Operations Management Waiting Lines
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Operations Management Waiting Lines
description
Operations Management Waiting Lines. Objectives. Understanding the phenomenon of waiting Measures of waiting-line systems Waiting time, number of waiting orders Impact of variability/uncertainty & utilization rate Risk pooling effect in waiting line. The Article. - PowerPoint PPT Presentation
Transcript of Operations Management Waiting Lines
Operations Management
Waiting Lines
2Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines1
Understanding the phenomenon of waiting Measures of waiting-line systems
Waiting time, number of waiting orders Impact of variability/uncertainty & utilization rate Risk pooling effect in waiting line
Objectives
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The Psychology of Waiting Lines About experience of waiting Actual waiting time versus waiting time that feels like
Laws of service Satisfaction = Perception – Expectation It is hard to play catch-up ball
The Article
4Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines1
Unoccupied time feels longer than occupied time Pre-process waits feels longer than in-process waits Anxiety makes waits seem longer Uncertain waits are longer than known, finite waits Unexplained waits are longer than explained waits Unfair waits are longer than equitable waits The more valuable the service, the longer I will wait Solo waiting feels longer than group waiting
Principals of Waiting
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The time of the arrival of an order is not known ahead of time The time a telephone call is made is random
The service time is not known ahead of time The time a customers spends on the web page of
Amazon.com is random The time a customer spends speaking with the teller in
the bank is unknown
Characteristics of Queuing Systems
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This leads to: Idleness of resources Waiting time of customers (orders) to be processed
We are interested in evaluating: Average waiting time in the queue and in the system The average number of orders (customers) waiting to
be processed Waiting time and average number are measures
Characteristics of Queuing Systems
7Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines1
This leads to: Idleness of resources Waiting time of customers (orders) to be processed
We are interested in evaluating: Average waiting time in the queue and in the system The average number of orders (customers) waiting to
be processed Waiting time and average number are measures
Characteristics of Queuing Systems
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Questions: Can we process the orders? How many orders will wait
in the queue? How long will orders wait
in the queue? What is the utilization
rate of the facility?
A Deterministic System: Example 1
Experiment # 1
Arrival time: Service time:0 910 920 930 940 950 960 970 980 990 9
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A Deterministic System: Example 1
Interarrival time Throughput TimeDeparture TimeWaiting Time in Queue9.0 9.0 0.0
10.0 9.0 19.0 0.010.0 9.0 29.0 0.010.0 9.0 39.0 0.010.0 9.0 49.0 0.010.0 9.0 59.0 0.010.0 9.0 69.0 0.010.0 9.0 79.0 0.010.0 9.0 89.0 0.010.0 9.0 99.0 0.0
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A Deterministic System: Example 1
78910
Graph #2: Total #in system:
0
1
2
0 20 40 60 80 100 120
Graph #1: Total time spent in System per Job
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140
TIME
Job
#
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Arrival rate = 1/10 per minutes Processing rate = time 1/9 per minute Utilization – AR/PR = (1/10)/(1/9) = 0.9 or 90% On average 0.9 person is in the system
Utilization
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A Deterministic System: Example 1
Utilization: 90%
Variability: 0.00
Average Throughput time: 9.00 minutes
Average Wait in Queue: 0.00 minutes
Average Number in system: 0.90 jobs
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What if arrivals are not exactly every 10 minutes? Let’s open the spreadsheet.
Known but Uneven Demand: Example 2
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A Deterministic System: Example 2
Graph #1: Total time spent in System per Job
0
2
4
6
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12
0 20 40 60 80 100 120 140
TIME
Job
#
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A Deterministic System: Example 2
Arrival Time
Service Time
Interarrival time
Throughput time Departure
Waiting time in Queue
0 9 9 9 012 9 12 9 21 020 9 8 10 30 134 9 14 9 43 040 9 6 12 52 344 9 4 17 61 851 9 7 19 70 1069 9 18 10 79 185 9 16 9 94 090 9 5 13 103 4
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A Deterministic System: Example 2
Graph #2: Total #in system:
0
1
2
3
4
0 20 40 60 80 100 120
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Observations: 1. Utilization is below 100% (machine is idle 14% of the
time).2. There are 1.12 orders (on average) waiting to be
processed.
A Deterministic System: Example 2
Average Interarrival time 10.000 minutes Utilization 86%
Average Service time 9.000 minutes
Average Throughput Time 11.70
minutes
Std Service time 0.000 minutesAverage Wait in Queue 2.70
minutes
Thoughput rate 0.096jobs / min
Average # in the system 1.12 jobs
Capacity (Service rate) 0.111
jobs / min
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Why do we have idleness (low utilization) and at the same time orders are waiting to be processed?
Answer: Variability
A Deterministic System: Example 2
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How to measure variability?
Coefficient of variation:CV = Standard Deviation / Mean
Known but Uneven Demand: Example 2
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The interarrival time is either 5 periods with probability 0.5 or 15 periods with probability 0.5 Notice that the mean interarrival time is 10. (mean
interarrival = 0.5 * 15 + 0.5 * 5 = 10) The service time is 9 periods (with certainty). The only difference between example 3 and 1 is that
the interarrival times are random.
Uncertain Demand (Interarrival times): Example 3
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Simulation of Uncertain Demand (Inter-arrival times): Example 3
Arrival Start Finish Waiting Idleness
5 5 14 0 0
20 20 29 0 6
25 29 38 4 0
30 38 47 8 0
35 47 56 12 0
40 56 65 16 0
55 65 74 10 0
70 74 83 4 0
75 83 92 8 0
90 92 101 2 0
105 105 114 0 4
120 120 129 0 6
135 135 144 0 6
150 150 159 0 6
165 165 174 0 6
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(Recall that in Example 1, no job needed to wait.)
Uncertain Demand (Interarrival times): Example 3
Average Interarrival time 10.200 minutes
Average Througput time 18.98
Average Service time 9.000 minutes
Average wait in queue 9.98
Std Service time 0.000 minutesAverage # in queue 0.98
Thoughput rate 0.100jobs / min
Average in the system
1.86004
Capacity (Service rate) 0.111
jobs / min
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Suppose we change the previous example and assume: Inter-arrival time 17 0.5 probability Inter-arrival time 3 0.5 probability Average inter-arrival times as before 10 min.
Uncertain Demand (Inter-arrival times): Example 3
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The effect of variability: higher variability in inter-arrival times results in higher average # in queue.
Uncertain Demand (Interarrival times): Example 3
Average Interarrival time
10.200
minutes
Average Througput time 27.94
Average Service time 9.000
minutes
Average wait in queue 18.94
Std Service time 0.000minutes
Average # in queue 1.86
Thoughput rate 0.100jobs / min
Average in the system
2.73812
Capacity (Service rate) 0.111
jobs / min
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Can we manage demand?
What are other sources of variability/uncertainty?
Can we reduce demand variability/uncertainty?
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Up to now, our service time is exactly 9 minutes. What will happen to waiting-line and waiting-time if
we have a short service time (i.e., we have a lower utilization rate)?
What will happen if our service time is longer than 10 minutes?
Uncertain Demand (Inter-arrival times)
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The factors that determine the performance of the waiting lines: Variability Utilization rate Risk pooling effect
Key Concepts and Issues
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In general, if the variability, or the uncertainty, of the demand (arrival) or service process is large, the queue length and the waiting time are also large.
Rule 1
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As the utilization increases the waiting time and the number of orders in the queue increases exponentially.
Rule 2
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In general, pooling the demand (customers) into one common line improves the performance of the system.
Rule 3
