SOLUTION MANUAL FOR#z #z
Matching #zSupply #zwith #zDemand #zAn #zIntroduction #zto #zOperations #zManagement, #z5th #zEdition
#zCachon #zChapter #z2-19
Chapter #z2
The #zProcess #zView #zof #zthe #zOrganization
Q2.1 Dell
The following steps refer directly to Exhibit 2.1.
#1: For 2001, we find in Dell’s 10-k: Inventory = $400 (in million)
#2: For 2001, we find in Dell’s 10-k: COGS = $26,442 (in million)
26, 442$/ year
#3: Inventory turns 66.105 turns per year
400$
40% per year
#4: Per unit Inventory cost 0.605% per year
66.105 per year
Q2.2. Airline
We use Little’s law to compute the flow time, since we know both the flow rate as well
as the inventory level:
Flow Time Inventory/ Flow Rate 35 passengers/ 255 passengers per hour 0.137 hours
8.24 minutes
Q2.3 Inventory Cost
(a) Sales $60,000,000 per year / $2000 per unit 30,000 units sold per year
Inventory $20,000,000 / $1000 per unit 20,000 units in inventory
Flow Time Inventory/ Flow Rate 20,,000 per year year 8 months
Turns 1/ Flow Time 1/( year) 1.5 turns per year
Note: we can also get this number directly by writing: Inventory turns COGS / Inventory
(b) Cost of Inventory: 25% per year /1.5 turns 16.66%. For a $1000 product, this would
make an absolute inventory cost of $166.66 .
Q2.4. Apparel Retailing
(a) Revenue of $100M implies COGS of $50M (because of the 100% markup).
Turns COGS/ Inventory $50M/ $5M 10 .
(b) The inventory cost, given 10 turns, is 40%/10 4% . For a 30$ item, the inventory
cost is 0.4 $30 $1.20 per unit .
Q2.5. La Villa
(a) Flow Rate Inventory / Flow Time 1200 skiers /10 days 120 skiers per day
(b) Last year: on any given day, 10% (1 of 10) of skiers are on their first day of skiing
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw Hill LLC.
, This #zyear: #zon #zany #zgiven #zday, #z20% #z(1 #zof #z5) #zof #zskiers #zare #zon #ztheir #zfirst #zday #zof #zskiing
Average #zamount #zspent #zin #zlocal #zrestaurants #z(per #zskier)
Last #zyear #z #z0.1$50#z#z0.9$30 #z #z$32
#z This #z year #z #z0.2$50 #z #z0.8$30 #z
#z$34
% #zchange #z #z($34#z$32)#z/#z$32 #z#z6.25% #zincrease
Q2.6. #zHighway
We #zlook #zat #z1 #zmile #zof #zhighway #zas #zour #zprocess. #zSince #zthe #zspeed #zis #z60 #zmiles #zper
#zhour, #zit #ztakes #za #zcar #z1 #zminute #zto #ztravel #zthrough #zthe #zprocess #z(flow #ztime).
There #zare #z24 #zcars #zon #z¼ #zof #za #zmile, #zi.e. #zthere #zare #z96 #zcars #zon #zthe #z1 #zmile #zstretch
#z(inventory). #z Inventory #z = #zFlow #zRate #z* #zFlow #zTime: #z96 #zcars #z= #zFlow #zRate #z* #z1
#zminute
Thus, #zthe #zFlow #zRate #zis #z96 #zcars #zper #zminute, #zcorresponding #zto #z96*60 #z= #z5760 #zcars #zper #zhour.
Q2.7. #zStrohrmann #zBaking
The #zbread #zneeds #zto #zbe #zin #zthe #zoven #zfor #z12 #zminutes #z(flow #ztime). #zWe #zwant #zto
#zproduce #zat #za #zflow #zrate #zof #z4000 #zbreads #zper #zhour, #zor # z 4000/60 #z= #z66.66 # z breads
#zper #zminute.
Inventory #z= #zFlow #zRate #z* #zFlow #zTime: #zInventory #z= #z66.66 #zbreads #zper #zminute* #z12
#zminutes #zThus, #zInventory #z= #z800 #zbreads, #zwhich #zis #zthe #zrequired #zsize #zof #zthe #zoven.
