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19-1 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines
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Transcript of 19-1 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati...
19-1
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
19-2
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
WAITING LINES AND SIMULATION
PART SEVEN
•Chapter Nineteen•Waiting Lines
•Chapter 19 Supplement•Simulation
19-3
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Chapter 19
Waiting Lines
19-4
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Waiting Lines
• Queuing theory: Mathematical approach to the analysis of waiting lines.
• Goal of queuing analysis is to minimize the sum of two costs
– Customer waiting costs
– Service capacity costs
19-5
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
• Cost to provide waiting space• Loss of business
– Customers leaving– Customers refusing to wait
• Loss of goodwill• Reduction in customer satisfaction• Congestion may disrupt other business
operations
Implications of Waiting Lines
19-6
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Queuing Analysis
Optimum
Cost of service capacity
Cost of service capacity
Cost of customerswaiting
Cost of customerswaiting
Total costTotal cost
Co
st
Service capacity
Totalcost
Customerwaiting cost
Capacitycost= +
Figure 19-1
19-7
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
System Characteristics
• Population Source– Infinite source: customer arrivals are
unrestricted– Finite source: number of potential
customers is limited
• Number of observers (channels)
• Arrival and service patterns
• Queue discipline (order of service)
19-8
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Elements of Queuing System
Arrivals ServiceWaitingline
Exit
Processingorder
System
19-9
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Queuing Systems
Multiple channel
Multiple phase
19-10
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Poisson Distribution
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6 7 8 9 10 11 12
Figure 19-4
19-11
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
System Performance
• Average number of customers waiting
• Average time customers wait
• System utilization
• Implied cost
• Probability that an arrival will have to wait
Measured by:
19-12
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Waiting Time vs. Utilization
System Utilization
Av
era
ge
nu
mb
er o
n
tim
e w
ait
ing
in li
ne
0 100%
Figure 19-6
19-13
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
• Single channel, exponential service time
• Single channel, constant service time
• Multiple channel, exponential service time
• Multiple priority service, exponential service time
Queuing Models: Infinite-Source
19-14
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Queuing Models
• Single channel, exponential service time
• Single channel, constant service time
• Multiple channel, exponential service time
• Multiple priority service
19-15
McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Priority Model
Arrivals ServiceWaitingline
Exit
Processingorder
System
11231
Arrivals are assigneda priority as they arrive
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McGraw-Hill RyersonOperations Management, 2nd Canadian Edition, by Stevenson & HojatiCopyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Finite-Source Queuing
Not waiting or being served
WaitingBeingserved
J L H
U W T
FJ H
J L H
