Two MSOM online homework
ZYBH
md_waiting-line_model.ppt© 2006 Prentice Hall, Inc.
D – *
Operations Management
Module D –
Waiting-Line Models
© 2006 Prentice Hall, Inc.
PowerPoint presentation to accompany
Heizer/Render
Principles of Operations Management, 6e
Operations Management, 8e
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© 2006 Prentice Hall, Inc.
D – *
Outline
- Characteristics Of A Waiting-Line System
- Arrival Characteristics
- Waiting-Line Characteristics
- Service Facility Characteristics
- Measuring the Queue’s Performance
- Queuing Costs
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© 2006 Prentice Hall, Inc.
D – *
Learning Objectives
When you complete this module, you should be able to:
Identify or Define:
- The assumptions of the four basic waiting-line models
- How to apply waiting-line models
- How to conduct an economic analysis of queues
Describe or Explain:
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© 2006 Prentice Hall, Inc.
D – *
Common Queuing Situations
Table D.1
| Situation | Arrivals in Queue | Service Process |
| Supermarket | Grocery shoppers | Checkout clerks at cash register |
| Highway toll booth | Automobiles | Collection of tolls at booth |
| Doctor’s office | Patients | Treatment by doctors and nurses |
| Computer system | Programs to be run | Computer processes jobs |
| Telephone company | Callers | Switching equipment to forward calls |
| Bank | Customer | Transactions handled by teller |
| Machine maintenance | Broken machines | Repair people fix machines |
| Harbor | Ships and barges | Dock workers load and unload |
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This slide provides some reasons that capacity is an issue. The following slides guide a discussion of capacity.
© 2006 Prentice Hall, Inc.
D – *
Characteristics of Waiting-Line Systems
- Arrivals or inputs to the system
- Population size, behavior, statistical distribution
- Queue discipline, or the waiting line itself
- Limited or unlimited in length, discipline of people or items in it
- The service facility
- Design, statistical distribution of service times
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This slide provides some reasons that capacity is an issue. The following slides guide a discussion of capacity.
© 2006 Prentice Hall, Inc.
D – *
Arrival Characteristics
- Size of the population
- Unlimited (infinite) or limited (finite)
- Behavior of arrivals
- Scheduled or random, often a Poisson distribution
- Behavior of arrivals
- Wait in the queue and do not switch lines
- Balking or reneging
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This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Parts of a Waiting Line
Figure D.1
Arrival Characteristics
- Size of the population
- Behavior of arrivals
- Statistical distribution of arrivals
Waiting Line Characteristics
- Limited vs. unlimited
- Queue discipline
Service Characteristics
- Service design
- Statistical distribution of service
Dave’s
Car Wash
enter
exit
Population of
dirty cars
Arrivals
from the
general
population …
Queue
(waiting line)
Service
facility
Exit the system
Arrivals to the system
Exit the system
In the system
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Waiting-Line Characteristics
- Limited or unlimited queue length
- Queue discipline - first-in, first-out is most common
- Other priority rules may be used in special circumstances
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Service Characteristics
- Queuing system designs
- Single-channel system, multiple-channel system
- Single-phase system, multiphase system
- Service time distribution
- Constant service time
- Random service times, usually a negative exponential distribution
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Queuing System Designs
Figure D.3
Single-channel, single-phase system
Single-channel, multiphase system
Your family dentist’s office
McDonald’s dual window drive-through
Departures
after service
Queue
Arrivals
Arrivals
Departures
after service
Phase 1 service facility
Phase 2 service facility
Service facility
Queue
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Queuing System Designs
Figure D.3
Multi-channel, single-phase system
Most bank and post office service windows
Arrivals
Queue
Departures
after service
Service facility
Channel 1
Service facility
Channel 2
Service facility
Channel 3
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Queuing System Designs
Figure D.3
Multi-channel, multiphase system
Some college registrations
Arrivals
Queue
Departures
after service
Phase 2 service facility
Channel 1
Phase 2 service facility
Channel 2
Phase 1 service facility
Channel 1
Phase 1 service facility
Channel 2
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Measuring Queue Performance
- Average time that each customer or object spends in the queue
- Average queue length
- Average time in the system
- Average number of customers in the system
- Probability the service facility will be idle
- Utilization factor for the system
- Probability of a specified number of customers in the system
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Queuing Models
Table D.2
Model Name Example
A Single channel Information counter
system at department store
(M/M/1)
Number Number Arrival Service
of of Rate Time Population Queue
Channels Phases Pattern Pattern Size Discipline
Single Single Poisson Exponential Unlimited FIFO
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Queuing Models
Table D.2
Model Name Example
B Multichannel Airline ticket
(M/M/S) counter
Number Number Arrival Service
of of Rate Time Population Queue
Channels Phases Pattern Pattern Size Discipline
Multi- Single Poisson Exponential Unlimited FIFO
channel
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Queuing Models
Table D.2
Model Name Example
C Constant Automated car
service wash
(M/D/1)
Number Number Arrival Service
of of Rate Time Population Queue
Channels Phases Pattern Pattern Size Discipline
Single Single Poisson Constant Unlimited FIFO
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Queuing Models
Table D.2
Model Name Example
D Limited Shop with only a
population dozen machines
(finite) that might break
Number Number Arrival Service
of of Rate Time Population Queue
Channels Phases Pattern Pattern Size Discipline
Single Single Poisson Exponential Limited FIFO
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Model A - Single Channel
- Arrivals are FIFO and every arrival waits to be served regardless of the length of the queue
- Arrivals are independent of preceding arrivals but the average number of arrivals does not change over time
- Arrivals are described by a Poisson probability distribution and come from an infinite population
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
© 2006 Prentice Hall, Inc.
D – *
Model A - Single Channel
- Service times vary from one customer to the next and are independent of one another, but their average rate is known
- Service times occur according to the negative exponential distribution
- The service rate is faster than the arrival rate
*
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