Q2.8. #zMt #zKinley #zConsulting
We #zhave #zthe #zfollowing #zinformation #zavailable #zfrom #zthe #zquestion:
Level Inventory #z(number #zof #zconsultants #zat Flow #zTime #z(time #zspent #zat #zthat
that #zlevel) level)
Associate 200 4 #zyears
Manager 60 6 #zyears
Partner 20 10 #zyears
(a) We #zcan #zuse #zLittle’s #zlaw #zto #zfind #zthe #zflow #zrate #zfor #zassociate #zconsultants:
#z Inventory #z= #zFlow #zRate #z* #zFlow #zTime; #z200 #zconsultants #z= #zFlow #zRate #z* #z4
#z years; #zthus, #zthe #zflow #zrate #zis #z50 #zconsultants #zper #z year, #zwhich #zneed #zto #zbe
#zrecruited #zto #zkeep #zthe #zfirm #zin #zits #zcurrent #zsize #z(note: #zwhile #zthere #zare #zalso #z50
#zconsultants #zleaving #zthe #zassociate #zlevel, #zthis #zsays #znothing #zabout #zhow #zmany #zof
#zthem #zare #zdismissed #zvs #zhow #zmany #zof #zthem #zare #zpromoted #zto #zManager #zlevel).
(b) We #zcan #zperform #za #zsimilar #zanalysis #zat #zthe #zmanager #zlevel, #zwhich #zindicates #zthat
#zthe #zflow #zrate #zthere #zis #z10 #zconsultants. #z In #zorder #zto #zhave #z10 #zconsultants #zas #za
#zflow #zrate #zat #zthe #zmanager #zlevel, #zwe #zneed #zto #zpromote #z10 #zassociates #zto #zmanager
#zlevel #z(remember, #zthe #zfirm #zis #znot #zrecruiting #zto #zthe #zhigher #zranks #zfrom #zthe
#zoutside). #zHence, #zevery #z year, #zwe #zdismiss #z40 #zassociates #zand #zpromote #z10
© #zMcGraw #zHill #zLLC. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution #zwithout #zthe #zprior #zwritten
#zconsent #zof #zMcGraw #zHill #zLLC.
, #zassociates #zto #zthe #zmanager #zlevel #z(the #zodds #zat #zthat #zlevel #zare #z20%)
Now, #zconsider #zthe #zpartner #zlevel. #zThe #zflow #zrate #zthere #zis #z2 #zconsultants #zper #zyear
#z(obtained #zvia #zthe #zsame #zcalculations #zas #zbefore). #zThus, #zfrom #zthe #z10 #zmanager #zcases
#zwe #zevaluate #zevery #z year, #z8 #zare #zdismissed #zand #z2 #zare #zpromoted #zto #zpartner #z(the #zodds
#zat #zthat #zlevel #zare #zthereby #zalso #z20%).
In #zorder #zto #zfind #zthe #zodds #zof #za #znew #zhire #zto #zbecome #zpartner, #zwe #zneed #zto #zmultiply
#zthe #zpromotion #zprobabilities: #z0.2*0.2 #z= #z0.04. #zThus, #za #znew #zhire #zhas #za #z4% #zchance #zof
#zmaking #zit #zto #zpartner.
Q2.9. #zMajor #zUS #zRetailers
a. Product #zstays #zon #zaverage #zfor #z31.9 #zdays #zin #zCostco’s #zinventory
b. Costco #zhas #zfor #za #z$5 #zproduct #zan #zinventory #zcost #zof #z$0.1311 #zwhich #zcompares #zto #za
$0.2049 #z at #zWal-Mart
Q2.10. #zMcDonald’s
a. Inventory #zturns #zfor #zMcDonald’s #zwere #z92.3. #zThey #zwere #z30.05 #zfor #zWendy’s.
b. McDonald’s #zhas #zper #zunit #zinventory #zcosts #zof #z0.32%, #zwhich #zfor #za #z3$ #zmeal #zabout
$0.00975. #zThat #zcompares #zto #z0.998% #zat #zWendy’s #zwhere #zthe #zcost #zper #zmeal #zis # z $0.0299#z.
