module 4 slides.ppt

7/25/2019 Module 4 slides.ppt

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Prof. Christian Terwiesch

Response Time

Introduction


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Example

-Patients arrive, on average, every five minutes- It takes ten minutes to serve a patient- Patients are willing to wait

What is the implied utiliation of the !ar!er shop"

#ow long will patients have to wait"

Physician office


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Example

-Patients arrive, on average, every five minutes- It takes four minutes to serve a patient- Patients are willing to wait

What is the utiliation of the !ar!er shop"

#ow long will patients have to wait"

Physician office


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Numberofcases

3ore Realistic .ervice Process


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4aria!ility 5eads to Waiting Time


7/47Prof. Christian Terwiesch

The 6urse of 4aria!ility - .ummary

4aria!ility hurts flowWith !uffers% we see waiting times even though there exists excess capacity

4aria!ility is 78 and it does not average itself out

9ew models are needed to understand these effects



Waiting time models% The

need for excess capacity

Response Time



Processing

3odeling 4aria!ility in :low

Inflow8emand process is ;randomprocessing times?

Outflow

9o loss, waiting onlyThis re@uires uA'&&B1utflow=Inflow

Flow Rate

3inimumC8emand, 6apacityD = 8emand = 'a



verage flowtime #

#$eoretica %o& #ime

Ftiliation '&&B

Increasin'

ariabiity

Waiting Time Formula

.ervice time factor

Ftiliation factor

4aria!ility factor

+

=

21

22pa CVCV

nutilizatio

nutilizatioTimeActivityqueueinTime

Inflow 1utflow

Inventorywaiting I)

Entry to system 8eparture7egin .ervice

Time in @ueue #) .ervice Time*

:low Time #+#),*

%o& rate

The Waiting Time :ormula



Example% Walk-in 8oc

9ewt Philly needs to get some medical advise2 #e knows that his 8oc, :rancoise, has a patient arrive every )&minutes >with a standard deviation of )& minutes?2 typical consultation lasts '+ minutes >with a standard

deviation of '+ minutes?2 The 8oc has an open-access policy and does not offer appointments2If 9ewt walks into :rancoisGs practice at '&am, when can he expect to leave the practice again"



.ummary

Even though the utiliation of a process might !e less than '&&B, it might still re@uire long customer wait time

4aria!ility is the root cause for this effect

s utiliation approaches '&&B, you will see a very steep increase in the wait time

If you want fast service, you will have to hold excess capacity



3ore on Waiting time models

.taffing to 8emand

Response Time



+

=

+

21

221)1(2pa

m CVCV

nutilizatio

nutilizatio

m

timeActivityqueueinTime

Waiting Time Formula for Multiple (m) Serers

Inflow 1utflow

Inventorywaiting I)

Entry to system 8eparture7egin .ervice

Time in @ueue #) .ervice Time*

:low Time #+#),*

Inventoryin service I*

:low rate

Waiting Time :ormula for 3ultiple, Parallel Resources



6ustomers send emails to a help desk of an online retailer every (minutes, on average, and the standard deviation of the inter-arrival timeis also ( minutes2 The online retailer has three employees answeringemails2 It takes on average * minutes to write a response email2 Thestandard deviation of the service times is ( minutes2

Estimate the average customer wait !efore !eing served2

Example% 1nline retailer



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Entry tosystem

8eparture7egin.ervice

Waiting Time #) .ervice Time*

:low Time #+#),*

:low unit

Inventoryin service I*

Ftiliation >9ote% make sure A'?

Time related measures

Inventory related measures >:low rate=1-a?

.ummary of Hueuing nalysis



6ustomers send emails to a help desk of an online retailer every (minutes, on average, and the standard deviation of the inter-arrival timeis also ( minutes2 The online retailer has three employees answeringemails2 It takes on average * minutes to write a response email2 Thestandard deviation of the service times is ( minutes2

#ow many employees would we have to add to get the average waittime reduced to x minutes"

.taffing 8ecision



What to 8o With .easonal 8ata

Measure the true !eman! !ata

Slice the !ata "# the hour ($%min& 'min)

ppl# waiting mo!el in each slice

5evel the demand

ssume demand is ;stationary< within a slice



Target Wait Time >TWT?.ervice 5evel = Pro!a!ilityCWaiting TimeTWTDExample% 7ig 6all 6enter - starting point diagnostic% )&B of calls answered within (& seconds - target% &B of calls answered within (& seconds

&

&2(

&2*

&2/

&2

'

& +& '&& '+& (&&

Waiting time *secon!s+

Fraction of

customers who

hae to wait ,secon!s or less "aitin' times for t$ose customers

&$o .o not 'et serve. imme.iatey

%raction of customers &$o 'et serve.

