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operationsma
nagement
Waiting LineWaiting Line
ModelsModelsand Serviceand Service
Im rovement
??
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Im rovement
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Waiting is a part of lifeWaiting is a part of life
need it always be?need it always be?
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Waiting is a part of lifeWaiting is a part of life
need it always be?need it always be?
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Waiting Lines / Queues
Waiting in lines does notadd enjoyment
Waiting in lines does notgenerate revenue
There are costs in providing waiting space Lines can result in loss of business
(customers leave, refusing to wait)
Loss of goodwill
Overall reduction in customer satisfaction
Congestion may disrupt other business operations
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operationsma
nagement
What can help reduce
waiting times?
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Approaches that help
Reduceperceivedwaiting time Magazines in waiting rooms
Radio/television
In-flight movies
Filling out forms
mirrors
When all else fails, derive benefits from waiting
Place impulse buy items near checkout (endcaps)
Advertise other goods/services
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Whats important to the Customer?
Length of the line when I arrive
How long I have to wait
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Whats important to the ServiceProvider?
How many people I have to hire to servicecustomers (clerks, cashiers, baggers, etc.)
(Hopefully) the level of service provided
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Waiting Lines
You have just been hired as the new assistant
manager of a new Costco store. You are incharge of customer service. You determine
that: 60 shoppers arrive per hour on average You can process 50 shoppers per hour on
average with the number of cashiers
Will your service be any good?
Will your customers be satisfied?
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Waiting Lines
60 shoppers arrive per hour on average
You can process 60 shoppers per hour onaverage
Will your service be any good?
Will your customers be satisfied?
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Waiting Lines
60 shoppers arrive per hour on average
You can process 70 shoppers per hour onaverage
Will your service be any good?
Will your customers be satisfied?
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Waiting Lines: United States
Whats an acceptable time to wait in line at:
Starbucks
Outback Steakhouse
Post Office
DMV
Grocery store
Planning Department
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Waiting Lines
What is a reasonable waiting time?
Is your willingness to wait dependent
upon the type of establishment?
Are there cultural differences?
Can we establish a model of wait time toreduce average wait time?
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Who is this
woman, and
why is shesmiling???
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Waiting in line to get addWaiting in line to get add
slips signed in HTM302slips signed in HTM302
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Elements of Waiting Line Analysis
QueueA single waiting line
Waiting line system consists ofArrivals
Servers
Waiting line structures
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Components of Queuing System
Source ofcustomerscallingpopulation
ServerArrivals Waiting Lineor
Queue
Servedcustomers
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Elements of a Waiting Line
Calling populationSource of customers
Arrival rate ( )Frequency of customer arrivals at waiting line
system
Typically follows Poisson distribution
Service rateFrequency of customer services
Often follows negative exponential distribution
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Elements of a Waiting Line
Arrival rate ( ) must be less than service
rate ( or system never clears out
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Elements of a Waiting Line
Queue disciplineOrder in which customers are served
First come, first served is mostcommon
Length can be infinite or finite
Infinite is most common assumptionFinite is limited by some physical
structure
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Basic Waiting Line Structures
Channels are the number of
parallel servers
Phases denote number of
sequential servers the customermust go through
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Single-Channel Structures
Single-channel, single-phase
Waiting line Server
Single-channel, multiple phases
ServersWaiting line
CSUSM Convenience Store (1 cashier)
Starbucks Coffee (single cashier/barrista)
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Multi-Channel Structures
Servers
Multiple-channel, single phase
Waiting line
CSUSM Convenience Store (3 cashiers)
Frys Electronics (72 cashiers)
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Predicting Waiting Times
Later well show how you can mathematicallypredict the performance of a waiting line,
in terms of:
Number of people waiting in line Expected waiting time
But first, lets look first at some model results toget an intuitive feel as to what happens.
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A Single-Server ModelNumber of Customers Waiting In Line
with 60 customer arrivals per hour
0
2
4
6
8
10
12
65 69 73 77 81 85 89 93 97 101
105
109
113
117
121
Customer Served Per Hour
Customers
InLine
70
120
Asweapproachser
vice
timesof60/hour,line
growsexpone
ntially
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A Single-Server ModelCustomer Wait Time (in hours)
with 60 customer arrivals per hour
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
65 69 73 77 81 85 89 93 97 101
105
109
113
117
121
Customers Served per Hour
WaitTime(h
ours)
70
120
Asweapproachser
vice
timesof60/hour
,wait
growsexpone
ntially
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A Single-Server ModelProbability Customer Waits
with 60 customer arrivals per hour
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
65 69 73 77 81 85 89 93 97 101
105
109
113
117
121
Customers served per Hour
Probability
70 120
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Multi-Channel Structures
Servers
Waiting line
Multiple-channel, multiple-phase
Starbucks (3 cashiers, 3 barristas)
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Which is better?