Q2.11. #zBCH
I #z= #z400 #zassociates, #zT #z= #z2 #zyears. #zR #z #zI#z/#zT #z #z400 #zassociates#z/#z2 #zyrs #z #z200 #zassociates#z/ #zyr #z.
Q2.12. #zKroger
Turns #z #zR #z/ #zI #z #z76858#z/ #z6244 #z12.3
Matching Supply with Demand: An Introduction to Operations
#z #z #z #z #z #z #z
Management 5e #z #z
Solutions #zto #zChapter #zProblems
#zChapter #z3
Understanding #zthe #zSupply #zProcess: #zEvaluating #zProcess #zCapacity
Q3.1 #zProcess #zAnalysis #zwith #zOne #zFlow #zUnit
(a) Capacity #zof #zthe #zthree #zresources #zin #zunits #zper #zhour #zare # z 602 #z/10 #z12 #z,
# z 601/ #z6 #z10; #z603 #z/16 #z11.25 #z. #zThe #zbottleneck #zis #zthe #zresource #zwith #zthe
#zlowest #zcapacity, #zwhich #zis #zresource #z2.
(b) The #zprocess #zcapacity #zis #zthe #zcapacity #zof #zthe #zbottleneck, #zwhich #zis # z 10 #zunits/hr #z.
(c) If # z # z demand #z#z8 #zunits #z/ #zhr #z, #zthen #zthe #zprocess #zis #zdemand #zconstrained #zand #zthe #zflow #zrate #zis
8 #zunits/hr
(d) Utilization #z= #zFlow #zRate #z/ #zCapacity#z. #zFor #zthe #zthree #zresources #zthey #zare # z 8#z/#z12#z, # z 8#z/#z10#z, #zand
8#z/11.25#z.
© #zMcGraw #zHill #zLLC. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution #zwithout #zthe #zprior #zwritten
#zconsent #zof #zMcGraw #zHill #zLLC.
, Q3.2 #zProcess #zAnalysis #zwith #zMultiple #zFlow #zUnits
a) Bottleneck #zis #zresource #z3 #zbecause #zit #zhas #zthe #zhighest #zimplied #zutilization #zof #z125%.
#zThe #zdemands #zper #zhour #zof #zthe #zthree #zproducts #zare # z 40 #z/ #z8 #z #z5 , # z 50 #z/ #z8 #z #z6.25 #zand
# z 60 #z/ #z8 #z #z7.5. # z # z The
total #zminutes #zof #zwork #zdemanded #zper #zhour #zat #zresource #z1 #zis #z5 #z× #z5 #z+ #z6.25 #z* #z5 #z+ #z7.5 #z* #z5 #z=
93.75. #zTwo #zworkers #zat #zresource #z1 #zproduce #z2 #z* #z60 #z= #z120 #zmin #zof #zwork #zper
#zhour. #zSo #zresource #z1’s #zutilization #zis # z 93.75 #z/120 #z #z0.78. #zUtilization #zat #zthe
#zother #zresources #zare #zsimilarly #zevaluated.
b) The #zcapacity #zof #zresource #z3 #zis # z 60 #z/15 #z #z4 #zunits # z per #zhour. #zGiven #zthe #zratio #zof
#zunits #zproduced #zmust #zbe #z4 #zto #z5 #zto #z6, #zthe #zprocess #zcan #zproduce # z 4 #zunits/ #zhr # z of
#zA, # z 5 #zunits #z/ #zhr #zof #zB #zand
6 #zunits#z/ #zhr#zof #zC.