&it$out &aitin' at a

90/ of cas $a. to

&ait 25 secon.s oress

.ervice 5evels in Waiting .ystems



6apacity Pooling

Response Time



In.e*en.ent esources

2(m+1!

Pooe. esources

(m+2!

3anagerial Responses to 4aria!ility% Pooling

-,ample

Processing time=* minutesInter-arrival time=+ minutes >at each server?m=', 6va=64p='

T@ =

Processing time=* minutesInter-arrival time=(2+ minutesm=(, 6va=64p='

T@ =



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WaitingTime #)

Ftiliation u

3anagerial Responses to 4aria!ility% Pooling



Pooling% .hifting the Efficient :rontier


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.ummary

What is a good wait time"

:ire truck or IR."


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5imitations of Pooling

ssumes flexi!ility

Increases complexity of work-flow

6an increase the varia!ility of service time

Interrupts the relationship with the customer one-face-to-the-customer

Jroup clinics

Electricity grid smart grid

:lexi!le production plants


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The Three Enemies of 1perations

dditional costs due to varia!ility indemand and activity times

Is associated with longer wait timesand or customer loss

Re@uires process to hold excesscapacity >idle time?

4aria!ility

Fse of resources !eyond what isneeded to meet customer

re@uirements 9ot adding value to the product,

!ut adding cost

Reducing the performance of theproduction system

$ different types of waste

WasteWork 4alue-adding

WasteWork 4alue-adding

Waste

Inflexi!ility

dditional costs incurred !ecause of supplydemand mismatches

Waiting customers or Waiting >idle capacity?

6apacity

6ustomerdemand


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.cheduling ccess

Response Time


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:low units are se@uenced in the waiting area >triage step?

Provides an opportunity for us to move some units forwards and some !ackwards

:irst-6ome-:irst-.erve

- easy to implement- perceived fairness- lowest variance of waiting time

.e@uence !ased on importance- emergency cases- identifying profita!le flow units

3anagerial Responses to 4aria!ility% Priority Rulesin Waiting Time .ystems


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Service times

9 minutes

10 minutes

4 minutes

8 minutes

9 min

19 min

23 min

#ota &ait time 9,19,23+51min

4 min

12 min

21 min

#ota &ait time 4,13,21+38 min

.hortest Processing Time Rule- 3inimies average waiting time- Pro!lem of having ;true< processing times

3anagerial Responses to 4aria!ility% Priority Rulesin Waiting Time .ystems


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1pen ccess

ppointment systems

ppointments


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Redesign the .erviceProcess

Response Time


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Reasons for 5ong Response Times>nd Potential Improvement .trategies? Insufficient capacity on a permanent !asis

=K Fnderstand what keeps the capacity low

8emand fluctuation and temporal capacity shortfalls

Fnpredicta!le wait times =K Extra capacity Reduce varia!ility in demand

Predicta!le wait times =K .taff to demand Takt time

5ong wait times !ecause of low priority=K lign priorities with customer value

3any steps in the process poor internal process flow >often driven !y handoffsand rework loops?=K Redesign the service process

http%www2minyanville2com!usinessmarketsarticlesdrive-thrus-emissions-fast-food-mcdonalds+'((&'&id((/'
http://www.minyanville.com/businessmarkets/articles/drive-thrus-emissions-fast-food-mcdonalds/5/12/2010/id/28261http://www.minyanville.com/businessmarkets/articles/drive-thrus-emissions-fast-food-mcdonalds/5/12/2010/id/28261


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The 6ustomerGs Perspective

Driving Parking Check-in Vitals Waiting PCP Appt. Check outLabs Drive home

20 minutes

#ow much time does a patient spend on a primary care encounter"

Two types of wasted time%uxiliary activities re@uired to get to value add activities >result of process location lay-out?Wait time >result of !ottlenecks insufficient capacity?

