Time Response Planning
Stephen Shum
ISOM - HKUST
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Stephen Shum - HKUST
Where does our time go?
In a life time, the average
American will spend-SIX MONTHS: Waiting at stoplights
EIGHT MONTHS: Opening junk mail
ONE YEAR: Looking for misplaced objects
TWO YEARS: Unsuccessfully returning phone calls
FOUR YEARS: Doing housework
FIVE YEARS: Waiting in line
SIX YEARS: Eating
Source: US News & World Report, January 30, 1989, p. 81.
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Firms Perspective
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Stephen Shum - HKUST
Course Structure
Design
Plan
Deliver
Manufacturing
& Service
Planning
Improve
Basics
Capacity
Planning
Model
Response
Time
Planning
Customer
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Stephen Shum - HKUST
HK Immigration Booths
Travelers arrive EXACTLY every 6
minutes.
The officer needs EXACTLY 6
minutes to process each traveler.
There is one officer.
What happens if 10 travelers arrive in the first hour and 6 travelers arrive in
the second hour?
What happens if the service times of three consecutive travelers are 8, 5 and 5
minutes respectively?
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Stephen Shum - HKUST
Impact of Variability
Without Variability
1
2
3
1
4
2
5
3
4
5
With Variability
1
2
3
4
1
0
1
2
2
1
3
010
6
5
4
5
0
Stephen Shum - HKUST
Server Utilization
Server utilization
average arrival rate
average p otential service rate
average busy time
t otal available t ime
Example:
There are 2 counters. The average arrival rate is 10 per
hour. The average service time is 10 minutes.
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Throughput Delay Curve
Average
Customer
Flow Time
Utilization Effect + Variability Effect
High Variability
Medium Variability
Low Variability
Service
Time
No Variability
Utilization ()
100%
r
Trade-off between asset utilization and service quality.
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How to Reduce Waiting Time?
Safety
Capacity
Variability
Reduction
Waiting
Time
Reduction
Safety Capacity
capacity carried in excess of expected demand to cover
for system variability
Reduction in variability
How?
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Stephen Shum - HKUST
Course Structure
Design
Plan
Deliver
Manufacturing
& Service
Planning
Improve
Basics
Capacity
Planning
Model
Response
Time
Planning
Customer
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Stephen Shum - HKUST
The Queuing Process Model
L=Lq+Ls
Queue
Length (Lq)
Inventory (L)
Number in
Service (Ls)
Throughput
Rate (R)
Servers
providing
service
Incoming customers
Customers
on hold
Queue Time (Wq)
Service Time (Ws)
Departing customers
W=Wq+Ws
Flow Time (W)
From Littles Law: L = RW, Lq=RWq, Ls=RWs
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Stephen Shum - HKUST
Queuing Model Parameters
Service
Rate ()
Arrival
Rate ()
Incoming customers
Customers
on hold
Servers
providing
service
Departing customers
Number of
Servers (S)
X/X/X
Number of servers
Service time pattern
Arrival pattern
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For this course
M / D/ n
M / M/ n
Random
Random
Service time
No variability
Random
# of servers
Any (n)
Any (n)
Arrival
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Measuring Customer Arrivals
Inter-arrival time:
time between the arrivals of 2 consecutive customers
1
2
3
4
5
Arrival rate:
Number of arrivals in each period (e.g., minute, hour)
1
2
Period 1
3
Period 2
4
Period 3
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Period 4
5
Period 5
Stephen Shum - HKUST
Random Arrival and Service
Processes
Inter-arrival
time (min)
Service time
(min)
Customer
Arrival time
1
9:00 am
2
9:05 am
5
6
3
9:15 am
10
3
4
9:18 am
3
5
5
9:24 am
6
2
6
9:32 am
8
5
7
9:36 am
4
4
4
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Arrival Process
Probability Distribution
Example
Mean arrival rate () ~ Poisson
3 customers per hour
Mean inter-arrival time (1/) ~ Exponential
customer
20 minutes per
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Pizza Vending Machine
An automated pizza vending
machine heats and dispenses a slice
of pizza in 4 minutes (with no
variability).
