclecounters,andeffectivetrainingandeducationofallstaff,fromengineeringthroughcyclecounters,sothateachunderstandstheentiresystemandtheimportanceofmaintainingaccurateinventory.Wewouldalsowanttobeassuredthatallconcernedemployeesunderstandtheimportanceofaccurate inventoryrecords, tight inventorycontrol,and locked stockrooms. Management would have to exhibit theproper leadership and support of the entire system, includingaccuratebillsofmaterial,rapidissuingofECNs,trainingbudgets,etc.
ADDITIONAL CASE STUDIES*SOUTHWESTERNUNIVERSITY:F
KeyPoints:Thiscaseletsthestudentlookatasimpleinventoryproblem that can be discussed at several levels. By using astandardEOQformula,thestudentgetsafast,easysolutionthatisclose.However,thecaselendsitselftofurtherdiscussionthatcanmakethelimitationsofEOQreadilyapparent.
*ThesecasestudiesappearonourCompanionWebsite,www.pearsonglobaleditions.com/heizer.
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CHAPTER 12MANAGING INVENTORY 180
1.Becausethisisaoneyeardemand,demandviolatestheEOQassumptionofconstantdemand.Therefore,thenumberofordersshouldnotbeprorated(asdoesthestandardEOQcomputation)norareallordersattheEOQoptimumof60,000.Thetotalcostandtotalprofitwillnotbeaccurateifthetheoreticalsolutionisused.
Theoretical Solution: Maddux should order 60,000 perorderfromFirstPrinting.ThesimpletheoreticalEOQsolutionis
133 ordersof60,000eachforasetupcostof$1,000,andthetotal
is$310,600.Theinstructorcanacceptthisaslessthanprecise,butadequate.ThesolutionisclosebecausethetotalEOQlineissoflat(robust)aroundtheoptimum.Alternatively,theinstructorcanexpandthediscussiontotherealapplication.
Excel OMsoftware output (theoretical solution) is shownbelow:
DataDemand rate, D 200,000Setup cost, S 300Holding cost %, I 0.5
Range 1 Range 2 Range 3 Range 4Minimumquantity
10,000 30,000 60,000 250,000
Unit price, P 1.62 1.53 1.44 1.26
Actual Solution: The demand is not constant. Maddux needs200,000programsthisyear.Theprogramswillbedifferentnextyearwhenhewillalsohaveanewforecasteddemand,dependingonhowtheteamdoesthisyear.Madduxsrealsolutionwillbemore like this one: Maddux should order programsfromFirstPrinting.Heplaces3ordersfor60,000and1for20,000atanactualtotalcostof$308,800.
Theoreticalunitcost ($1.44200,000)$288,000Actualunitcost ($1.44360,000)($1.53
20,000)$259,200$30,600$289,600
Theoreticalorderingcost ( 133 $300)$1,000Actualorderingcost butinfact4ordersmustbeplaced;
3 at 60,000 and 1 at 20,000. Foursetupscost$1,200(4$300)
Theoreticalholdingcost 50%of$1.44(60,000/2)$21,600ActualholdingcostLastorderisforonly20,000units,so
his average order (and maximum inventory) is only 50,000(200,000/4ordersor[(360,000)20,000]/450,000,soacasecanbemadethathisholdingcostis50%of1.44(50,000/2)$18,000.
