Transcript Production and Operations Management: Manufacturing and

Chapter 7 TN
Waiting Line Management
 Waiting
 Some
line characteristics
waiting line management tips
 Examples
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(Models 1, 2, 3, and 4)
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Suggestions for Managing Queues
 Do
not overlook the effects of perceptions
management.
 Determine the acceptable waiting time for your
customers.
 Install distractions that entertain and physically
involve the customer.
 Get customers out of line.
 Only make people conscious of time if they grossly
overestimate waiting times.
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Suggestions for Managing Queues
 Modify
 Keep
customer arrival behavior.
resources not serving customers out of sight.
 Segment
customers by personality types.
 Adopt
a long-term perspective.
 Never
underestimate the power of a friendly server.
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Components of the Queuing Phenomenon
Servicing System
Servers
Customer
Arrivals
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Waiting Line
Exit
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Population Sources
Population Source
Finite
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Infinite
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Service Rate
Service
Rate
Constant
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Variable
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Line Structures
Single
Phase
Multiphase
Single Channel
One-person
barber shop
Car wash
Multichannel
Bank tellers’
windows
Hospital
admissions
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Degree of Patience
No Way!
BALK
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No Way!
RENEG
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Waiting Line Models
Model
1
Layout
Single channel
Source
Population
Infinite
2
Single channel
Infinite
Constant
3
Multichannel
Infinite
Exponential
4
Single or Multi
Finite
Exponential
Service Pattern
Exponential
These four models share the following characteristics:
 Single phase
 Poisson arrival
 FCFS
 Unlimited queue length
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Example: Model 1
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.
A)
B)
C)
D)
E)
F)
What is the average utilization of the employee?
What is the average number of customers in line?
What is the average number of customers in the system?
What is the average waiting time in line?
What is the average waiting time in the system?
What is the probability that exactly two cars will be
waiting in line?
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Example: Model 1
A) What is the average utilization of the employee?
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Example: Model 1
B) What is the average number of customers in line?
C) What is the average number of customers in the system?
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Example: Model 1
D) What is the average waiting time in line?
E) What is the average waiting time in the system?
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Example: Model 1
F) What is the probability that exactly two cars will be
waiting in line?
pn
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 
= (1 - )( )
 
n
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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.
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Example: Model 2
A) The average number of customers in line.
B) The average total waiting time in the system.
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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?
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Example: Model 3
Average number of cars in the system

n = n +

s
l
Total time customers wait before being served
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