Q3.3. #zCranberry
Cranberries #zarrive #zat #za #zrate #zof #z150 #zbarrels #zper #zhour. #zThey #zget #zprocessed #zat #za #zrate #zof
#z100 #zbarrels #zper #zhour. #zThus, #zinventory #zaccumulates #zat #za #zrate #zof #z150-100 #z= #z50 #zbarrels
#zper #zhour. #zThis #zhappens #zwhile #ztrucks #zarrive, #zi.e. #zfrom #z6am #zto #z2pm. #zThe #zhighest
#zinventory #zlevel #zthereby #zis #z8h*50 #zbarrels #zper #zhour #z= #z400 #zbarrels. #zFrom #zthese #z400 #zbarrels,
#z200 #zbarrels #zare #zin #zthe #zbins, #zthe #zother #z200 #zbarrels #zare #zin #ztrucks.
(a) 200 #zbarrels
(b) From #z2pm #zonwards, #zno #zadditional #zcranberries #zare #zreceived. #zInventory #zgets #zdepleted #zat
#za #zrate #zof #z100 #zbarrels #zper #zhour. #zThus, #zit #zwill #ztake #z2h #zuntil #zthe #zinventory #zlevel #zhas
#zdropped #zto #z200 #zbarrels, #zat #zwhich #ztime #zall #zwaiting #zcranberries #zcan #zbe #zstored #zin #zthe
#zbins #z(no #zmore #ztruck #zwaiting)
(c) It #zwill #ztake #zanother #z2 #zhours #zuntil #zall #zthe #zbins #zare #zempty
(d) Since #zthe #zseasonal #zworkers #zonly #zstart #zat #z10:00am, #zthe #zfirst #z4 #zhours #zof #zthe #zday #zwe
#zaccumulate #z4hours #z* #z50barrels #zper #zhour #z= #z200 #zbarrels. #zFor #zthe #zremaining #ztime #zthat
#zwe #zreceive #zincoming #zcranberries, #zour #zprocessing #zrate #zis #zhigher #z(125 #zbarrels #zper
#zhour). #zThus, #zinventory #zonly #zaccumulates #zat #za #zrate #zof #z25 #z(150-125 #zbarrels #zper #zhour).
#zGiven #zthat #zthis #zhappens #zover #z4 #zhours, #zwe #zget #zanother #z100 #zbarrels #zin #zinventory. #zAt
#z2pm, #zwe #zthereby #zhave #z300 #zbarrels #zin #zinventory. #zAfter #z2pm, #zwe #zreceive #zno #zfurther
#zcranberries, #z yet #zwe #zinitially #zprocess #zcranberries #zat #za #zrate #zof #z125 #zbarrels #zper #zhour.
#zThus, #zit #zonly #ztakes # z 100 #zbarrels #z/125 #zbarrels/hour #z #z0.8 #zhours #z #z48 #zminutes
until #zall #zbins #zare #zempty. #zFrom #zthen, #zwe #zneed #zanother #z2h #zuntil #zthe #zbins #zare #zempty.
Q3.4. #zWestern #zPennsylvania #zMilk
We #zstart #zthe #zday #zwith #z25,000 #zgallons #zof #zmilk #zin #zinventory. #zFrom #z8am #zonwards, #zwe
#zproduce #z5,000 #zgallons, #z yet #zwe #zship #z10,000 #zgallons. #zThus #zinventory #zis #zdepleted #zat #za #zrate
#zof #z5000 #zgallons #zper #zhour, #zwhich #zleaves #zus #zwithout #zmilk #zafter #z5 #zhours #z(at #z1pm). #zFrom
#zthen #zonwards, #zclients #zwill #zhave #zto #zwait. #zThis #zsituation #zgets #zworse #zand #zworse #zand #zby
#z6pm #z(last #zclient #zarrives), #zwe #zare #zshort #z25,000 #zgallons.
(a) 1pm
(b) Clients #zwill #zstop #zwaiting #zwhen #zwe #zhave #zworked #zoff #zour #z25,000 #zgallon #zbacklog #zthat
#zwe #zare #zfacing #zat #z6pm. #zSince #zwe #zare #zdoing #zthis #zat #za #zrate #zof #z5,000 #zgallon #zper
#zhour, #zclients #zwill #zstop #zwaiting #zat #z11pm #z(after #z5 #zmore #zhours).
© #zMcGraw #zHill #zLLC. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution #zwithout #zthe #zprior #zwritten
#zconsent #zof #zMcGraw #zHill #zLLC.
