Chap 17 in Class Queuing

7/31/2019 Chap 17 in Class Queuing

1/50

operationsma

nagement

Waiting LineWaiting Line

ModelsModelsand Serviceand Service

Im rovement

??


2/50

Im rovement

o

peration

smana

gement

2

Waiting is a part of lifeWaiting is a part of life

need it always be?need it always be?


3/50

o

peration

smana

gement

3

Waiting is a part of lifeWaiting is a part of life

need it always be?need it always be?


4/50

o

peration

smana

gement

4

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


5/50

operationsma

nagement

What can help reduce

waiting times?


6/50

o

peration

smana

gement

6

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


7/50o

peration

smana

gement

7

Whats important to the Customer?

Length of the line when I arrive

How long I have to wait


8/50o

perationsmana

gement

8

Whats important to the ServiceProvider?

How many people I have to hire to servicecustomers (clerks, cashiers, baggers, etc.)

(Hopefully) the level of service provided


9/50o

perationsmana

gement

9

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?


10/50o

perationsmana

gement

10

Waiting Lines

60 shoppers arrive per hour on average

You can process 60 shoppers per hour onaverage




11/50o

perationsmana

gement

11

Waiting Lines

60 shoppers arrive per hour on average

You can process 70 shoppers per hour onaverage




12/50o

perationsmana

gement

12

Waiting Lines: United States

Whats an acceptable time to wait in line at:

Starbucks

Outback Steakhouse

Post Office

DMV

Grocery store

Planning Department


13/50o

perationsmana

gement

13

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?


14/50


15/50o

perationsmana

gement

15

Who is this

woman, and

why is shesmiling???


16/50o

perationsmana

gement

16

Waiting in line to get addWaiting in line to get add

slips signed in HTM302slips signed in HTM302


17/50o

perationsmana

gement

17

Elements of Waiting Line Analysis

QueueA single waiting line

Waiting line system consists ofArrivals

Servers

Waiting line structures


18/50o

perationsmana

gement

18

Components of Queuing System

Source ofcustomerscallingpopulation

ServerArrivals Waiting Lineor

Queue

Servedcustomers


19/50o

perationsmana

gement

19

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


20/50o

perationsmana

gement

20


Arrival rate ( ) must be less than service

rate ( or system never clears out


21/50o

perationsmana

gement

21


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


22/50o

perationsmana

gement

22

Basic Waiting Line Structures

Channels are the number of

parallel servers

Phases denote number of

sequential servers the customermust go through


23/50o

perationsmana

gement

23

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)


24/50o

perationsmana

gement

24

Multi-Channel Structures

Servers

Multiple-channel, single phase

Waiting line

CSUSM Convenience Store (3 cashiers)

Frys Electronics (72 cashiers)


25/50o

perationsmana

gement

25

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.


26/50o

perationsmana

gement

26

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


27/50o

perationsmana

gement

27

A Single-Server ModelCustomer Wait Time (in hours)


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


28/50o

perationsmana

gement

28

A Single-Server ModelProbability Customer Waits


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


29/50

o

perationsmana

gement

29


Servers

Waiting line

Multiple-channel, multiple-phase

Starbucks (3 cashiers, 3 barristas)


30/50

o

perationsmana

gement

30

Which is better?

Servers

Waiting line

ServersWaiting line


31/50

o

perationsmana

gement

31

Which is better?

Servers

Waiting line

ServersWaiting line

T f ibiliti hi h


32/50

o

perationsmana

gement

32

Two servers, four possibilities; whichis best?

Servers

Waiting lineServers

Waiting line

ServersWaiting line

Servers

Waiting line

M lti Channel Str ct res


33/50

o

perationsmana

gement

33

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


34/50

o

perationsmana

gement

34

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


35/50

o

perationsmana

gement

35


ParkingFeeWaiting lines

$

$

$

$

$

$

EntranceFee

TicketCollection

Heh, whyisnt this linemoving??!?


36/50

o

perationsmana

gement

36

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


37/50

o

perationsmana

gement

37

Cost Relationship in Waiting LineAnalysis

Expecte

d

costs

Level of service

Waiting Cost

The customers arepaying these costs



38/50

o

perationsmana

gement

38


Expecte

d

costs

Level of service

Service costThe businesses arepaying these costs



39/50

o

perationsmana

gement

39


Expecte

d

costs

Level of service

Total cost

Service cost

Waiting Costs

Waiting Line Costs and Quality


40/50

o

perationsmana

gement

40

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



41/50

o

perationsmana

gement

41


Expecte

d

costs

Level of service

Total cost

Service cost

Waiting Costs

Traditional suggestedservice level



42/50

o

perationsmana

gement

42


Expecte

d

costs

Level of service

Total cost

Service cost

Waiting Costs

Better service, highercost to business

Poorer service, highercost to customer


43/50

o

perationsmana

gement

43

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


44/50

o

perationsmana

gement

44

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


45/50

o

perationsmana

gement

45

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


46/50

o

perationsmana

gement

46

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?


47/50

o

perationsmana

gement

47

An example

2 cashiers

Waiting line

cashier baggerWaiting line


48/50

o

perationsmana

gement

48

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


49/50

opera

tionsmanagem

ent

Simulation Model
http://courses.csusm.edu/htm302jh/examples/QueueModel.xlshttp://courses.csusm.edu/htm302jh/examples/QueueModel.xls


50/50

perationsmana

gement

Informal feedback

Write a 2 minute journal to be handed inimmediately

The journal should briefly summarize:

Major points learned

Areas not understood or requiringclarification

Documents

Chap 17 in Class Queuing