#ota vaue a.. time of a unit

#ota time a unit is in t$e *rocess%o& #ime fficiency (or /#! +


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Process 3apping .ervice 7lue Prints

.ource% Lves Pigneur

Customer

actions

5ine of interaction

Onstage

actions

5ine of visi!ility

/ac0stage

actions

5ine of internalinteraction

Support

processes

Walk into the

!ranch talk toagent

6ollect !asicinformation

Pre pprovalprocessM set upworkflow accountresponsi!ility

6ustomer

supplies moredata

Re@uest for moredata

6ustomer

supplies moredata

Re@uest for moredata

Pre pprovalprocessM set upworkflow accountresponsi!ility

Run formal creditscoring model

Explain finaldocument

.ign contracts

Process 3apping .ervice 7lue Prints


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Process 3apping .ervice 7lue Prints#ow to Redesign a .ervice Process

3ove work off the stageExample% online check-in at an airport

Reduce customer actions rely on support processesExample% checking in at a doctorGs office

Instead of optimiing the capacity of a resource, try to eliminate the step altogetherExample% #ert Jold N 6heck-in offers no valueM go directly to the car

void fragmentation of work due to specialiation narrow Oo! responsi!ilitiesExample% 5oan processing hospital ward

If customers are likely to leave the process !ecause of long wait times, have the wait occurlater in the process re-se@uence the activities

Example% .tar!ucks N Pay early, then wait for the coffee

#ave the waiting occur outside of a line

Example% Restaurants in a shopping malls using !uersExample% ppointment

6ommunicate the wait time with the customer >set expectations?Example% 8isney


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5oss 3odels

Response Time

8ifferent 3odels of 4aria!ility


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8ifferent 3odels of 4aria!ility

Waiting pro"lems

Ftiliation has to !e less than '&&B

Impact of varia!ility is on :low Time

1oss pro"lems

8emand can !e !igger than capacity

Impact of varia!ility is on :low Rate

Pure waitingpro!lem, all customersare perfectly patient2

ll customersenter the process,some leave due totheir impatience

6ustomers do notenter the process once!uffer has reached acertain limit

6ustomers are lostonce all servers are!usy

Same if customers are *atient Same if buffer sie+0

Same if buffer sie is etremey ar'e

4aria!ility is always !ad N you pay through lower flow rate andor longer flow time

7uffer or suffer% if you are willing to tolerate waiting, you donGt have to give up on flow rate


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nalying 5oss .ystems

#rauma center moves to

.iversion status once a

servers are busy

incomin' *atients

are .irecte. to

ot$er ocations

Resources

) trauma !ays >m+3?

2eman! Process

1ne trauma case comesin every ) hours

>a=) hours?

ais the interarrival time

Exponential interarrival times

Serice Process

Patient stays in trauma !ayfor an average of ( hours

>*=( hours?

*is the service time

6an have any distri!ution

What is Pm& the pro"a"ilit# that all m resources are utili3e!4

m!ulances #elicopters

. > ?


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nalying 5oss .ystems% :inding Pm>r?

8efine r + * - a

Example% r= ( hours ) hours r=&2/$

Recall m=)

Fse Erlang 5oss Ta!le

:ind that P) >&2/$?=&2&(++

5ien Pm(r)we can compute

Time per day that system has to deny access:low units lost = 'a Pm >r?

' ( ) * +

&2'& &2&0&0 &2&&*+ &2&&&( &2&&&& &2&&&&

&2(& &2'//$ &2&'/* &2&&'' &2&&&' &2&&&&

&2(+ &2(&&& &2&(** &2&&(& &2&&&' &2&&&&

&2)& &2()&, &2&))+ &2&&)) &2&&&) &2&&&&

&2)) &2(+&& &2&*&& &2&&** &2&&&* &2&&&&

&2*& &2(,+$ &2&+*' &2&&$( &2&&&$ &2&&&'

&2+& &2)))) &2&$/0 &2&'($ &2&&'/ &2&&&(&2/& &2)$+& &2'&'' &2&'0, &2&&)& &2&&&*

&2/$ &2*&&& &2''$/ &2&(++ &2&&*( &2&&&/

&2$& &2*'', &2'(/& &2&(,/ &2&&+& &2&&&$

&2$+ &2*(,/ &2'),+ &2&))+ &2&&/( &2&&&0

&2,& &2**** &2'+&0 &2&),$ &2&&$$ &2&&'(

&20& &2*$)$ &2'$+$ &2&+&' &2&''' &2&&(&

'2&& &2+&&& &2(&&& &2&/(+ &2&'+* &2&&)'

r = p / a

m

Implied utiliation vs pro!a!ility of having all


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Implie! utili3ation

Pro"a"ilit#

that all serers

are utili3e!

