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Waiting Lines:Queuing Analysis, System Characteristics, Priority Model

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Production and Operations Management ­MGT613
VU
Lesson 45
Waiting Lines
Learning Objectives
After completing the lecture, we should be able to explain the formation of waiting lines in unloaded
systems, identify the goal of queuing ( waiting line) analysis, list the measures of system performance
that are used in queuing analysis. We should be able to understand the importance of simulation and at
the same time we should look beyond the Production Operations Management class as business
graduate professionals adding value to the society.
Visit to a Cricket Stadium
1. Waiting in lines does not add enjoyment
2. Waiting in lines does not generate revenue
3. Waiting Lines
4. Waiting lines are non-value added occurrences
5. Are formed at airports, cricket stadiums, post offices.
6. Formed due to non scheduled random arrivals
7. Often regarded as poor service quality
Waiting Line Examples
1.
Orders waiting to be filled
2.
Trucks waiting to be loaded or unloaded
3.
Job waiting to be processed
4.
Equipment waiting to be loaded
5.
Machines waiting to be repaired.
Service Station as a Waiting Line Example
Service station is usually designed to provide service on average service time. At macro level system is
unloaded at micro level the system is overloaded a Paradox
Customers arrive at random rate
Service requirements vary only oil change or even tuning or maintenance activity in order to change oil
Waiting Lines
Queuing theory: Mathematical approach to the analysis of waiting lines.
1. Goal of queuing analysis is to minimize the sum of two costs Customer waiting costs and
Service capacity costs.
2. Waiting lines are non-value added occurrences
Implications of Waiting Lines
1. Cost to provide waiting space
2. Loss of business
a. Customers leaving
b. Customers refusing to wait
3. Loss of goodwill
4. Reduction in customer satisfaction
5. Congestion may disrupt other business operations
Queuing Analysis
Organizations carry out queuing analysis to ensure that they are able to balance the service levels with
costs which the organization can incur. The ultimate goal of queuing analysis is to minimize the sum of
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two costs that is the service capacity cost ( represented on x axis) and customer waiting
Capacity
Total
Customer
=
+
waiting cost
cost
cost
Cost
Total cost
Cost of
Service
Capacity
Cost of
Customers
Waiting
Service capacity
Optimum
costs.
Negative Exponential Distribution: Another example of Common Queuing System
F(t)
Pt≥T)=.RN
(
0
T
t
Queue discipline is considered to be a primary requirement in service systems. However hospital
emergency rooms, rush orders in a factory and main frame computer processing of jobs do not follow
Queue Discipline.
System Characteristics
1. Population Source
a. Infinite source: customer arrivals are unrestricted
b. Finite source: number of potential customers is limited
2. Number of observers (channels)
3. Arrival and service patterns
4. Queue discipline (order of service)
Elements of Queuing System
Population Source, Arrivals, Waiting Lines, Processing Order, Service, System and Exit are the
common identifiable elements of a Queuing System.
Processing
Order
Waiting
Arrivals
Service
Exit
Line
System
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Queuing Systems
The System characteristics are
1. Population Source
2. Number of Servers( Channels)
3. Arrival and Service Patterns
4. Queue Discipline
Multiple Channels
Multiple Phases
Channel: A server in a service system
Poisson Distribution
Poisson distribution is a discrete probability distribution and expresses the probability of a number of
events occurring in a fixed period of time if these events occur with a known average rate, and are
independent of the time since the last event.
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Waiting Line Models
As a student of Operations Management we can identify the following types of Waiting Line Models in
our day to day routine activities.
1.
Patient :Customers enter the waiting line and remain until served
2.
Reneging: Waiting customers grow impatient and leave the line
3.
Jockeying: Customers may switch to another line
4.
Balking: Upon arriving, decide the line is too long and decide not to enter the line
Waiting Time vs. Utilization
The figure represents an increase in system utilization at the expense of increase in both length of the
waiting line and average waiting time. These values increase as the utilization approaches 100 percent.
The implication is that under normal circumstances, 100 percent utilization is not a realization goal.
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Average number
on time waiting
in line
0
100
System
Waiting Time vs. Utilization
System Performance
1. Average number of customers waiting
2. Average time customers wait
3. System utilization
4. Implied cost
5. Probability that an arrival will have to wait
Example Service Station
Queuing Models: Infinite-Source
1. Single channel, exponential service time
2. Single channel, constant service time
3. Multiple channel, exponential service time
4. Multiple priority service, exponential service time
Priority Model
Processing
order
1
3
2
1
1
Waiting
Arrival
Exit
Service
line
Arrivals are assigned
System
a priority as they arrive
Finite-Source Formulas
T
Service Factor X =
T +U
Average Number Waiting L = N (1 - F )
L(T + U )  T (1 - F )
AverageWaiting TimeW =
=
N -L
XF
Average Number Running J = NF (1 - X )
Average Number being Served H = FNX
Number in Population N = J + L + H
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Finite-Source Queuing
Not waiting or
Being
Waiting
being served
served
J
L
H
U
W
T
Where we use the formula
Other Approaches Non Mathematical Approaches
1.