Customers arrive randomly at an
average rate of one every 6 minutes.
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Stephen Shum - HKUST
Those formula will be applicable
when The arrival rate must equal
to the service rate
M/D/1 Queuing Model
Inventory (# of
customers)
Average flow
time
In the queue
Receiving service
Total
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Pizza Vending Machine
A) The average number of customers waiting in line.
B) The average amount of time a customer waits
before getting the pizza from the machine.
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Ollivanders Wand Shop
Customers arrive randomly at the
average rate of 25 per hour.
Different customers need a different
amount of time to come to a
matching wand. On average, it takes
2 minutes for Garrick Ollivander to
find a matching wand for a customer.
1. What is the fraction of time
Garrick Ollivander is busy?
2. On average, how long does each
customer have to wait in line?
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M/M/1 Queuing Model
Inventory (# of
customers)
Provided on the
table in the exam
Average flow
time
In the queue
Receiving service
Total
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Stephen Shum - HKUST
Ollivanders Wand Shop
1. What is the fraction of time Garrick Ollivander
is busy?
2. On average, how long does each customer
have to wait in line?
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Ollivanders Wand Shop
Customers arrive randomly at the
average rate of 25 per hour.
Different customers need a different
amount of time to come to a
matching wand. On average, it takes
Garrick Ollivander to find a matching
wand for a customer.
If Garrick Ollivander hires a shop
assistant, so that each can serve one
customer at any time. What is the
average waiting time of customers?
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M/M/n Queuing Model
Inventory (# of
customers)
Average flow
time
In the queue
Receiving service
Total
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Stephen Shum - HKUST
Ollivanders Wand Shop
If Garrick Ollivander hires a shop assistant, so that each
can serve one customer at any time. What is the average
waiting time of customers?
Lq 0.176
Lq
.176 customers
Wq =
=
= .007hour / 0.4 min
25 customers/hour
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Ollivanders Wand Shop
What is the Benefit of Adding an Extra Employee?
1 Employee
Average Queue
Length
Average Number
of Customers
Average Waiting
Time
2 Employees
4.167
0.176
5
1.009
10 min
0.4 min
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Stephen Shum - HKUST
The Secretary Problem
There are two professors two and secretaries. On average, each
professor writes 4 documents per hour and each secretary types 5
documents per hour.
Suppose each secretary works for only one professor. How long
does a document wait on average before being typed by the
secretary?
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Stephen Shum - HKUST
The Effect of Pooling
Suppose the secretaries are pooled. That is, each secretary can
work for any one of the two professors. What is the average waiting
time of a document?
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Stephen Shum - HKUST
Emergency Room Staffing
The average arrival rate the emergency room of Queen Elizabeth
Hospital is 5.9 patients per hour
Average time spent by a doctor with a patient is 29 minutes. That is,
each doctor can serve an average of (60/29) = 2.07 patients per
hour.
The Hospital Authority wants the average waiting time to be no more
than 15 minutes.
What is the minimum number of doctors in the emergency room?
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Stephen Shum - HKUST
Reducing Waiting Time
Some patient group requests the Hospital Authority to reduce the
average waiting time to no more than 1 minute.
The Hospital Authority replies, This means reducing the average
time by 15 times, and hence increasing the number of doctors by 15
times.
Is that correct?
Dont be fooled!
