SOLUTION MANUAL FOR. .
Matching.Supply.with.Demand.An.Introduction.to.Operations.Management,.5th.Edition.Cachon.Cha
pter.2-19
Chapter.2
The.Process.View.of.the.Organization
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.i
nventory.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.Inve
ntory.=.$20,000,000./.$1000.per.unit.=.20,000.units.in.inventory
Flow. Time.=.Inventory/.Flow. Rate.=.20,000./.30,000. per. year. =.2./.3.year. =.8.months.Turns.=.1/.Fl
ow.Time.=.1/(2./.3.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.McG
raw.Hill.LLC.
, This.year:.on.any.given.day,.20%.(1.of.5).of.skiers.are.on.their.first.day.of.skiing
Average.amount.spent.in.local.restaurants.(per.skier)
Last.year.=.0.1$50.+.0.9$30.=.$32.This.
year.=.0.2$50.+.0.8$30.=.$34
%.change.=.($34.−$32)./.$32.=.6.25%.increase
Q2.6..Highway
We.look.at.1.mile.of.highway.as.our.process..Since.the.speed.is.60.miles.per.hour,.it.takes.a.car.
1.minute.to.travel.through.the.process.(flow.time).
There.are.24.cars.on.¼.of.a.mile,.i.e..there.are.96.cars.on.the.1.mile.stretch.(inventory)..Inventor
y.=.Flow.Rate.*.Flow.Time:.96.cars.=.Flow.Rate.*.1.minute
Thus,.the.Flow.Rate.is.96.cars.per.minute,.corresponding.to.96*60.=.5760.cars.per.hour.
Q2.7..Strohrmann.Baking
The.bread.needs.to.be.in.the.oven.for.12.minutes.(flow.time)..We.want.to.produce.at.a.flow.rate.
of.4000.breads.per.hour,.or. 4000/60.=.66.66. breads.per.minute.
Inventory.=.Flow.Rate.*.Flow.Time:.Inventory.=.66.66.breads.per.minute*.12.minutes.Thus,.I
nventory.=.800.breads,.which.is.the.required.size.of.the.oven.
Q2.8..Mt.Kinley.Consulting
We.have.the.following.information.available.from.the.question:
Level Inventory.(number.of.consultants.at Flow.Time.(time.spent.at.that
that.level) level)
Associate 200 4.years
Manager 60 6.years
Partner 20 10.years
(a) We.can.use.Little’s.law.to.find.the.flow.rate.for.associate.consultants:.Inventory.=.Flow.Ra
te.*.Flow.Time;.200.consultants.=.Flow.Rate.*.4.years;.thus,.the.flow.rate.is.50.consultants.
per.year,.which.need.to.be.recruited.to.keep.the.firm.in.its.current.size.(note:.while.there.are.
also.50.consultants.leaving.the.associate.level,.this.says.nothing.about.how.many.of.them.a
re.dismissed.vs.how.many.of.them.are.promoted.to.Manager.level).
(b) We.can.perform.a.similar.analysis.at.the.manager.level,.which.indicates.that.the.flow.rate.t
here.is.10.consultants..In.order.to.have.10.consultants.as.a.flow.rate.at.the.manager.level,.w
e.need.to.promote.10.associates.to.manager.level.(remember,.the.firm.is.not.recruiting.to.th
e.higher.ranks.from.the.outside)..Hence,.every.year,.we.dismiss.40.associates.and.promote.
10.associates.to.the.manager.level.(the.odds.at.that.level.are.20%)
©.McGraw.Hill.LLC..All.rights.reserved..No.reproduction.or.distribution.without.the.prior.written.consent.of.McG
raw.Hill.LLC.
, Now,.consider.the.partner.level..The.flow.rate.there.is.2.consultants.per.year.(obtained.via.the.s
ame.calculations.as.before)..Thus,.from.the.10.manager.cases.we.evaluate.every.year,.8.are.dis
missed.and.2.are.promoted.to.partner.(the.odds.at.that.level.are.thereby.also.20%).
In.order.to.find.the.odds.of.a.new.hire.to.become.partner,.we.need.to.multiply.the.promotion.pro
babilities:.0.2*0.2.=.0.04..Thus,.a.new.hire.has.a.4%.chance.of.making.it.to.partner.
