2019/5/12 1 Managing Waiting Lines • The Economies of Waiting • Features of Queuing Systems • Estimating Waiting Times • Waiting Line Management Shin‐Ming Guo NKFUST What are waiting lines and why do they form? Answer: Waiting Lines form due to a temporary imbalance between the demand for service and the capacity of the system to provide the service. Customer population Service system Waiting line Priority rule Service facilities Served customers
Microsoft PowerPoint - Service_Managing_Waiting_Time_2019.pptxWhat
are waiting lines and why do they form?
Answer: Waiting Lines form due to a temporary
imbalance between the demand for service and the
capacity of the system to provide the service.
Customer population
Service system
Waiting line
Priority rule
Service facilities
Served customers
Cost of Waiting
Cost of Capacity
Service Capacity LargeSmall
Total Cost per hour = Cost of Capacity per hour + Cost of Customer Waiting
I. The Operation of a Typical Call Center
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Calls on Hold
Sales reps processing
$$$ Revenue $$$Cost of capacity
Cost per customer
At peak, 80% of calls
dialed received a busy signal.
Customers getting through
had to wait on
average 10 min. .
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5
Caller Arrival Time
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7:10 7:20 7:30 7:40 7:50 8:007:00
caller 1 caller 3 caller 5 caller 7
caller 9 caller 11
caller 2 caller 4 caller 6 caller 8
caller 10 caller 12
0
1
2
3
2 min. 3 min. 4 min. 5 min. 6 min. 7 min.
Service times
N um
be r
of c
as es
7
Inventory (callers on line)
Wait time
Service time
Service Time
1 2 3 4 5 6 7 8 9 10 11 12
0 7 9 12 18 22 25 30 36 45 51 55
5 6 7 6 5 2 4 3 4 2 2 3
Variability: Where does it come from?
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Input • Random arrivals
(randomness is the rule,
not the exception)
• Unpredicted Volume swings • Product Mix •
Incoming quality
Resources • Breakdowns / Maintenance •
Operator absence • Setup times
Tasks • Inherent variation • Lack of SOPs •
Quality (scrap / rework)
Buffer Processing
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Customer Arrival Process
Random arrival rate varying with time
Facility controlled
00:23
01:24
00:34
02:24
00:36
00:38
Time6:01 6:02 6:03 6:04 6:05 6:066:00
Call 1 Call 2 Call 3 Call 4 Call 5 Call 6 Call 7
IA1 IA2 IA3 IA4 IA5 IA6
mean
Modeling Customer Arrivals
Pn = for n = 0, 1, 2,… (T)n
n!
=
Average numbers of arrivals per period
1 aCV
Temporal Variation in Arrival Rates
An arrival process is not stationary if the average number of arrivals in
any given time interval is not fixed over the entire time period.
Queue Configuration
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Round robin Priority Preemptive Processing time
of customers (SPT rule)
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17
3. Mean service rate:
7. Mean number of customers in queue:
8. Mean number of customers in the system:
Begin Service
Reduce Arrival Variability •
appointment/reservation: how to handle late arrivals or noshows
•
encourage customers to avoid peak hours.
Reduce Service Time Variability •
training and technology •
limit service selection •
reduce customer involvement
20
21
Ls 1
Ls 0 0
0.2 0.25
0.5 1
0.8 4
0.9 9
0.99 99
Multiple, Parallel Resources with One Queue
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Time in queue Wq Service Time 1/μ
Time in system Ws=Wq + 1/μ
number in service
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1
24
0
20
40
60
80
100
120
140
160
Number of CSRs
17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
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25
Reducing average waiting time does not
guarantee customer satisfaction.
A small percentage of customers may
experience long waits and complain bitterly.
Solution: service guarantee and/or service
recovery
Perception of Waiting and Service Level
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Perceived Wait Time
Amount of time customers
believe they have waited
prior to receiving service.
Has a greater effect on
customer satisfaction than
actual waiting time
t* 0
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•
That Old Empty Feeling: Unoccupied time goes slowly
•
A Foot in the Door: Preservice waits seem longer that
inservice waits
•
The Light at the End of the Tunnel: Reduce anxiety with
attention
•
Excuse Me, But I Was First: Social justice with FCFS
queue discipline
•
They Also Serve, Who Sit and Wait: Avoids idle service
capacity
Factors Affecting Perceived Wait Times
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Customer’s own tolerance
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1. Determine an acceptable waiting time for your customers
2. Inform your customers of what to expect
3. Try to divert your customer’s attention
4. Segment customers (Din Tai Fung, pay more)
5. Encourage customers to use slack periods
6. Appointment (no show?)
7. Provide limited service or selfservice
8. Provide flexible
service hours or internet access
9. Technology: barcode, OCR, RFID (ETC),
beeper, fast Lane, customer database
10. Take a longterm perspective (redesign the system)
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Summary
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Variability is the norm, not the exception
understand where it comes from and eliminate what you can
Variability leads to waiting times although utilization<100%
Operations benefit from flexibility in capacity
Demand can exhibit seasonality → Time varying capacity
Pooling resources can reduce waiting times
Managing customers’ perceived wait times