Transcript Queuing System

CHAPTER 5
SERVICE
PROCESSES
Learning Objectives
After completing the chapter you will:
 Understand the characteristics of service processes
and how they are different from manufacturing
processes
 Be able to classify service processes
 Understand what waiting line (queuing) analysis is
 Be able to model some common waiting line
situations and estimate server utilization, the
length of the waiting line, and average customer
wait time
DHL’sSupply Chain Services
 DHL offers a variety of value-added supply chain-
related services
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
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
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Order management
Call center management
Global inventory management
Consolidated billing services
Freight and customs solutions
Service Businesses
A service business is the management of
organizations whose primary business
requires interaction with the customer
to produce the service
Classification of Services
 Service organizations are generally classified by
 Who the customer is


E.g., individuals, other businesses
The service they provide

E.g., financial services, health services, transportation services,
and so on
 Not appropriate for OSM purposes because they tell
us little about the process
Classification of Services
 One additional item
 Information to reflect the fact that the customer is involved in
the production system
 Which operationally distinguishes one from another
 The extent of customer contact in the creation of the
service
Classification of Services
 Customer contact
 The physical presence of the customer in the system
 Creation of the service
 The work process involved in providing the service itself
 Extent of contact
 Percentage of time the customer must be in the system relative
to the total time it takes to perform the customer service
Classification of Services
 High degree of customer contact
 More difficult to control and more difficult to rationalize
 The customer can affect
the time of demand,
 the exact nature of the service,
 the quality, or perceived quality, of service

 Low degree of customer contact
Designing Service Organizations
 Distinctive characteristic of services
 We cannot inventory services
 We must meet demand as it arises
 Important design parameter in services
 What capacity should we aim for?
 Assistance of marketing
 It is difficult to separate the OM functions from marketing in
services
Service Encounter
 Service encounter is defined as
 All activities involved in the service delivery process
 Can be configured in a number of different ways
 Structuring service encounter
 Service-system design matrix

6 common alternatives
Service-System Design Matrix
Degree of customer/server contact
High
Buffered
core (none)
Permeable
system (some)
Reactive
system (much)
Low
Face-to-face
total
customization
Face-to-face
loose specs
Sales
Opportunity
Face-to-face
tight specs
Mail contact
Low
Internet &
on-site
technology
Production
Efficiency
Phone
Contact
High
Six alternatives
 Mail contact
 Customers have little interaction with the system
 Allows the system to work more efficiently
 Relatively little opportunity for additional product sales
 Internet and on-site technology
 Internet clearly buffers the company from the customers
 Can provide information and services
 System can be made to interface with real employees
Six alternatives
 Phone contact
 Face-to-face tight specs

Little variation in the service processes

E.g., fast-food restaurant, Disney land
 Face-to-face loose specs

Generally understood processes with options

E.g., full service restaurant, car sales agency
 Face-to-face total customization

Service encounter specs must be developed through some interaction
between the customer and server

E.g., legal and medical services
Extension of Design
of Workers, Operations, and Innovations Relative to the Degree of
Customer/Service Contact
Waiting Line
 A central problem in service settings
 Management of waiting line
 Cost trade-off decision
 Waiting is cost
 Decision could be reduced to dollar terms
Practical View of Waiting Line
Practical View of Waiting Line
 Control arrivals
 Short line, Specific hours for specific customers, Specials
 Control services
 Faster or slower servers, machines, different tooling, material,
layout, faster setup time, etc.
 Waiting lines are
 Not a fixed condition of a productive system
 But are largely within the control of the system management
and design
Practical View of Waiting Line
 Suggestions for managing queues
 Segment the customers
 Train your servers to be friendly
 Inform your customers of what to expect
 Try to divert the customer’s attention when waiting
 Encourage customers to come during slack periods
Queuing System
Customer Arrivals
 Finite population
 Limited-size customer pool
 Probabilities of the customer arrivals varies
 Ex. (Machine maintenance system)

Six machines by one repairperson
 Chance of one of six breaking down is certainly more than that of one of five
breaking down
 Infinite population
 Customer pool size is large enough
 Probability is not significantly affected
 E.g.,
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A repairman with 100 machines
A physician with 1000 patients
A department store with 10000 customers
Distribution of Arrivals
 The manner in which customers (or the waiting units)
are arranged for service
 Arrival rate


The number of units per period (λ)
Types
Constant arrival distribution
 Variable arrival distribution

