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S P CHHEDA & CO
18-1 Waiting Lines
William J. Stevenson
Operations Management
8th edition
S P CHHEDA & CO
18-2 Waiting Lines
S P CHHEDA & CO
18-3 Waiting Lines
Disney World
Waiting in lines does not add enjoyment
Waiting in lines does not generate revenue
Waiting lines are non-value added occurrences
S P CHHEDA & CO
18-4 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
Waiting lines are non-value added occurrences
S P CHHEDA & CO
18-5 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
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18-6 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 18.1
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18-7 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)
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18-8 Waiting Lines
Elements of Queuing System
Arrivals ServiceWaitingline
Exit
Processingorder
System
Figure 18.2
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18-9 Waiting Lines
Queuing Systems
Multiple channel
Multiple phase
Figure 18.3
Channel: A server in a service system
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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 18.4
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18-11 Waiting Lines
Waiting line Models Patient
Customers enter the waiting line and remain until served Reneging
Waiting customers grow impatient and leave the line Jockeying
Customers may switch to another line Balking
Upon arriving, decide the line is too long and decide not to enter the line
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18-12 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 18.6
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18-13 Waiting Lines
System Performance
1. Average number of customers waiting
2. Average time customers wait
3. System utilization
4. Implied cost
5. Probability that an arrival will have to wait
Measured by:
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18-14 Waiting Lines
1. Single channel, exponential service time
2. Single channel, constant service time
3. Multiple channel, exponential service time
4. Multiple priority service, exponential service time
Queuing Models: Infinite-Source
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18-15 Waiting Lines
Priority Model
Arrivals ServiceWaitingline
Exit
Processingorder
System
11231
Arrivals are assigneda priority as they arrive
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18-16 Waiting Lines
Finite-Source FormulasX
T
T UL N F
WL T U
N L
T F
XFJ NF X
H FNX
N 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 18.6
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18-17 Waiting Lines
Finite-Source Queuing
Not waiting or being served
WaitingBeingserved
J L H
U W T
FJ H
J L H
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18-18 Waiting Lines
Other Approaches
Reduce perceived waiting time Magazines in waiting rooms Radio/television In-flight movies Filling out forms
Derive benefits from waiting Place impulse items near checkout Advertise other goods/services
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