Reduce perceived waiting time
J +H
F=
2.
Magazines in waiting rooms
J +L+H
3.
Radio/television
4.
In-flight movies
5.
Filling out forms
6.
Derive benefits from waiting
7.
Place impulse items near checkout
8.
Advertise other goods/services
Simulation
Simulation: a descriptive technique that enables a decision maker to evaluate the behavior of a model
under various conditions.
1. Simulation models complex situations
2. Models are simple to use and understand
3. Models can play "what if" experiments
4. Extensive software packages available
Simulation Process
1. Identify the problem
2. Develop the simulation model
3. Test the model
4. Develop the experiments
5. Run the simulation and evaluate results
6. Repeat 4 and 5 until results are satisfactory
Monte Carlo Simulation
Monte Carlo method: Probabilistic simulation technique used when a process has a random component
1. Identify a probability distribution
2. Setup intervals of random numbers to match probability distribution
3. Obtain the random numbers
4. Interpret the results
Example Showing the use of Microsoft Excel
An Operations Manager makes best use of the power of Microsoft Excel by carrying out simulation.
The first picture below shows a snapshot which carries the formulae and the second picture represents
the actual values.
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Simulating Distributions commonly used are the Poisson and Normal Distributions.
Poisson Distribution: Mean of distribution is required
Normal Distribution: Need to know the mean and standard deviation
Stimulated Value= Mean + Random Number X Standard Deviation
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Uniform Distribution
F(x)
0
a
b
x
Stimulated Value= a+ (b-a)(Random number as a percentage)
Computer Simulation
Simulation languages
1. SIMSCRIPT II.5
2. GPSS/H
3. GPSS/PC
4. RESQ
Advantages of Simulation
1. Solves problems that are difficult or impossible to solve mathematically
2. Allows experimentation without risk to actual system
3. Compresses time to show long-term effects
4. Serves as training tool for decision makers
Limitations of Simulation
1. Does not produce optimum solution
2. Model development may be difficult
3. Computer run time may be substantial
4. Monte Carlo simulation only applicable to random systems
Why Simulation is necessary
1. Mathematics involved is too complicated
2. Easier to manipulate than reality
3. Software and hardware permit modeling
Simulation Steps
1. Problem formulation
2. Model building
3. Data acquisition
4. Model translation
5. Verification & validation
6. Experiment planning & execution
7. Analysis
8. Implementation & documentation
Operations Strategy
1. The central idea for formulating an Operations Strategy for Waiting Line concept is designing a
service system to achieve a balance between service capacity and customer waiting time.
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2. The operations strategy should be able to identify an appropriate and acceptable level of service
capacity as well as quality so waiting lines are not formed or formed which are manageable and
acceptable to the customers.
3. Often Organizations when challenged by lack of practical solutions or space constraints opt for
a more tangible quality based solutions by engaging the waiting customers in activities which
give the customers not only an opportunity to make use of the time but also to make the waiting
time less painful and more pleasant.
Summary
Analysis of waiting lines can be an important milestone in the design of improved service systems.
Waiting lines have a tendency to form in even those systems which in a macro sense are under loaded or
unloaded.
The arrival of customers at random times and variability of service times combine to create temporary
overloads. When this happens, waiting lines appear.
A major consideration in the analysis of the queuing systems is whether the number of potential
customers is limited (finite source) or whether entry to the system is unrestricted (infinite source).Of the
5 models we studied, 4 dealt with infinite source and 1 with finite source population.
As a rule, the models assume that customer arrival rates are described by Poisson distribution and
service time can be described by a negative exponential distribution.
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POMA Strategies beyond the final exam
1. In the long run (when factors of production change, any or combination of the factors of labor,
land, technology), productivity growth is almost everything if not everything.
2. Do not create artificial non operational management strategies means to balance capacity to
demand (It can cause competitive advantage to shift towards your competitor and your
organization losing the competition.
3. How much does it really cost to manufacture a product or develop a service ( refer to the
concept of total costs, which we learnt in our discussions on inventory management, alternative
capacity, quality, maintenance and waiting lines)
4. Competitive advantage in operational and organization strategy creates a win win situation for
the organization.
5. Operations Manager should learn to think at the margin (an addition in cost by 1 Rupee(unit
cost) would increase or decrease the revenue by 1 Rupee(unit revenue/benefit)).