Matching #zSupply #zwith #zDemand #zAn #zIntroduction #zto #zOperations #zManagement, #z5th #zEdition
#zCachon #zChapter #z2-19
Chapter #z2
The #zProcess #zView #zof #zthe #zOrganization
Q2.1 Dell
The following steps refer directly to Exhibit 2.1.
#1: For 2001, we find in Dell’s 10-k: Inventory = $400 (in million)
#2: For 2001, we find in Dell’s 10-k: COGS = $26,442 (in million)
26, 442$/ year
#3: Inventory turns 66.105 turns per year
400$
40% per year
#4: Per unit Inventory cost 0.605% per year
66.105 per year
Q2.2. Airline
We use Little’s law to compute the flow time, since we know both the flow rate as well
as the inventory level:
Flow Time Inventory/ Flow Rate 35 passengers/ 255 passengers per hour 0.137 hours
8.24 minutes
Q2.3 Inventory Cost
(a) Sales $60,000,000 per year / $2000 per unit 30,000 units sold per year
Inventory $20,000,000 / $1000 per unit 20,000 units in inventory
Flow Time Inventory/ Flow Rate 20,,000 per year year 8 months
Turns 1/ Flow Time 1/( year) 1.5 turns per year
Note: we can also get this number directly by writing: Inventory turns COGS / Inventory
(b) Cost of Inventory: 25% per year /1.5 turns 16.66%. For a $1000 product, this would
make an absolute inventory cost of $166.66 .
Q2.4. Apparel Retailing
(a) Revenue of $100M implies COGS of $50M (because of the 100% markup).
Turns COGS/ Inventory $50M/ $5M 10 .
(b) The inventory cost, given 10 turns, is 40%/10 4% . For a 30$ item, the inventory
cost is 0.4 $30 $1.20 per unit .
Q2.5. La Villa
(a) Flow Rate Inventory / Flow Time 1200 skiers /10 days 120 skiers per day
(b) Last year: on any given day, 10% (1 of 10) of skiers are on their first day of skiing
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw Hill LLC.
, This #zyear: #zon #zany #zgiven #zday, #z20% #z(1 #zof #z5) #zof #zskiers #zare #zon #ztheir #zfirst #zday #zof #zskiing
Average #zamount #zspent #zin #zlocal #zrestaurants #z(per #zskier)
Last #zyear #z #z0.1$50#z#z0.9$30 #z #z$32
#z This #z year #z #z0.2$50 #z #z0.8$30 #z
#z$34
% #zchange #z #z($34#z$32)#z/#z$32 #z#z6.25% #zincrease
Q2.6. #zHighway
We #zlook #zat #z1 #zmile #zof #zhighway #zas #zour #zprocess. #zSince #zthe #zspeed #zis #z60 #zmiles #zper
#zhour, #zit #ztakes #za #zcar #z1 #zminute #zto #ztravel #zthrough #zthe #zprocess #z(flow #ztime).
There #zare #z24 #zcars #zon #z¼ #zof #za #zmile, #zi.e. #zthere #zare #z96 #zcars #zon #zthe #z1 #zmile #zstretch
#z(inventory). #z Inventory #z = #zFlow #zRate #z* #zFlow #zTime: #z96 #zcars #z= #zFlow #zRate #z* #z1
#zminute
Thus, #zthe #zFlow #zRate #zis #z96 #zcars #zper #zminute, #zcorresponding #zto #z96*60 #z= #z5760 #zcars #zper #zhour.
Q2.7. #zStrohrmann #zBaking
The #zbread #zneeds #zto #zbe #zin #zthe #zoven #zfor #z12 #zminutes #z(flow #ztime). #zWe #zwant #zto
#zproduce #zat #za #zflow #zrate #zof #z4000 #zbreads #zper #zhour, #zor # z 4000/60 #z= #z66.66 # z breads
#zper #zminute.
Inventory #z= #zFlow #zRate #z* #zFlow #zTime: #zInventory #z= #z66.66 #zbreads #zper #zminute* #z12
#zminutes #zThus, #zInventory #z= #z800 #zbreads, #zwhich #zis #zthe #zrequired #zsize #zof #zthe #zoven.
