Transcript Class 3

Operations Management
Queuing (Part 2) - Lecture 7
(Chapter 8)
Dr. Ursula G. Kraus
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Review
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Performance Measures for Queuing
Systems
Special Queuing Model: M/M/1
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Agenda
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Review: General Queuing Models
Special Queuing Models
SofOptics
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Agenda
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Review: General Queuing Models
Special Queuing Models
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Example: Calling Center
Consider a mail order company that has one customer service representative
(CSR) taking calls. When the CSR is busy, the caller is put on hold. The calls
are taken in the order received.
Each minute a caller spends on hold costs the company $2 in telephone
charges, customer dissatisfaction and loss of future business. In addition, the
CSR is paid $20 an hour.
Assume that calls arrive exponentially at the rate of one every 3 minutes. The
CSR takes on average 2.5 minutes to complete the order. The time for service
is also assumed to be exponentially distributed.
(a) What is the capacity utilization?
(b) How many customers will be on average on hold?
(c) What is the average time spent on hold?
(d) Estimate the average hourly cost of operating the call center.
Source: Managing Business Process Flows (1999)
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Expected costs
Cost of Service Tradeoff
Total cost
(Service)
Capacity Cost
(Customer)
Waiting Cost
Level of service
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Example: Ticket Outlet
Customers arrive at a suburban ticket outlet at a rate of 14
per hour on Monday mornings. Selling the tickets and
providing general information takes an average of 3
minutes per customer. There is one ticket agent on duty on
Mondays. Assume exponential interarrival and service
times.
a)
b)
c)
d)
What percentage of time is the ticket agent busy?
How many customers are in line, on average?
How many minutes, on average, will a customer spend in
the system?
What is the average waiting time in queue?
Source: Managing Business Process Flows (1999)
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Performance Measures to Focus on
 Sales
– Throughput (R)
– Abandoning rate (Ra )
 Cost
– Capacity utilization (r)
– Queue length (Iq) ; Total number in process (I)
 Customer Service
– Waiting time in queue (Tq ); Total time in process (T)
– Blocking rate (Rb )
Source: Managing Business Process Flows (1999)
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Levers for System Improvements
 Increase process capacity Rp
– adding more servers
– working faster (decreasing Tp)
 Reduce waiting time Tq and queue length Iq
– reduce variability
– decrease arrival rate (not desirable in general)
Source: Managing Business Process Flows (1999)
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Example: Calling Center
with 2 CSRs (2 servers)
2 phone numbers
I.
–
Company hires a second CSR who is assigned
a new telephone number. Customers are now
free to call either of the two numbers. Once
they are put on hold customers tend to stay on
line since the other may be worse
50%
Queue Server
50%
Queue Server
1 phone number: pooling
II.
–
Both CSRs share the same telephone number
and the customers on hold are in a single queue
Queue
Servers
Source: Managing Business Process Flows (1999)
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Agenda
•
•
•
Review: General Queuing Models
Special Queuing Models
SofOptics
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