m+1

m+2

m+5 m+10

m+20

&

&2'

&2(

&2)

&2*

&2+

&2/

& &2' &2( &2) &2* &2+ &2/ &2$ &2 &20 ' '2'

m+3

Implied utiliation vs pro!a!ility of having allserversutilied% Pooling Revisited

-rlang 1oss Ta"le m' ( ) * + / $ , 0 '&


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&2'& &2&0&0 &2&&*+ &2&&&( &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&

&2(& &2'//$ &2&'/* &2&&'' &2&&&' &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&

&2(+ &2(&&& &2&(** &2&&(& &2&&&' &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&

&2)& &2()&, &2&))+ &2&&)) &2&&&) &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&

&2)) &2(+&& &2&*&& &2&&** &2&&&* &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&

&2*& &2(,+$ &2&+*' &2&&$( &2&&&$ &2&&&' &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&

&2+& &2)))) &2&$/0 &2&'($ &2&&'/ &2&&&( &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&

&2/& &2)$+& &2'&'' &2&'0, &2&&)& &2&&&* &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&

&2/$ &2*&&& &2''$/ &2&(++ &2&&*( &2&&&/ &2&&&' &2&&&& &2&&&& &2&&&& &2&&&&

&2$& &2*'', &2'(/& &2&(,/ &2&&+& &2&&&$ &2&&&' &2&&&& &2&&&& &2&&&& &2&&&&

&2$+ &2*(,/ &2'),+ &2&))+ &2&&/( &2&&&0 &2&&&' &2&&&& &2&&&& &2&&&& &2&&&&

&2,& &2**** &2'+&0 &2&),$ &2&&$$ &2&&'( &2&&&( &2&&&& &2&&&& &2&&&& &2&&&&

&20& &2*$)$ &2'$+$ &2&+&' &2&''' &2&&(& &2&&&) &2&&&& &2&&&& &2&&&& &2&&&&

'2&& &2+&&& &2(&&& &2&/(+ &2&'+* &2&&)' &2&&&+ &2&&&' &2&&&& &2&&&& &2&&&&

'2'& &2+(), &2(()$ &2&$+, &2&(&* &2&&*+ &2&&&, &2&&&' &2&&&& &2&&&& &2&&&&

'2(& &2+*++ &2(*// &2&,0, &2&(/( &2&&/) &2&&'( &2&&&( &2&&&& &2&&&& &2&&&&

'2(+ &2+++/ &2(+$$ &2&0$& &2&(0* &2&&$) &2&&'+ &2&&&) &2&&&& &2&&&& &2&&&&

'2)& &2+/+( &2(/,$ &2'&*) &2&)(, &2&&,+ &2&&', &2&&&) &2&&&' &2&&&& &2&&&&

'2)) &2+$'* &2($+0 &2'&0( &2&)+' &2&&0) &2&&(' &2&&&* &2&&&' &2&&&& &2&&&&

'2*& &2+,)) &2(,00 &2''0( &2&*&& &2&''' &2&&(/ &2&&&+ &2&&&' &2&&&& &2&&&&

'2+& &2/&&& &2)'&) &2')*) &2&*,& &2&'*( &2&&)+ &2&&&, &2&&&' &2&&&& &2&&&&

'2/& &2/'+* &2)(00 &2'*0/ &2&+/+ &2&'$$ &2&&*$ &2&&'' &2&&&( &2&&&& &2&&&&

'2/$ &2/(+& &2)*(+ &2'+0, &2&/(* &2&(&* &2&&+/ &2&&') &2&&&) &2&&&' &2&&&&

'2$& &2/(0/ &2)*,/ &2'/+& &2&/++ &2&(', &2&&/' &2&&'+ &2&&&) &2&&&' &2&&&&

'2$+ &2/)/* &2)+$$ &2'$(/ &2&$&( &2&(*& &2&&/0 &2&&'$ &2&&&* &2&&&' &2&&&&

r + *-a '2,& &2/*(0 &2)//+ &2',&) &2&$+& &2&(/) &2&&$, &2&&(& &2&&&+ &2&&&' &2&&&&'20& &2/++( &2),)/ &2'0++ &2&,+& &2&)') &2&&0, &2&&($ &2&&&/ &2&&&' &2&&&&