Q2.9..Major.US.Retailers
a. Product.stays.on.average.for.31.9.days.in.Costco’s.inventory
b. Costco.has.for.a.$5.product.an.inventory.cost.of.$0.1311.which.compares.to.a
$0.2049. at.Wal-Mart
Q2.10..McDonald’s
a. Inventory.turns.for.McDonald’s.were.92.3..They.were.30.05.for.Wendy’s.
b. McDonald’s.has.per.unit.inventory.costs.of.0.32%,.which.for.a.3$.meal.about
$0.00975..That.compares.to.0.998%.at.Wendy’s.where.the.cost.per.meal.is. $0.0299..
Q2.11..BCH
I.=.400.associates,.T.=.2.years..R.=.I./.T.=.400.associates./.2.yrs.=.200.associates./.yr..
Q2.12..Kroger
Turns.=.R./.I. =.76858./.6244.=12.3
Matching Supply with Demand: An Introduction to Operations Management 5e
. . . . . . . . .
Solutions.to.Chapter.Problems.Chapt
er.3
Understanding.the.Supply.Process:.Evaluating.Process.Capacity
Q3.1.Process.Analysis.with.One.Flow.Unit
(a) Capacity.of.the.three.resources.in.units.per.hour.are. 602./10.=12.,. 601/.6.=10;.603./16.
=11.25...The.bottleneck.is.the.resource.with.the.lowest.capacity,.which.is.resource.2.
(b) The.process.capacity.is.the.capacity.of.the.bottleneck,.which.is. 10.units/hr..
(c) If. . demand. =.8.units./.hr.,.then.the.process.is.demand.constrained.and.the.flow.rate.is
8.units/hr
(d) Utilization.=.Flow.Rate./.Capacity...For.the.three.resources.they.are. 8./.12.,. 8./.10.,.and
8./11.25..
©.McGraw.Hill.LLC..All.rights.reserved..No.reproduction.or.distribution.without.the.prior.written.consent.of.McG
raw.Hill.LLC.
, Q3.2.Process.Analysis.with.Multiple.Flow.Units
a) Bottleneck.is.resource.3.because.it.has.the.highest.implied.utilization.of.125%..The.demands.
per.hour.of.the.three.products.are. 40./.8.=.5, . 50./.8.=.6.25.and. 60./.8.=.7.5.. . The
total.minutes.of.work.demanded.per.hour.at.resource.1.is.5.×.5.+.6.25.*.5.+.7.5.*.5.=
93.75..Two.workers.at.resource.1.produce.2.*.60.=.120.min.of.work.per.hour..So.resour
ce.1’s.utilization.is. 93.75./120.=.0.78..Utilization.at.the.other.resources.are.similarly.ev
aluated.
b) The.capacity.of.resource.3.is. 60./15.=.4.units. per.hour..Given.the.ratio.of.units.produced.must.b
e.4.to.5.to.6,.the.process.can.produce. 4.units/.hr. of.A,. 5.units./.hr.of.B.and
6.units./.hr.of.C.
Q3.3..Cranberry
Cranberries.arrive.at.a.rate.of.150.barrels.per.hour..They.get.processed.at.a.rate.of.100.barrels.per.hour..
Thus,.inventory.accumulates.at.a.rate.of.150-
100.=.50.barrels.per.hour..This.happens.while.trucks.arrive,.i.e..from.6am.to.2pm..The.highest.invento
ry.level.thereby.is.8h*50.barrels.per.hour.=.400.barrels..From.these.400.barrels,.200.barrels.are.in.the.bi
ns,.the.other.200.barrels.are.in.trucks.
(a) 200.barrels
(b) From.2pm.onwards,.no.additional.cranberries.are.received..Inventory.gets.depleted.at.a.rate.of.10
0.barrels.per.hour..Thus,.it.will.take.2h.until.the.inventory.level.has.dropped.to.200.barrels,.at.whi
ch.time.all.waiting.cranberries.can.be.stored.in.the.bins.(no.more.truck.waiting)
(c) It.will.take.another.2.hours.until.all.the.bins.are.empty
(d) Since.the.seasonal.workers.only.start.at.10:00am,.the.first.4.hours.of.the.day.we.accumulate.4hours
.*.50barrels.per.hour.=.200.barrels..For.the.remaining.time.that.we.receive.incoming.cranberries,.o
ur.processing.rate.is.higher.(125.barrels.per.hour)..Thus,.inventory.only.accumulates.at.a.rate.of.25.