Servers
Waiting line
ServersWaiting line
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Which is better?
Servers
Waiting line
ServersWaiting line
T f ibiliti hi h
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Two servers, four possibilities; whichis best?
Servers
Waiting lineServers
Waiting line
ServersWaiting line
Servers
Waiting line
M lti Channel Str ct res
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Multi-Channel Structures(that the book doesnt deal with)
ServersWaiting lines
Multiple-channel, single-phase
Large Stores(Wal Mart, grocery stores, etc.)
Multi Channel Structures
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Multi-Channel Structures(that the book doesnt deal with)
ParkingFeeWaiting lines
Multiple-channel, multiple-phase
$
$
$
$
$
$
Amusement Parks (Legos, Disneyland, etc.)Sporting Parks (Qualcomm, Sports Arena, etc.)Concerts (Coors Amphitheater, etc.)
EntranceFee
TicketCollection
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Multi-Channel Structures
ParkingFeeWaiting lines
$
$
$
$
$
$
EntranceFee
TicketCollection
Heh, whyisnt this linemoving??!?
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Operating Characteristics
The mathematics of alternative multi-channeland multi-phase waiting lines can become verycomplex
Mathematicsof queuing theorydoes notprovide optimal or best solutions
However we can describe system performance
by calculating operating characteristics
Cost Relationship in Waiting Line
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Cost Relationship in Waiting LineAnalysis
Expecte
d
costs
Level of service
Waiting Cost
The customers arepaying these costs
Cost Relationship in Waiting Line
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Cost Relationship in Waiting LineAnalysis
Expecte
d
costs
Level of service
Service costThe businesses arepaying these costs
Cost Relationship in Waiting Line
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Cost Relationship in Waiting LineAnalysis
Expecte
d
costs
Level of service
Total cost
Service cost
Waiting Costs
Waiting Line Costs and Quality
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Waiting Line Costs and QualityService
Traditional view is that the level ofservice should coincide with
minimum point on total cost curve
TQM approach is that absolute
quality service will be the most cost-effective in the long run
Cost Relationship in Waiting Line
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Cost Relationship in Waiting LineAnalysis
Expecte
d
costs
Level of service
Total cost
Service cost
Waiting Costs
Traditional suggestedservice level
Cost Relationship in Waiting Line
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Cost Relationship in Waiting LineAnalysis
Expecte
d
costs
Level of service
Total cost
Service cost
Waiting Costs
Better service, highercost to business
Poorer service, highercost to customer
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Basic Single-Server Model
Assumptions:Poisson arrival rateExponential service times
First-come, first-served queue disciplineInfinite queue lengthInfinite calling population
= mean arrival rate = mean service rate
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Formulas for Single-Server Model
Average number ofcustomers in the system
L = -
Probability that no customersare in the system (either in thequeue or being served)
P0 = 1 -
Probability of exactly ncustomers in the system
Pn = P0
n
= 1 -
n
Average number of
customers in the waiting line
Lq =
( -
= mean arrival rate= mean service rate
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Formulas for Single-Server Model
Probability that the serveris busy and the customerhas to wait
=
Average time a customerspends in the queuing system
W = =1
-
L
Probability that the serveris idle and a customer canbe served
I = 1 -
= 1 - = P0
Average time a customerspends waiting in line tobe served
Wq =( - )
= mean arrival rate
= mean service rate
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An example
You manage a small grocery store, with one checker for
scanning, collecting payment, and bagging groceries. The
arrival rate is 24/hr, service rate 30/hr, so average waiting
time is 8 minutes. You want to improve checkout time, so
you are considering adding: A second employee to bag groceries
OR
A second checker
Which is better?
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An example
2 cashiers
Waiting line
cashier baggerWaiting line
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Waiting Line Cost Results
Adding an employee results in savings andimproved customer service
Adding a 2nd counter results in slightly
greater savings (~$20/week) and improvedcustomer service (~1 min less waiting), butonly after the initial investment has beenrecovered (~ 5 months)
A new counter results in more idle time foremployees
A new counter would take up potentially
valuable floor space
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tionsmanagem
ent
Simulation Model
http://courses.csusm.edu/htm302jh/examples/QueueModel.xlshttp://courses.csusm.edu/htm302jh/examples/QueueModel.xls7/31/2019 Chap 17 in Class Queuing
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Informal feedback
Write a 2 minute journal to be handed inimmediately
The journal should briefly summarize:
Major points learned
Areas not understood or requiringclarification