operations management solution manual (chapter 12)

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


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.

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


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


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


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


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.


(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


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


(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.


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).


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


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:


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


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


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


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

1

2


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

1

1

2


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.


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


$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

2


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

operations management solution manual (chapter 12)

Engineering