(150-
125.barrels.per.hour)..Given.that.this.happens.over.4.hours,.we.get.another.100.barrels.in.inventory
..At.2pm,.we.thereby.have.300.barrels.in.inventory..After.2pm,.we.receive.no.further.cranberries,.y
et.we.initially.process.cranberries.at.a.rate.of.125.barrels.per.hour..Thus,.it.only.takes. 100.barrels./1
25.barrels/hour.=.0.8.hours.=.48.minutes
until.all.bins.are.empty..From.then,.we.need.another.2h.until.the.bins.are.empty.
Q3.4..Western.Pennsylvania.Milk
We.start.the.day.with.25,000.gallons.of.milk.in.inventory..From.8am.onwards,.we.produce.5,000.gallo
ns,.yet.we.ship.10,000.gallons..Thus.inventory.is.depleted.at.a.rate.of.5000.gallons.per.hour,.which.leav
es.us.without.milk.after.5.hours.(at.1pm)..From.then.onwards,.clients.will.have.to.wait..This.situation.g
ets.worse.and.worse.and.by.6pm.(last.client.arrives),.we.are.short.25,000.gallons.
(a) 1pm
(b) Clients.will.stop.waiting.when.we.have.worked.off.our.25,000.gallon.backlog.that.we.are.facin
g.at.6pm..Since.we.are.doing.this.at.a.rate.of.5,000.gallon.per.hour,.clients.will.stop.waiting.at.1
1pm.(after.5.more.hours).
(c) At.6pm,.we.have.a.backlog.of.25,000.gallons,.which.is.equivalent.to.20.trucks
(d) The.waiting.time.is.the.area.in.the.triangle
©.McGraw.Hill.LLC..All.rights.reserved..No.reproduction.or.distribution.without.the.prior.written.consent.of.McG
raw.Hill.LLC.
Matching.Supply.with.Demand.An.Introduction.to.Operations.Management,.5th.Edition.Cachon.Cha
pter.2-19
Chapter.2
The.Process.View.of.the.Organization
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.i
nventory.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.Inve
ntory.=.$20,000,000./.$1000.per.unit.=.20,000.units.in.inventory
Flow. Time.=.Inventory/.Flow. Rate.=.20,000./.30,000. per. year. =.2./.3.year. =.8.months.Turns.=.1/.Fl
ow.Time.=.1/(2./.3.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.McG
raw.Hill.LLC.
, This.year:.on.any.given.day,.20%.(1.of.5).of.skiers.are.on.their.first.day.of.skiing
Average.amount.spent.in.local.restaurants.(per.skier)
Last.year.=.0.1$50.+.0.9$30.=.$32.This.
year.=.0.2$50.+.0.8$30.=.$34
%.change.=.($34.−$32)./.$32.=.6.25%.increase
Q2.6..Highway
We.look.at.1.mile.of.highway.as.our.process..Since.the.speed.is.60.miles.per.hour,.it.takes.a.car.
1.minute.to.travel.through.the.process.(flow.time).
There.are.24.cars.on.¼.of.a.mile,.i.e..there.are.96.cars.on.the.1.mile.stretch.(inventory)..Inventor
y.=.Flow.Rate.*.Flow.Time:.96.cars.=.Flow.Rate.*.1.minute
Thus,.the.Flow.Rate.is.96.cars.per.minute,.corresponding.to.96*60.=.5760.cars.per.hour.
Q2.7..Strohrmann.Baking
The.bread.needs.to.be.in.the.oven.for.12.minutes.(flow.time)..We.want.to.produce.at.a.flow.rate.
of.4000.breads.per.hour,.or. 4000/60.=.66.66. breads.per.minute.
Inventory.=.Flow.Rate.*.Flow.Time:.Inventory.=.66.66.breads.per.minute*.12.minutes.Thus,.I
nventory.=.800.breads,.which.is.the.required.size.of.the.oven.
