OPS MGMT Module 4 – Homework Questions

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Module'4 – Homework'Questions

The!Right!to!Vote!(and!not!to!wait)

In!the!previous!two!presidential!elections!in!the!United!States,!very!long!wait!times!have!been!

witnessed!at!precincts!(voting!stations)!in!states!that!ultimately!decided!the!election!(Florida!in!

2000!and!Ohio!in!2004).

!In!Philadelphia!as!well,!some!voters!complained!about!the!long!lines!in!some!precincts,!with!

most!complaints!coming!from!precinct!A.!In!2004,!the!average!number!of!voters!arriving!at!

Precinct!A!was!35!per!hour,!and!the!arrivals!of!voters!were!random!with!interNarrival!times!that!

had!a!coefficient!of!variation!of!1!(CVa=1).

Philadelphia!had!deployed!1!voting!machine!in!Precinct!A.!Suppose!that!each!voter!spent!on!

average!of!100!seconds!in!the!voting!booth!(this!is!the!time!needed!to!cast!her/his!vote!using!a!

voting!machine),!with!a!standard!deviation!of!120!seconds.

RTV1.!How!long!on!average!did!a!voter!have!to!wait!in!line!precinct!at!A!in!2004!before!entering!

in!a!booth!to!cast!her/his!vote?

Grand!Hotel

The!managers!of!the!Grand!Hotel!are!evaluating!the!possibility!of!setting!up!a!computer!area!

where!conference!attendees!can!check!their!eNmail!on!computers!provided!by!the!conference!

organizers.!There!will!be!one!common!queue!for!all!computers,!and!only!one!person!uses!a!

computer!at!a!time.!On!average!there!are!12!attendee!arrivals!per!hour,!and!the!standard!

deviation!of!the!time!between!arrivals!is!2.5!minutes.!The!average!time!that!a!person!spends!on!

the!computer!is!20!minutes,!with!a!standard!deviation!of!10!minutes.!

Suppose!the!organizers!decide!to!install!5!computers.

GH1.'What!is!the!average!utilization!of!the!5!computers?!

GH2.'What!is!the!expected!time!(in!minutes)!that!an!attendee!will!have!to!wait!for!a!computer!

to!become!available?!

GH3.!How!long!(in!minutes)!will!the!average!computer!be!empty!during!an!8Nhour!day?

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GH4.'What!is!going!to!be!the!average!number!of!attendees!in!the!computer!area!(either!waiting!

for!a!computer!or!using!a!computer)?!(Your!answer!does!NOT!have!to!be!an!integer.)

GH5.'The!firm!does!not!want!the!average!waiting!time!to!be!higher!than!0.1!minute.!What!is!

the!minimum!total!number!of!computers!that!the!firm!will!have!to!install!to!meet!this!goal?

UPS!Shipping

A!UPS!employee,!Davis,!packs!and!labels!three!types!of!packages:!basic packages,!business!

packages,!and!oversized!packages.!Business!packages!take!priority!over basic!packages!and!

oversized!packages!because!those!customers!paid!a!premium!to!have guaranteed!twoNday!

delivery.!During!his!9Nhour!shift,!he!has,!on!average,!one!container of!packages!containing!a!

variety!of!basic,!business,!and!oversized!packages!to!process!every 3!hours.!As!soon!as!Davis!

processes!a!package,!he!passes!it!to!the!next!employee,!who!loads it!onto!a!truck.!The!times!it!

takes!him!to!process!the!three!different!types!of!packages!and the!average!number!of!packages!

per!container!are!shown!in!the!table!below.

Basic Business Oversized

Avg!#!of!min!to!label!

and!package!each!

unit

5!min 4!min 6!min

Avg!#!of!units!per!

container

10! 10! 5!

Davis!currently!processes!packages!from!each!container!as!follows.!First,!he!processes

all!business!packages!in!the!container.!Then!he!randomly!selects!either!basic!packages!or

oversized!packages!for!processing!until!the!container!is!empty.!However,!his!manager!

suggested to!Davis!that,!for!each!container,!he!should!process!all!the!business!packages!first,

then!the!basic!packages!second,!and!then!the!oversized!packages!last.

UPS1. If!Davis!follows!his!supervisor’s!advice,!what!will!happen!to!Davis’s!utilization?

a. His!utilization!will!increase

b. His!utilization!will!decrease

c. His!utilization!will!stay!the!same

UPS2. What!will!happen!to!the!average!time!that!a!package!spends!in!the!container?

a. The!average!wait!time!will!increase

b. The!average!wait!time!will!decrease

c. The!average!wait!time!will!stay!the!same

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Process!Design

Consider!the!following!three!process!designs!to!organize!a!call!center!with!12!employees.!The!

center!handles!calls!for!two!customer!types.!Type!1!customers!call!with!credit!cardNrelated!

questions!and!type!2!customers!call!with!questions!related!to!online!account!opening.!!On!a!

busy!day!the!call!center!receives!60!calls!per!hour!from!type!1!customers!and!30!calls!per!hour!

from!type!2!customers.!!It!takes!on!average!2!minutes!to!service!both!kinds!of!calls.!!

Process!design!1:!!6!employees!handle!type!1!calls;!the!other!6!employees!handle!type!2!calls

Process!design!2:!!8!employees!handle!type!1!calls;!4!employees!type!2!calls

Process!design!3:!!12!persons!(crossNtrained)!handle!all!calls

PD1.!Which!of!the!three!process!designs!leads!to!the!shortest!and!longest!average!waiting!

times!for!a!random!incoming!request?

a. 1!is!the!shortest,!2!is!the!longest

b. 2!is!the!shortest,!1!is!the!longest

c. 3!is!the!shortest,!2!is!the!longest

d. 2!is!the!shortest,!3!is!the!longest

e. 3!is!the!shortest,!1!is!the!longest

f. 1!is!the!shortest,!3!is!the!longest

g. 3!is!the!shortest,!1!and!2!are!the!same

h. Cannot!be!determined

i. None!of!the!above

Train!Massage

There!are!5!coinNoperated!massage!chairs!at!Philadelphia’s!30th!Street!train!station.!The!length!

of!time!that!each!customer!spends!in!a!massage!chair!averages!12!minutes!and!has!a!standard!

deviation!of!5!minutes.!Customers!pay!$0.50!per!minute!for!the!massage.!On!average,!every!

hour!there!are!15!potential!customers!interested!in!receiving!a!massage!at!one!of!these!chairs.!

The!interNarrival!times!are!assumed!to!be!exponentially!distributed.!If!no!spot!is!available!when!

the!customer!arrives,!then!the!customer!goes!away.

TM1.'What!is!the!probability!that!an!arriving!customer!will!find!all!massage!chairs!occupied?!

TM2.!On!average,!how!much!revenue!does!Train!Massage!collect!over!the!course!of!one!hour?

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TM3.!How!would!that!number!change!if!the!coefficient!of!variation!of!the!massage!time!were

reduced!to!zero?