(2&& &2///$ &2*&&& &2('&+ &2&0+( &2&)/$ &2&'(' &2&&)* &2&&&0 &2&&&( &2&&&&

(2'& &2/$$* &2*'+/ &2((+* &2'&+, &2&*(+ &2&'*$ &2&&** &2&&'' &2&&&) &2&&&'

(2(& &2/,$+ &2*)&/ &2(*&& &2''// &2&*,, &2&'$/ &2&&++ &2&&'+ &2&&&* &2&&&'

(2(+ &2/0() &2*)$, &2(*$( &2'((' &2&+(' &2&'0( &2&&/' &2&&'$ &2&&&* &2&&&'

(2)& &2/0$& &2***0 &2(+*) &2'($/ &2&++* &2&(&, &2&&/, &2&&'0 &2&&&+ &2&&&'

(2)) &2$&&& &2**0+ &2(+0' &2')') &2&+$$ &2&((& &2&&$) &2&&(' &2&&&+ &2&&&'

(2*& &2$&+0 &2*+,/ &2(/,* &2'),$ &2&/(* &2&(** &2&&,) &2&&(+ &2&&&$ &2&&&(

(2+& &2$'*) &2*$'$ &2(,(( &2'*00 &2&/0$ &2&(,( &2&'&& &2&&)' &2&&&0 &2&&&(

(2/& &2$((( &2*,*( &2(0+/ &2'/'( &2&$$) &2&)(* &2&''0 &2&&)0 &2&&'' &2&&&)

(2/$ &2$($) &2*0() &2)&** &2'/,$ &2&,(+ &2&)+* &2&')) &2&&** &2&&') &2&&&)

(2$& &2$(0$ &2*0/) &2)&,$ &2'$(+ &2&,+( &2&)/0 &2&'*& &2&&*$ &2&&'* &2&&&*

(2$+ &2$))) &2+&(' &2)'+( &2'$,' &2&,0( &2&)0) &2&'+( &2&&+( &2&&'/ &2&&&*

(2,& &2$)/, &2+&$, &2)('+ &2',)$ &2&0)) &2&*'$ &2&'/* &2&&+$ &2&&', &2&&&+

(20& &2$*)/ &2+',, &2))*& &2'0*0 &2'&'/ &2&*/, &2&'0& &2&&/, &2&&(( &2&&&/

)2&& &2$+&& &2+(0* &2)*/( &2(&/' &2''&' &2&+(( &2&('0 &2&&,' &2&&($ &2&&&,

)2'& &2$+/' &2+)0/ &2)+,& &2('$( &2'',$ &2&+$, &2&(*0 &2&&0/ &2&&)) &2&&'&

)2(& &2$/'0 &2+*0* &2)/0+ &2((,' &2'($* &2&/)/ &2&(,) &2&''( &2&&*& &2&&')

)2(+ &2$/*$ &2++*' &2)$+' &2())/ &2')', &2&/// &2&)&& &2&'(& &2&&*) &2&&'*

)2)& &2$/$* &2++,$ &2),&$ &2()0& &2')/( &2&/0$ &2&)', &2&')& &2&&*$ &2&&'/

)2)) &2$/0( &2+/', &2),*) &2(*(/ &2')0( &2&$', &2&))' &2&')/ &2&&+& &2&&'$

)2*& &2$$($ &2+/$, &2)0'+ &2(*0$ &2'*+( &2&$/& &2&)+/ &2&'*0 &2&&+/ &2&&'0

)2+& &2$$$, &2+$/+ &2*&(' &2(/&) &2'+*' &2&,(+ &2&)0/ &2&'$& &2&&// &2&&()

)2/& &2$,(/ &2+,*, &2*'(* &2($&$ &2'/)' &2&,0' &2&*), &2&'0) &2&&$$ &2&&(,

)2/$ &2$,+$ &2+0&( &2*'0' &2($$+ &2'/0' &2&0)$ &2&*/, &2&('& &2&&,+ &2&&)'