Q2.8..Mt.Kinley.Consulting
We.have.the.following.information.available.from.the.question:
Level Inventory.(number.of.consultants.at Flow.Time.(time.spent.at.that
that.level) level)
Associate 200 4.years
Manager 60 6.years
Partner 20 10.years
(a) We.can.use.Little’s.law.to.find.the.flow.rate.for.associate.consultants:.Inventory.=.Flow.Ra
te.*.Flow.Time;.200.consultants.=.Flow.Rate.*.4.years;.thus,.the.flow.rate.is.50.consultants.
per.year,.which.need.to.be.recruited.to.keep.the.firm.in.its.current.size.(note:.while.there.are.
also.50.consultants.leaving.the.associate.level,.this.says.nothing.about.how.many.of.them.a
re.dismissed.vs.how.many.of.them.are.promoted.to.Manager.level).
(b) We.can.perform.a.similar.analysis.at.the.manager.level,.which.indicates.that.the.flow.rate.t
here.is.10.consultants..In.order.to.have.10.consultants.as.a.flow.rate.at.the.manager.level,.w
e.need.to.promote.10.associates.to.manager.level.(remember,.the.firm.is.not.recruiting.to.th
e.higher.ranks.from.the.outside)..Hence,.every.year,.we.dismiss.40.associates.and.promote.
10.associates.to.the.manager.level.(the.odds.at.that.level.are.20%)
©.McGraw.Hill.LLC..All.rights.reserved..No.reproduction.or.distribution.without.the.prior.written.consent.of.McG
raw.Hill.LLC.
, Now,.consider.the.partner.level..The.flow.rate.there.is.2.consultants.per.year.(obtained.via.the.s
ame.calculations.as.before)..Thus,.from.the.10.manager.cases.we.evaluate.every.year,.8.are.dis
missed.and.2.are.promoted.to.partner.(the.odds.at.that.level.are.thereby.also.20%).
In.order.to.find.the.odds.of.a.new.hire.to.become.partner,.we.need.to.multiply.the.promotion.pro
babilities:.0.2*0.2.=.0.04..Thus,.a.new.hire.has.a.4%.chance.of.making.it.to.partner.
Q2.9..Major.US.Retailers
a. Product.stays.on.average.for.31.9.days.in.Costco’s.inventory
b. Costco.has.for.a.$5.product.an.inventory.cost.of.$0.1311.which.compares.to.a
$0.2049. at.Wal-Mart
Q2.10..McDonald’s
a. Inventory.turns.for.McDonald’s.were.92.3..They.were.30.05.for.Wendy’s.
b. McDonald’s.has.per.unit.inventory.costs.of.0.32%,.which.for.a.3$.meal.about
$0.00975..That.compares.to.0.998%.at.Wendy’s.where.the.cost.per.meal.is. $0.0299..
Q2.11..BCH
I.=.400.associates,.T.=.2.years..R.=.I./.T.=.400.associates./.2.yrs.=.200.associates./.yr..
Q2.12..Kroger
Turns.=.R./.I. =.76858./.6244.=12.3
Matching Supply with Demand: An Introduction to Operations Management 5e
. . . . . . . . .
Solutions.to.Chapter.Problems.Chapt
er.3
Understanding.the.Supply.Process:.Evaluating.Process.Capacity
Q3.1.Process.Analysis.with.One.Flow.Unit
(a) Capacity.of.the.three.resources.in.units.per.hour.are. 602./10.=12.,. 601/.6.=10;.603./16.
=11.25...The.bottleneck.is.the.resource.with.the.lowest.capacity,.which.is.resource.2.
(b) The.process.capacity.is.the.capacity.of.the.bottleneck,.which.is. 10.units/hr..
(c) If. . demand. =.8.units./.hr.,.then.the.process.is.demand.constrained.and.the.flow.rate.is
8.units/hr
(d) Utilization.=.Flow.Rate./.Capacity...For.the.three.resources.they.are. 8./.12.,. 8./.10.,.and
8./11.25..
©.McGraw.Hill.LLC..All.rights.reserved..No.reproduction.or.distribution.without.the.prior.written.consent.of.McG
raw.Hill.LLC.