Q2.8. #zMt #zKinley #zConsulting
We #zhave #zthe #zfollowing #zinformation #zavailable #zfrom #zthe #zquestion:
Level Inventory #z(number #zof #zconsultants #zat Flow #zTime #z(time #zspent #zat #zthat
that #zlevel) level)
Associate 200 4 #zyears
Manager 60 6 #zyears
Partner 20 10 #zyears
(a) We #zcan #zuse #zLittle’s #zlaw #zto #zfind #zthe #zflow #zrate #zfor #zassociate #zconsultants:
#z Inventory #z= #zFlow #zRate #z* #zFlow #zTime; #z200 #zconsultants #z= #zFlow #zRate #z* #z4
#z years; #zthus, #zthe #zflow #zrate #zis #z50 #zconsultants #zper #z year, #zwhich #zneed #zto #zbe
#zrecruited #zto #zkeep #zthe #zfirm #zin #zits #zcurrent #zsize #z(note: #zwhile #zthere #zare #zalso #z50
#zconsultants #zleaving #zthe #zassociate #zlevel, #zthis #zsays #znothing #zabout #zhow #zmany #zof
#zthem #zare #zdismissed #zvs #zhow #zmany #zof #zthem #zare #zpromoted #zto #zManager #zlevel).
(b) We #zcan #zperform #za #zsimilar #zanalysis #zat #zthe #zmanager #zlevel, #zwhich #zindicates #zthat
#zthe #zflow #zrate #zthere #zis #z10 #zconsultants. #z In #zorder #zto #zhave #z10 #zconsultants #zas #za
#zflow #zrate #zat #zthe #zmanager #zlevel, #zwe #zneed #zto #zpromote #z10 #zassociates #zto #zmanager
#zlevel #z(remember, #zthe #zfirm #zis #znot #zrecruiting #zto #zthe #zhigher #zranks #zfrom #zthe
#zoutside). #zHence, #zevery #z year, #zwe #zdismiss #z40 #zassociates #zand #zpromote #z10
© #zMcGraw #zHill #zLLC. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution #zwithout #zthe #zprior #zwritten
#zconsent #zof #zMcGraw #zHill #zLLC.
, #zassociates #zto #zthe #zmanager #zlevel #z(the #zodds #zat #zthat #zlevel #zare #z20%)
Now, #zconsider #zthe #zpartner #zlevel. #zThe #zflow #zrate #zthere #zis #z2 #zconsultants #zper #zyear
#z(obtained #zvia #zthe #zsame #zcalculations #zas #zbefore). #zThus, #zfrom #zthe #z10 #zmanager #zcases
#zwe #zevaluate #zevery #z year, #z8 #zare #zdismissed #zand #z2 #zare #zpromoted #zto #zpartner #z(the #zodds
#zat #zthat #zlevel #zare #zthereby #zalso #z20%).
In #zorder #zto #zfind #zthe #zodds #zof #za #znew #zhire #zto #zbecome #zpartner, #zwe #zneed #zto #zmultiply
#zthe #zpromotion #zprobabilities: #z0.2*0.2 #z= #z0.04. #zThus, #za #znew #zhire #zhas #za #z4% #zchance #zof
#zmaking #zit #zto #zpartner.
Q2.9. #zMajor #zUS #zRetailers
a. Product #zstays #zon #zaverage #zfor #z31.9 #zdays #zin #zCostco’s #zinventory
b. Costco #zhas #zfor #za #z$5 #zproduct #zan #zinventory #zcost #zof #z$0.1311 #zwhich #zcompares #zto #za
$0.2049 #z at #zWal-Mart
Q2.10. #zMcDonald’s
a. Inventory #zturns #zfor #zMcDonald’s #zwere #z92.3. #zThey #zwere #z30.05 #zfor #zWendy’s.
b. McDonald’s #zhas #zper #zunit #zinventory #zcosts #zof #z0.32%, #zwhich #zfor #za #z3$ #zmeal #zabout
$0.00975. #zThat #zcompares #zto #z0.998% #zat #zWendy’s #zwhere #zthe #zcost #zper #zmeal #zis # z $0.0299#z.