)2$& &2$,$( &2+0(0 &2*((* &2(,&0 &2'$(' &2&0/& &2&*,) &2&(', &2&&,0 &2&&))

)2$+ &2$,0+ &2+0/, &2*($) &2(,/& &2'$// &2&00* &2&+&/ &2&()( &2&&0/ &2&&)/

)2,& &2$0'$ &2/&&$ &2*)(' &2(0'& &2','' &2'&(0 &2&+(0 &2&(*+ &2&'&( &2&&)0

)20& &2$0+0 &2/&,( &2**'+ &2)&&0 &2'0&' &2''&& &2&+$$ &2&($* &2&''$ &2&&*/*2&& &2,&&& &2/'+* &2*+&$ &2)'&$ &2'00' &2''$( &2&/($ &2&)&* &2&')) &2&&+)

Probability{all mservers busy}=

!...

!2!11

!)(21

m

rrr

m

r

rPm

m

m

++++

=

Erlang 5oss Ta!le


42/47


Review

Response Time

(M#6law com)


43/47


(M#6law.com)

3y-law2com is a recent start-up trying to cater to customers in search of legal services online2 Fnlike traditionallaw firms, 3y-law2com allows for extensive interaction !etween lawyers and their customers via telephone andthe Internet2 This process is used in the upfront part of the customer interaction, largely consisting ofanswering some !asic customer @uestions prior to entering a formal relationship2 In order to allow customers tointeract with the firmGs lawyers, customers are encouraged to send e-mails to my-lawyerQ3y-law2com2 :rom

there, the incoming e-mails are distri!uted to the lawyer who is currently ;on call2< Jiven the !road skills of thelawyers, each lawyer can respond to each incoming re@uest2

E-mails arrive from 232 to / P232 at a rate of '& e-mails per hour >coefficient of variationfor the arrivals is '?2 t each moment in time, there is exactly one lawyer ;on call,with a standard deviation of '& minutes?2 P: has astaff of + computer technicians2 .ervice times average around *& minutes >with a standard deviation of *&minutes?2

6'2 If im walks into P:, how long must he wait in line !efore he can see a technician" >1nly include thewaiting time, not any service time?

6(2 #ow many customers will, on average, !e waiting for their computer to !e fixed"

Real Compute


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Real6ompute offers real-time computing services2 The company owns * supercomputers that can !e accessedthrough the internet2 Their customers send Oo!s that arrive on average every * minutes >inter-arrival times areexponentially distri!uted and, thus, the standard deviation of the inter-arrival times is * minutes?2

Each Oo! takes on average '& minutes of one of the supercomputers >during this time, the computer cannotperform any other work?2 6ustomers pay S(& for the execution of each Oo!2 Jiven the time-sensitive nature of

the calculations, if no supercomputer is availa!le, the Oo! is redirected to a supercomputer of a partner companycalled 1n6omp, which charges S*& per Oo! to Real 6ompute >1n6omp always has supercomputer capacityavaila!le?2

R6'2 What is the pro!a!ility with which an incoming Oo! can !e executed !y one of the supercomputers owned!y Real6ompute"

R6(2 #ow much does Real6ompute pay on average to 1n6omp >in Ss per hour?"

Contractor


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Contractor

contractor !uilding houses and doing renovation work has currently six proOects planned for the season2 7eloware the items, and the estimated times to complete them%

9ew construction at .pringfield - /& days7athroom remodeling at #erne - '& days

Training time for solar roof installation - ( daysFpdate we!-site - / daysRenovation of deck at #averford - days9ew kitchen at Rosemont - (& days.uppose the contractor starts immediately with the first proOect, no other proOects get added to this list, and thecontractor se@uences them so as to minimie the average time the proOect waits !efore it gets started2 What willthe contractor !e doing in )& days from the start date of the first proOect"

Call Center


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6onsider a call center that has a constant staffing level2 7ecause of increased demand in the morning,the call center has a very high utiliation in the morning and a very low utiliation in the afternoon2 Whichof the following will decrease the average waiting time in the call center">a? dd more servers>!? 8ecrease the service time coefficient of variation

>c? 8ecrease the average service time>d? 5evel the demand !etween the morning hours and the afternoon hours>e? ll of the a!ove

module 4 slides.ppt

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