, Q3.2.Process.Analysis.with.Multiple.Flow.Units
a) Bottleneck.is.resource.3.because.it.has.the.highest.implied.utilization.of.125%..The.demands.
per.hour.of.the.three.products.are. 40./.8.=.5, . 50./.8.=.6.25.and. 60./.8.=.7.5.. . The
total.minutes.of.work.demanded.per.hour.at.resource.1.is.5.×.5.+.6.25.*.5.+.7.5.*.5.=
93.75..Two.workers.at.resource.1.produce.2.*.60.=.120.min.of.work.per.hour..So.resour
ce.1’s.utilization.is. 93.75./120.=.0.78..Utilization.at.the.other.resources.are.similarly.ev
aluated.
b) The.capacity.of.resource.3.is. 60./15.=.4.units. per.hour..Given.the.ratio.of.units.produced.must.b
e.4.to.5.to.6,.the.process.can.produce. 4.units/.hr. of.A,. 5.units./.hr.of.B.and
6.units./.hr.of.C.
Q3.3..Cranberry
Cranberries.arrive.at.a.rate.of.150.barrels.per.hour..They.get.processed.at.a.rate.of.100.barrels.per.hour..
Thus,.inventory.accumulates.at.a.rate.of.150-
100.=.50.barrels.per.hour..This.happens.while.trucks.arrive,.i.e..from.6am.to.2pm..The.highest.invento
ry.level.thereby.is.8h*50.barrels.per.hour.=.400.barrels..From.these.400.barrels,.200.barrels.are.in.the.bi
ns,.the.other.200.barrels.are.in.trucks.
(a) 200.barrels
(b) From.2pm.onwards,.no.additional.cranberries.are.received..Inventory.gets.depleted.at.a.rate.of.10
0.barrels.per.hour..Thus,.it.will.take.2h.until.the.inventory.level.has.dropped.to.200.barrels,.at.whi
ch.time.all.waiting.cranberries.can.be.stored.in.the.bins.(no.more.truck.waiting)
(c) It.will.take.another.2.hours.until.all.the.bins.are.empty
(d) Since.the.seasonal.workers.only.start.at.10:00am,.the.first.4.hours.of.the.day.we.accumulate.4hours
.*.50barrels.per.hour.=.200.barrels..For.the.remaining.time.that.we.receive.incoming.cranberries,.o
ur.processing.rate.is.higher.(125.barrels.per.hour)..Thus,.inventory.only.accumulates.at.a.rate.of.25.
(150-
125.barrels.per.hour)..Given.that.this.happens.over.4.hours,.we.get.another.100.barrels.in.inventory
..At.2pm,.we.thereby.have.300.barrels.in.inventory..After.2pm,.we.receive.no.further.cranberries,.y
et.we.initially.process.cranberries.at.a.rate.of.125.barrels.per.hour..Thus,.it.only.takes. 100.barrels./1
25.barrels/hour.=.0.8.hours.=.48.minutes
until.all.bins.are.empty..From.then,.we.need.another.2h.until.the.bins.are.empty.
Q3.4..Western.Pennsylvania.Milk
We.start.the.day.with.25,000.gallons.of.milk.in.inventory..From.8am.onwards,.we.produce.5,000.gallo
ns,.yet.we.ship.10,000.gallons..Thus.inventory.is.depleted.at.a.rate.of.5000.gallons.per.hour,.which.leav
es.us.without.milk.after.5.hours.(at.1pm)..From.then.onwards,.clients.will.have.to.wait..This.situation.g
ets.worse.and.worse.and.by.6pm.(last.client.arrives),.we.are.short.25,000.gallons.
(a) 1pm
(b) Clients.will.stop.waiting.when.we.have.worked.off.our.25,000.gallon.backlog.that.we.are.facin
g.at.6pm..Since.we.are.doing.this.at.a.rate.of.5,000.gallon.per.hour,.clients.will.stop.waiting.at.1
1pm.(after.5.more.hours).
(c) At.6pm,.we.have.a.backlog.of.25,000.gallons,.which.is.equivalent.to.20.trucks
(d) The.waiting.time.is.the.area.in.the.triangle
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