Transcript Operations

SUPPLEMENT
Simulation Analysis
Reid & Sanders, Operations Management
© Wiley 2002
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Learning Objectives
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Describe the role of simulation analysis
Describe different types of simulation models
Identify the steps in simulation modeling
Simulate the passage of time
Generate random phenomena
Evaluate simulation output
Describe simulation software
Reid & Sanders, Operations Management
© Wiley 2002
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Simulation
• A simulation model is a set
mathematical functions, probability
distributions, and decision rules that
mimic the way a system acts under
specific conditions.
• The goal is description, not optimization.
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© Wiley 2002
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Common Applications
• Evaluation of alternative designs &
operating procedures:
– Production & queuing systems
– Capacity planning
– Machine & personnel scheduling
– Shop routing
– Facility layout & location
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Example: Inventory Analysis
• How much of a product should be ordered &
when?
• What is the best level of safety stock to hold
for crucial raw materials?
• In a system with multiple locations, where
should inventories be held & how much at
each location?
• How much work-in-process inventory should
be held between workstations?
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© Wiley 2002
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Terminology
• Entities:
– Interrelated system components
• Attributes:
– The system variables under observation
• States:
– The status of the attributes at a point in time
• Events:
– A measurable change in the system
Reid & Sanders, Operations Management
© Wiley 2002
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Types of Models
• The nature of events:
– Continuous event models: changes to the system
(events) occur rapidly & relatively uninterrupted
– Discrete event models: events occur at readily
identifiable points in time
• Randomness of change:
– Stochastic models include random (or
probabilistic) changes to system attributes
– Deterministic models assume no random
phenomenon
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© Wiley 2002
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Step-by-Step:
Modeling & Analysis
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Understand the system
Construct the system components
Test the model
Plan the experimental design
Execute the model runs
Analyze the output
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© Wiley 2002
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Understand the System
• Questions to explore:
– What is the purpose of the simulation (what do
you want to learn)?
– What entities & relationships are important?
– What attributes describe the state of the system?
– Do events occur in a random or discrete fashion?
– Do attribute values change randomly?
– How is system performance evaluated?
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© Wiley 2002
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Construct Components
• Break the system into manageable pieces
– Example: customer arrivals, waiting line queues, etc.
• Observe actual behavior (gather performance data)
• Identify probability distributions that estimate any
random phenomena
– Poisson, binominal, normal distributions, etc.
– Confirm using chi-square analysis
• Identify the decision rules (define how system attributes
change when an event occurs)
– Example: first come-first served; reservations given priority
• Code the modules & the system links
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© Wiley 2002
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Test the Model
• First, test each module for accuracy
– Does the model estimate the actual performance
observed?
• Second, link the components together & test
the entire model:
– If the system being modeled already exists,
compare the computer model’s performance with
the performance of the existing system (they
should match)
– Track down any problems & reprogram the model
Reid & Sanders, Operations Management
© Wiley 2002
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Experimental Design
• Terminology:
– Experiment: one configuration of the
simulation model
– Run: a single sampling of the experiment
• Design the Experiment:
– Identify the alternatives to explore (often
changes to decision rules)
– Identify criteria to compare the relative
performance of each alternative
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© Wiley 2002
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Execute Model Runs
& Analyze Output
• Use relatively short runs to narrow your
focus & then longer runs of better
alternatives
• Compare performance of various
alternatives suing statistical methods
– Confidence intervals, t-tests, ANOVA, etc.
– Are differences statistically significant?
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© Wiley 2002
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Simulating Time
• Quickly estimate system performance over a
long period of time:
– Fixed-Time Incrementing:
• Determine what unit of time is appropriate (e.g.: minutes,
days, months) given how rapidly the system changes
• Each cycle through the system might represent the
passage of a unit of time
– Next-Event Incrementing:
• If events occur irregularly, jump ahead to the next time
something happens (using a representative probability
distribution)
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© Wiley 2002
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Random Number Generators
• Random number generators provide a
sequence of values that approximate a
randomly observed value from a continuous,
uniform distribution between one and zero.
• Often we use pseudorandom numbers (the
same sequence of ‘random’ values for each
experiment) to allow us to directly compare
different system configurations.
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© Wiley 2002
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Generating Discrete
Random Values
• Use random generators to provide the next r
(a random or pseudorandom value, uniformly
distributed between one & zero)
• For discrete variables, identify an appropriate
range to correspond with each possible value
– The width of the assigned range should
correspond with the probability of that discrete
value occurring
– For example: when modeling a coin toss, if r is
greater than 0.5 then the coin equals ‘heads’, if r is
less than 0.5, the coin equals ‘tails’.
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Generating Continuous
Random Values
• Use the random number generator to
provide the next r, then convert r to an
observation (x) from the appropriate
probability distribution.
• For example:
– Uniform distribution:
When a  x  b, then x  a  r b  a
– Poisson distribution:
When   arrival rate, then x  ln r  /  
Reid & Sanders, Operations Management
© Wiley 2002
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Evaluating Output
• Consider using pseudorandom numbers to
allow direct performance comparisons
between experiments
• Evaluate average performance and the
distribution of performance measures
– Example: in some experiments you may find short
average waiting times, but that a few times wait a
very, very long time to be processed (this might
not be acceptable – particularly if you’re modeling
customers waiting in a queue).
Reid & Sanders, Operations Management
© Wiley 2002
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Computer Software
• Special-purpose simulation software
– E.g.: Simfactory, Map/1
– Easy to code, but lack flexibility
• General-purpose simulation software
– E.g.: Slam, Simscript, GPSS, Siman
– Still relatively easy to program, more flexibility
• General-purpose programming languages
– E.g: Fortran, Basic, C++
– Require more programming skill, but provide
maximum flexibility
Reid & Sanders, Operations Management
© Wiley 2002
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Considerations
• Programming languages versus simulation packages:
– The complexity of the simulation planned
– The variety of simulations likely to be performed in the future
– The modeling & programming skills of the user
• Choosing between simulation software:
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Can new subroutines be added to increase flexibility?
How easy is it to compute statistics on system performance?
Is there a graphical interface or animation capability?
Are diagnostics aids and error messages provided to help
debug programming errors?
Reid & Sanders, Operations Management
© Wiley 2002
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The End
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Reid & Sanders, Operations Management
© Wiley 2002
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