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Stephen Shum - HKUST
Assumptions of the Queuing
Models
Buffer with Unlimited Size
Customers arrive independently of one
another
Inter-arrival times are independent
# of arrivals for different periods are
independent
Infinite population
No balking
No reneging
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Simulation models
A computer-based model for running experiments on a
real system:
Typically done on a computer using random number
generator to represent different events and activity times
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Advantages of simulation
models
A better understanding of the real system
Years of experience in the real system can be
compressed into seconds or minutes of computer time
Simulation does not disrupt ongoing activities of the real
system
Simulation can be used as a game for training experience
Simulation is far more general than mathematical
models
Simulation provides a more realistic replication of a
system than mathematical analysis
Simulation can be used to analyze transient conditions,
whereas mathematical techniques usually cannot
Simulation answers what-if questions
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Stephen Shum - HKUST
Disadvantages of simulation
models
Limitations on constructing simulation models
Building a simulation model can take time
Simulation may be less accurate than mathematical
analysis because it is randomly based
A significant amount of computer time may be
needed to run complex models
The technique of simulation still lacks a standardized
approach
Applicability of the model results
No guarantee that the model will indeed provide
good answers
Difficult to prove reliability
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Simulation and Model
Web link for a demo
http://staff.um.edu.mt/jskl1/simweb/simmm1.html
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Stephen Shum - HKUST
Queue Configurations
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Stephen Shum - HKUST
Course Structure
Design
Plan
Deliver
Manufacturing
& Service
Planning
Improve
Basics
Capacity
Planning
Model
Response
Time
Planning
Customer
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Stephen Shum - HKUST
Psychology of Waiting
Uncertain wait feels longer
Inform and update customers expected waiting time
Unexplained wait feels longer
Explain to customers the reasons for long waits
Unoccupied time feels longer
Install distractions that entertain and involve
customers
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Stephen Shum - HKUST
Psychology of Waiting
Preprocess wait feels longer
Convert preprocess wait to in-process wait
Anxiety makes waiting feel longer
Keep resources not serving customers out of sight
Unfair wait feels longer
Practice a fair waiting system, first-come first-served
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Stephen Shum - HKUST
Psychology of Waiting
Wait Longer for more Valuable Service
Never underestimate the power of a friendly server
Solo wait feels longer
Any suggestion?
The psychological experience of waiting is
complex but manageable.
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Stephen Shum - HKUST
Managing Customers at
Bank Branches
Banks have spent huge sums
refurbishing their branches, often
without a clear payback. They
should devote more effort to
managing customer visits.
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Stephen Shum - HKUST
Emotional Value Propositions
Wow comes from choosing
empathy over optimization
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Stephen Shum - HKUST
Managing Customers
Expectations
Satisfaction = Perception Expectation
Three basic questions for a service managers:
1. What is actually done?
2. What is perceived by the customer?
3. What is expected by the customer?
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After all,
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Cycle of Service Encounters
Customer requests
schedule information
Leaves
Airport
Makes
reservation
Receives
Baggage
Departs
Plane
Receives
in-flight
service
Arrives at
airport
Customer contact = moment of
truth
Checks
baggage and
checks in for
flight
Perceived service
= f(all previous moments of
truth)
Handoffs
between steps
critical!
Proceeds to gate
and security check
Boards
aircraft
Receives
boarding pass
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Stephen Shum - HKUST
Service Fail-safing: Poka Yokes
Poka-Yokes:
Japanese word
meaning avoid
mistakes
Keeping a mistake
from becoming a
service defect
Task
Treatment
Tangibles
How can we failsafe the three Ts?
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Have we compromised one of
the 3 Ts?
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Stephen Shum - HKUST
Corporate Culture
The master said, Govern the people by regulations, keep order
among them by chastisements, and they will flee from you, and
lose all self-respect. Govern them by moral force, keep order
among them by ritual, and they will keep their self-respect and
come to you of their own accord.
Ritz-Carlton, We are ladies and gentlemen serving ladies and
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gentlemen.
Internal Customers
Internal Supplier
Internal
Customer
External
Customer
Internal Supplier
How management treats a
worker is how the worker treats
the customer
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Stephen Shum - HKUST
To-Do List
Exercise
Books
OSM:
(2nd) p.103-125
(1st) p.111-129
Problems on Queuing
Models
OPM: p.156-161, 170177
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Stephen Shum - HKUST