6. How we as Operations Manager can play a part in minimization of costs of most important of
services in Pakistan i.e. education and medical. Trade off between Effectiveness and quality.
7. How and why Project Management concepts are equally important to Production Operations
Management and vice versa.
8. The importance of coordinating, planning, controlling, budgeting operations and project
activities in achieving our firms short and long term objectives.
9. The concepts of strategy, competitiveness and productivity, design of product and services,
design of work systems and facilities, concept of quality and system improvement as applicable
in organizations be applied to Pakistan.
10. How as Operations Manager we can communicate to masses the importance of Pakistani
domestic markets and how they help in capital formation. If we say no to foreign goods
consumption, foreign good would not come to our place and we can generate a well deserved
saving. That saving can be channelized to provide clean and drinkable water, better health care,
education or even used for infrastructural issues. e.g. if 1 % of Pakistani population saves Rs. 10
per week for 1 year alone we would have almost 780 million rupees or 12 to 13 Million US
dollars by which we can set biogas plants or waste incinerator boiler based power generation or
clean drinking waters or even institutions of higher learning.
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Table of Contents:
  1. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT
  2. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Decision Making
  3. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Strategy
  4. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Service Delivery System
  5. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Productivity
  6. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:The Decision Process
  7. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Demand Management
  8. Roadmap to the Lecture:Fundamental Types of Forecasts, Finer Classification of Forecasts
  9. Time Series Forecasts:Techniques for Averaging, Simple Moving Average Solution
  10. The formula for the moving average is:Exponential Smoothing Model, Common Nonlinear Trends
  11. The formula for the moving average is:Major factors in design strategy
  12. The formula for the moving average is:Standardization, Mass Customization
  13. The formula for the moving average is:DESIGN STRATEGIES
  14. The formula for the moving average is:Measuring Reliability, AVAILABILITY
  15. The formula for the moving average is:Learning Objectives, Capacity Planning
  16. The formula for the moving average is:Efficiency and Utilization, Evaluating Alternatives
  17. The formula for the moving average is:Evaluating Alternatives, Financial Analysis
  18. PROCESS SELECTION:Types of Operation, Intermittent Processing
  19. PROCESS SELECTION:Basic Layout Types, Advantages of Product Layout
  20. PROCESS SELECTION:Cellular Layouts, Facilities Layouts, Importance of Layout Decisions
  21. DESIGN OF WORK SYSTEMS:Job Design, Specialization, Methods Analysis
  22. LOCATION PLANNING AND ANALYSIS:MANAGING GLOBAL OPERATIONS, Regional Factors
  23. MANAGEMENT OF QUALITY:Dimensions of Quality, Examples of Service Quality
  24. SERVICE QUALITY:Moments of Truth, Perceived Service Quality, Service Gap Analysis
  25. TOTAL QUALITY MANAGEMENT:Determinants of Quality, Responsibility for Quality
  26. TQM QUALITY:Six Sigma Team, PROCESS IMPROVEMENT
  27. QUALITY CONTROL & QUALITY ASSURANCE:INSPECTION, Control Chart
  28. ACCEPTANCE SAMPLING:CHOOSING A PLAN, CONSUMER’S AND PRODUCER’S RISK
  29. AGGREGATE PLANNING:Demand and Capacity Options
  30. AGGREGATE PLANNING:Aggregate Planning Relationships, Master Scheduling
  31. INVENTORY MANAGEMENT:Objective of Inventory Control, Inventory Counting Systems
  32. INVENTORY MANAGEMENT:ABC Classification System, Cycle Counting
  33. INVENTORY MANAGEMENT:Economic Production Quantity Assumptions
  34. INVENTORY MANAGEMENT:Independent and Dependent Demand
  35. INVENTORY MANAGEMENT:Capacity Planning, Manufacturing Resource Planning
  36. JUST IN TIME PRODUCTION SYSTEMS:Organizational and Operational Strategies
  37. JUST IN TIME PRODUCTION SYSTEMS:Operational Benefits, Kanban Formula
  38. JUST IN TIME PRODUCTION SYSTEMS:Secondary Goals, Tiered Supplier Network
  39. SUPPLY CHAIN MANAGEMENT:Logistics, Distribution Requirements Planning
  40. SUPPLY CHAIN MANAGEMENT:Supply Chain Benefits and Drawbacks
  41. SCHEDULING:High-Volume Systems, Load Chart, Hungarian Method
  42. SEQUENCING:Assumptions to Priority Rules, Scheduling Service Operations
  43. PROJECT MANAGEMENT:Project Life Cycle, Work Breakdown Structure
  44. PROJECT MANAGEMENT:Computing Algorithm, Project Crashing, Risk Management
  45. Waiting Lines:Queuing Analysis, System Characteristics, Priority Model