Totalprogramcost(Unitcost)(Orderingcost)(Holdingcost)
$289,600$1,200$18,000
ResultsRange 1 Range 2 Range 3 Range 4
Q* (Square rootform)
12,171.61 12,524.48 12,909.94
13,801.31
Order quantity 12,171.61 30,000.00 60,000.00
250,000.00
Holding cost $4,929.50 $11,475.00 $21,600.00
$78,750.00
Setup cost $4,929.50 $2,000.00 $1,000.0 $240.00
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181 CHAPTER 12MANAGING INVENTORY
$308,8002.Theinsertorderingincludesanothersetofissues.Althoughsomestudentsmightuseastandardquantitydiscountmodelandsuggestthattheorderquantityshouldbe60,000units,purchasedfromFirstPrinting,asshownintheExcelOMprintoutbelow,therealproblemissomewhatdifferent:
DataDemand rate, D 200,000Setup cost, S 300Holding cost %, I 0.05
Range 1 Range 2 Range 3 Range 4Minimumquantity
10,000 30,000 60,000 250,000
Unit price, P 0.81 0.765 0.72 0.63
Madduxneeds40,000insertsforeachgameandmustorderthemonapergamebasis.Insertsforeachgameareunique,asstatisticsand lineup for each teamchanges as the season progresses. If60,000peoplearegoingtoattendthegame,then40,000insertsare required (2 of 3 people, or 2/3 of 60,000). Therefore, thequantity discount issue, although it should be evaluated, takessecondplacetothenecessityofordering40,000insertsforeachgame.
Therefore, Maddux should order 40,000 inserts from FirstPrintingforeachgameatacostof$32,430pergameand532,430(5games)$162,150perseason.
Unitcost$0.76540,000$30,600Orderingcost5ordersmustbeplaced@40,000inserts;
5setupscost$1,500@$300each.Holdingcost5%of$0.765(40,000/2)$1,530(assume
averageinventoryis20,000).
Pergameinsertcost ($0.765 40,000) ($300)(5%of$0.765 40,000 2)
$30,600 $300 $1,530 $32,430Perseasoninsertcost$32,4305games$162,150
3.Totalcostfortheseasonis:Programs$308,800Inserts$198,750
Totalcostforseason$507,5504.Madduxmightdoseveralthingstoimprovehissupplychain:
Askthepotentialvendorsifthereisanadditionaldiscountifhebuysprogramsandinsertsfromthesamevendor.
Askifhecanhavethesamediscountscheduleifheplacesablanketorderforall200,000,butasksforreleasesonapergamebasis.
HemayalsobeabletosavemoneyifhecanreducehistripstoFt.Worthbycombiningpickupsofprogramsandinserts.
He might also prevail upon the vendors to hold theprogramsandinsertsattheprintingplantuntiljustbeforethegame,reducinghisholdingcost.
ResultsRange 1 Range 2 Range 3 Range 4
Q* (Square root form) 54,433.1 56,011.2 57,735.0 61,721.3Order quantity 54,433.1 56,011.2 60,000 250,000Holding cost $1,102.27 $1,071.21 $1,080.00 $3,937.50Setup cost $1,102.27 $1,071.21 $1,000.00 $300.00Unit costs $162,000.00 $153,000.00 $144,000.00 $126,000.00Total cost $164,204.54 $155,142.43 $146,080.00 $130,237.50
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2
CHAPTER 12MANAGING INVENTORY 182
LAPLACEPOWERANDLIGHTTheoptimalorderquantityisgivenby:
2 2(499.5) 50*
41.4DS
QH
Q*34.74thousandfeetThereorderpointisgivenby:
ROP Dailydemand Leadtime
499.5(60)
260
ROP = 115.27thousandfeet
=
=
Currently,thecompanyiscommittedtotake1/12ofitsannualneed each month. Therefore, each month the storeroom issuesapurchaserequisitionfor41,625feetofcable.
499.5 41.625PresentTC (50) (41.4) (499.5)(414)
41.625 2
= 600+861.62+206,793= $208,254.62
499.5 34.74OptimumTC (50) (41.4) (499.5)(414)
34.74 2
= 718.91+719.12+206,793= $208,231.03
Savings PresentTC OptimumTC $23.59 Orderingcosts are assumedtobea linear functionbecausenomatterhowlargeanorderisorhowmanyordersaresentin,thecosttoorderanymaterialis$50perorder.
Thestudentshouldrecognizethatitisdoubtfulthefirmwillorshouldalteranycurrentorderingpolicyforasavingsofonly$23.
2 2 400 4080units
5DS
QH