 Two viewpoints for arrivals

Time between successive arrivals


~exponentially distributed
The number of arrivals per time

~Poison distributed
Exponential Distribution
Exponential Distribution
Poisson Distribution
Exponential and Poisson
 Continuous, discrete distribution
 Mean and variance?
 Can be derived from one another
Other Arrival Characteristics
 Arrival Patterns
 Controllable
Extra charge for Saturday service
 Off season sales, one-day-only sales
 Excursion and off-season rates
 Posting of business hours

 Uncontrollable
 Emergency medical demand
Other Arrival Characteristics
 Size of arrival units
 Single
 Batch
 Degree of patience
 Patient
 Impatient
Balking
 Reneging

Degree of Patience
No Way!
BALK
No Way!
RENEG
Arrival Characteristics
Queuing System
 Queuing system consists of
 Waiting line(s)
 Available number of servers
 Issues
 Waiting line characteristics and management
 Line structure
 Service rate
Waiting Lines
 Three factors
Queue Discipline
 Two major practical problems
 Customers know and follow the rules
 A system exists to enable employees to manage the line
Service Time Distribution
 Service time

Time that the customer or unit spends with the server once the
service has started
 Service rate

The capacity of the server in number of units per time period
 Types of service time
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Constant
Random
Exponentially distributed
 μ: Average number of units or customers that can be served per time
period
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Line Structures
Line Structures
 Single channel, single phase

One-person barbershop
 Single channel, multiphase

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Car wash
A critical factor is the amount of buildup of items allowed in front of
each service
 Multichannel, single phase


Tellers’ windows
Difficulty: unequal flow among the lines

Forming a single line
Line Structures
 Multichannel, multiphase

Admission of patients in a hospital
 Mixed

Multi-to-single channel
Bridge-crossing
 Subassembly lines feeding into a main line

 Alternative paths


Multichannel-multiphase with channel switch
Number of channels and phase vary after performance of the first
service
Examples of Line Structures
Single
Phase
One-person
Single Channel
barber shop
Multichannel
Bank tellers’
windows
Multiphase
Car wash
Hospital
admissions
Exiting
 Two exit fates
 Return to the source population


Routine repair of a machine
Low probability of reservice

Overhauling a machine
Waiting Line Models
 Three basic cases
The Queuing System
Length
Queue Discipline
Queuing
System
Service Time
Distribution
Number of Lines &
Line Structures
Notations
Example: Model 1
Assume a drive-up window at a fast food restaurant.
Customers arrive at the rate of 25 per hour.
The employee can serve one customer every two
minutes.
Assume Poisson arrival and exponential service
rates.
Determine:
A) What is the average utilization of the employee?
B) What is the average number of customers in line?
C) What is the average number of customers in the
system?
D) What is the average waiting time in line?
E) What is the average waiting time in the system?
F) What is the probability that exactly two cars will be
in the system?
Example: Model 1
A) What is the average utilization of the
employee?
 = 25 cust / hr
1 customer
 =
= 30 cust / hr
2 mins (1hr / 60 mins)

25 cust / hr
 =
=
= .8333

30 cust / hr
Example: Model 1
B) What is the average number of customers in
line?

(25)
Lq =
=
= 4.167
 (  -  ) 30(30 - 25)
2
2
C) What is the average number of customers in the
system?

25
Ls =
=
=5
 -  (30 - 25)
Example: Model 1
D) What is the average waiting time in line?
Wq =
Lq

= .1667 hrs = 10 mins
E) What is the average waiting time in the system?
Ws =
Ls

= .2 hrs = 12 mins
Example: Model 1
F) What is the probability that exactly two cars
will be in the system (one being served and the
other waiting in line)?
pn
 
= (1 - )( )
 
n
25 25 2
p 2 = (1- )( ) = .1157
30 30
Example: Model 2
An automated pizza vending machine
heats and
dispenses a slice of pizza in 4 minutes.
Customers arrive at a rate of one every 6
minutes with the arrival rate exhibiting a
Poisson distribution.
Determine:
A) The average number of customers in line.
B) The average total waiting time in the system.
Example: Model 2
A) The average number of customers in line.
2
(10) 2
Lq =
=
= .6667
2 (  -  ) (2)(15)(15 - 10)
B) The average total waiting time in the system.
Lq
.6667
Wq =
=
= .06667 hrs = 4 mins