Q2.11. #zBCH
I #z= #z400 #zassociates, #zT #z= #z2 #zyears. #zR #z #zI#z/#zT #z #z400 #zassociates#z/#z2 #zyrs #z #z200 #zassociates#z/ #zyr #z.
Q2.12. #zKroger
Turns #z #zR #z/ #zI #z #z76858#z/ #z6244 #z12.3
Matching Supply with Demand: An Introduction to Operations
#z #z #z #z #z #z #z
Management 5e #z #z
Solutions #zto #zChapter #zProblems
#zChapter #z3
Understanding #zthe #zSupply #zProcess: #zEvaluating #zProcess #zCapacity
Q3.1 #zProcess #zAnalysis #zwith #zOne #zFlow #zUnit
(a) Capacity #zof #zthe #zthree #zresources #zin #zunits #zper #zhour #zare # z 602 #z/10 #z12 #z,
# z 601/ #z6 #z10; #z603 #z/16 #z11.25 #z. #zThe #zbottleneck #zis #zthe #zresource #zwith #zthe
#zlowest #zcapacity, #zwhich #zis #zresource #z2.
(b) The #zprocess #zcapacity #zis #zthe #zcapacity #zof #zthe #zbottleneck, #zwhich #zis # z 10 #zunits/hr #z.
(c) If # z # z demand #z#z8 #zunits #z/ #zhr #z, #zthen #zthe #zprocess #zis #zdemand #zconstrained #zand #zthe #zflow #zrate #zis
8 #zunits/hr
(d) Utilization #z= #zFlow #zRate #z/ #zCapacity#z. #zFor #zthe #zthree #zresources #zthey #zare # z 8#z/#z12#z, # z 8#z/#z10#z, #zand
8#z/11.25#z.
© #zMcGraw #zHill #zLLC. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution #zwithout #zthe #zprior #zwritten
#zconsent #zof #zMcGraw #zHill #zLLC.
, Q3.2 #zProcess #zAnalysis #zwith #zMultiple #zFlow #zUnits
a) Bottleneck #zis #zresource #z3 #zbecause #zit #zhas #zthe #zhighest #zimplied #zutilization #zof #z125%.
#zThe #zdemands #zper #zhour #zof #zthe #zthree #zproducts #zare # z 40 #z/ #z8 #z #z5 , # z 50 #z/ #z8 #z #z6.25 #zand
# z 60 #z/ #z8 #z #z7.5. # z # z The
total #zminutes #zof #zwork #zdemanded #zper #zhour #zat #zresource #z1 #zis #z5 #z× #z5 #z+ #z6.25 #z* #z5 #z+ #z7.5 #z* #z5 #z=
93.75. #zTwo #zworkers #zat #zresource #z1 #zproduce #z2 #z* #z60 #z= #z120 #zmin #zof #zwork #zper
#zhour. #zSo #zresource #z1’s #zutilization #zis # z 93.75 #z/120 #z #z0.78. #zUtilization #zat #zthe
#zother #zresources #zare #zsimilarly #zevaluated.
b) The #zcapacity #zof #zresource #z3 #zis # z 60 #z/15 #z #z4 #zunits # z per #zhour. #zGiven #zthe #zratio #zof
#zunits #zproduced #zmust #zbe #z4 #zto #z5 #zto #z6, #zthe #zprocess #zcan #zproduce # z 4 #zunits/ #zhr # z of
#zA, # z 5 #zunits #z/ #zhr #zof #zB #zand
6 #zunits#z/ #zhr#zof #zC.
