chap 19 waiting lines and simulation
TRANSCRIPT
19-1
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 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
19-2
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Chapter 19
Waiting Lines
19-3
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 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
19-4
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 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
19-5
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Queuing Analysis
Optimum
Cost of service capacity
Cost of customerswaiting
Total cost
Cos
t
Service capacity
Totalcost
Customerwaiting cost
Capacitycost= +
Figure 19-1
19-6
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 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)
19-7
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Elements of Queuing System
Arrivals ServiceWaitingline
Exit
Processingorder
System
19-8
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Queuing Systems
Multiple channel
Multiple phase
19-9
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Poisson Distribution
00.050.1
0.150.2
0.25
0 1 2 3 4 5 6 7 8 9 10 11 12
Figure 19-4
19-10
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 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:
19-11
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Waiting Time vs Utilization
System Utilization
Ave
rage
num
ber o
n tim
e w
aitin
g in
line
0 100%
Figure 19-6
19-12
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 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
19-13
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 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
19-14
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 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
19-15
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Finite-Source Formulas
X TT U
L N F
W L T UN L
T FXF
J NF XH FNXN J L H
(1 )( ) (1 )
(1 )Average number being served
Service factor
Average number waiting
Average waiting time
Average number running
Number in population
Table 19-6
19-16
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Waiting Lines
Finite-Source Queuing
Not waiting or being served Waiting Being
served
J L H
U W T
F J HJ L H