10
1
1
Ws = Wq + = .06667 hrs +
= .1333 hrs = 8 mins

15/hr
Example: Model 3
Recall the Model 1 example:
Drive-up window at a fast food restaurant.
Customers arrive at the rate of 25 per hour.
The employee can serve one customer
every two minutes.
Assume Poisson arrival and exponential
service rates.
If an identical window (and an identically trained
server) were added, what would the effects be on
the average number of cars in the system and the
total time customers wait before being served?
Example: Model 3
Average number of cars in the system
Lq = 0.176
(Exhibit TN7.11 - -using linear interpolat ion)

25
Ls = Lq + = .176 + = 1.009

30
Total time customers wait before being served
Lq
.176 customers
Wq =
=
= .007 mins ( No Wait! )
 25 customers/ min
Queuing Approximation
This approximation is quick way to analyze a queuing situation. Now,
both interarrival time and service time distributions are allowed to be
general.
 In general, average performance measures (waiting time in queue,
number in queue, etc) can be very well approximated by mean and
variance of the distribution (distribution shape not very important).
 This is very good news for managers: all you need is mean and standard
deviation, to compute average waiting time

Define:
Standard deviation of X
Mean of X
Variance
2
Cx2  squared coefficient of variation (scv) = Cx  
mean2
Cx  coefficient of variation for r.v. X =
Queue Approximation
Inputs: S, , , Ca2 ,Cs2
(Alternatively: S, , , variances of interarrival and service time distributions)

Compute  
S

2( S 1)
Ca2  Cs2
Lq 

1 
2
as before, Wq 
Ls  Lq  S 
Lq

, and Ws 
Ls

Approximation Example
 Consider a manufacturing process (for example making
plastic parts) consisting of a single stage with five machines.
Processing times have a mean of 5.4 days and standard
deviation of 4 days. The firm operates make-to-order.
Management has collected date on customer orders, and
verified that the time between orders has a mean of 1.2 days
and variance of 0.72 days. What is the average time that an
order waits before being worked on?
Using our “Waiting Line Approximation” spreadsheet we
get:
Lq = 3.154 Expected number of orders waiting to be completed.
Wq = 3.78 Expected number of days order waits.
Ρ = 0.9 Expected machine utilization.
Question Bowl
a.
b.
c.
d.
e.
Which of the following is an example
of a Service Business?
Law firm
Hospital
Bank
Retail store
All of the above
Question Bowl
a.
b.
c.
d.
e.
Based on the Service-System Design
Matrix, which of the following has a
lower level of “production
efficiency”?
Face-to-face loose specs
Phone contact
Internet and on-site technology
Face-to-face tight specs
Mail contact
Question Bowl
The central problem for virtually all queuing
problems is which of the following?
a. Balancing labor costs and equipment
costs
b. Balancing costs of providing service with
the costs of waiting
c. Minimizing all service costs in the use of
equipment
d. All of the above
e. None of the above
Question Bowl
Customer Arrival “populations” in a
queuing system can be characterized
by which of the following?
a. Poisson
b. Infinite
c. Patient
d. FCFS
e. None of the above
Question Bowl
Customer Arrival “rates” in a queuing
system can be characterized by
which of the following?
a. Constant
b. Infinite
c. Finite
d. All of the above
e. None of the above
Question Bowl
An example of a “queue discipline” in a queuing
system is which of the following?
a. Single channel, multiphase
b. Single channel, single phase
c. Multichannel, single phase
d. Multichannel, multiphase
e. None of the above
Question Bowl
Withdrawing funds from an automated
teller machine is an example in a queuing
system of which of the following “line
structures”?
a. Single channel, multiphase
b. Single channel, single phase
c. Multichannel, single phase
d. Multichannel, multiphase
e. None of the above
Question Bowl
Refer to Model 1 in the textbook. If the
service rate is 15 per hour, what is the
“average service time” for this
queuing situation?
a. 16.00 minutes
b. 0.6667 hours
c. 0.0667 hours
d. 16% of an hour
e. Can not be computed from data above
Question Bowl
Refer to Model 1 in the textbook. If the
arrival rate is 15 per hour, what is the
“average time between arrivals” for
this queuing situation?
a. 16.00 minutes
b. 0.6667 hours
c. 0.0667 hours
d. 16% of an hour
e. Can not be computed from data above
Summary
 Classification of services
 Service-system design matrix
 Economics of the waiting line problem
 Queuing system
End of Chapter 5