Q3.3. #zCranberry
Cranberries #zarrive #zat #za #zrate #zof #z150 #zbarrels #zper #zhour. #zThey #zget #zprocessed #zat #za #zrate #zof
#z100 #zbarrels #zper #zhour. #zThus, #zinventory #zaccumulates #zat #za #zrate #zof #z150-100 #z= #z50 #zbarrels
#zper #zhour. #zThis #zhappens #zwhile #ztrucks #zarrive, #zi.e. #zfrom #z6am #zto #z2pm. #zThe #zhighest
#zinventory #zlevel #zthereby #zis #z8h*50 #zbarrels #zper #zhour #z= #z400 #zbarrels. #zFrom #zthese #z400 #zbarrels,
#z200 #zbarrels #zare #zin #zthe #zbins, #zthe #zother #z200 #zbarrels #zare #zin #ztrucks.
(a) 200 #zbarrels
(b) From #z2pm #zonwards, #zno #zadditional #zcranberries #zare #zreceived. #zInventory #zgets #zdepleted #zat
#za #zrate #zof #z100 #zbarrels #zper #zhour. #zThus, #zit #zwill #ztake #z2h #zuntil #zthe #zinventory #zlevel #zhas
#zdropped #zto #z200 #zbarrels, #zat #zwhich #ztime #zall #zwaiting #zcranberries #zcan #zbe #zstored #zin #zthe
#zbins #z(no #zmore #ztruck #zwaiting)
(c) It #zwill #ztake #zanother #z2 #zhours #zuntil #zall #zthe #zbins #zare #zempty
(d) Since #zthe #zseasonal #zworkers #zonly #zstart #zat #z10:00am, #zthe #zfirst #z4 #zhours #zof #zthe #zday #zwe
#zaccumulate #z4hours #z* #z50barrels #zper #zhour #z= #z200 #zbarrels. #zFor #zthe #zremaining #ztime #zthat
#zwe #zreceive #zincoming #zcranberries, #zour #zprocessing #zrate #zis #zhigher #z(125 #zbarrels #zper
#zhour). #zThus, #zinventory #zonly #zaccumulates #zat #za #zrate #zof #z25 #z(150-125 #zbarrels #zper #zhour).
#zGiven #zthat #zthis #zhappens #zover #z4 #zhours, #zwe #zget #zanother #z100 #zbarrels #zin #zinventory. #zAt
#z2pm, #zwe #zthereby #zhave #z300 #zbarrels #zin #zinventory. #zAfter #z2pm, #zwe #zreceive #zno #zfurther
#zcranberries, #z yet #zwe #zinitially #zprocess #zcranberries #zat #za #zrate #zof #z125 #zbarrels #zper #zhour.
#zThus, #zit #zonly #ztakes # z 100 #zbarrels #z/125 #zbarrels/hour #z #z0.8 #zhours #z #z48 #zminutes
until #zall #zbins #zare #zempty. #zFrom #zthen, #zwe #zneed #zanother #z2h #zuntil #zthe #zbins #zare #zempty.
Q3.4. #zWestern #zPennsylvania #zMilk
We #zstart #zthe #zday #zwith #z25,000 #zgallons #zof #zmilk #zin #zinventory. #zFrom #z8am #zonwards, #zwe
#zproduce #z5,000 #zgallons, #z yet #zwe #zship #z10,000 #zgallons. #zThus #zinventory #zis #zdepleted #zat #za #zrate
#zof #z5000 #zgallons #zper #zhour, #zwhich #zleaves #zus #zwithout #zmilk #zafter #z5 #zhours #z(at #z1pm). #zFrom
#zthen #zonwards, #zclients #zwill #zhave #zto #zwait. #zThis #zsituation #zgets #zworse #zand #zworse #zand #zby
#z6pm #z(last #zclient #zarrives), #zwe #zare #zshort #z25,000 #zgallons.
(a) 1pm
(b) Clients #zwill #zstop #zwaiting #zwhen #zwe #zhave #zworked #zoff #zour #z25,000 #zgallon #zbacklog #zthat
#zwe #zare #zfacing #zat #z6pm. #zSince #zwe #zare #zdoing #zthis #zat #za #zrate #zof #z5,000 #zgallon #zper
#zhour, #zclients #zwill #zstop #zwaiting #zat #z11pm #z(after #z5 #zmore #zhours).
© #zMcGraw #zHill #zLLC. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution #zwithout #zthe #zprior #zwritten
#zconsent #zof #zMcGraw #zHill #zLLC.
