Simulation Modeling and
Analysis
Session 13
Simulation Optimization
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Outline
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Introduction
Evolutionary Algorithms
Single Variable Optimization
An inventory control problem
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Introduction
• Optimization is the science of determining
“best” solutions to mathematically defined
problems, which are often models of
physical reality.
• Simulation is a methodology to transform
inputs (decision variables) into outputs
(performance measures).
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Simulation Optimization
• Simulation Optimization is a methodology
to discover the values of decision variables
required to minimize or maximize specific
measures of performance.
• Typically, from a starting set of inputs
simulation computes outputs. These are
used in turn by an optimization algorithm to
produce an improved set of inputs.
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How to find optima?
1.- Identify all possible decision variables affecting
the output of the system.
2.- Using all possible values of each decision
variable identify all possible solutions (I.e. the
response surface).
3.- Evaluate all solutions accurately
4.- Compare each solution fairly
5.- Select the best answer
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Optimization of well posed
problems
• Well posed problems
– Have unique solutions.
– Small changes in inputs produce
correspondingly small changes in output.
• Numerical methods such as NewtonRaphson and Linear Programming are
available to optimize well posed problems.
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Optimization of stochastic
simulation model problems
• Stochastic simulation models
– Not well posed
– Complex response surfaces
• Heuristic techniques are available to
optimize stochastic simulation problems.
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Evolutionary Algorithms
• EA conduct search of response surface
using a population of solutions.
• Information about the response surface is
then provided from many points at once.
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Steps in Evolutionary Algorithms
1.- Generate a population of solutions by randomly
distributing throughout solution space.
2.- Accurately compute the response of each
solution.
3.- Select the best solutions and apply genetic
operators to produce new offspring solutions.
4.- Return to step 2 until a single solution emerges.
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Single Variable Optimization
• The Transformed Ackley function
– Local optima
• Many maxima and minima
– Global optima
• Two maxima (x = +9.54 and x = -9.54)
• One minimum (x = 0)
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Ackley function
• Randomly select 10 values of x (initial
offspring size = 10) from -10 < x < -8
• Challenge: to evolve from the original
offspring to the minimum without stopping
at the local minima.
• Result: Global minimum is determined after
8 generations.
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Inventory Control Problem
• What is the minimum amount of inventory
required to support production in a JIT
environment where parts are pulled through
the system using kanban cards?
• Number of kanban cards influences WIP.
• Trigger values = number of kanban cards
that must accumulate before a workstation
begins production
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Two-Stage Pull Production
• Two-Stage Pull Production System
– Customer demand pulls subassemblies from Stage
One WIP to Assembly Lines.
– Kanban card sent to Stage One Process. When
trigger value is reached parts are pulled from Stage
Two WIP to process.
– Following processing, subassemblies and kanban
cards are sent to Stage One WIP.
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Two-Stage Pull Production contd
– Stage Two Line processes raw materials into
component parts to be pulled by Stage One.
– As components are pulled from Stage Two WIP
a kanban card is sent to the kanban post for
Stage Two Line. When trigger value is reached
production orders are issued to Stage Two Line.
– As orders are completed at Stage Two Line, orders
and kanban cards are sent to Stage Two WIP.
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Two-Stage Pull Production contd
• Goal: Minimize inventory at the State One
WIP location. Maximize throughput while
minimizing the number of kanban cards in
the system.
• Performance measure to be minimized
f(a) = C1 (A + M) - C2 (TK1) - C3 (TK2)
• Solution Vector (I = 11 part types)
a = (K1i,K2i,TK2i)
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Two-Stage Pull Production contd
• Model:
– Constant interarrival times for customer orders.
– Number of defective subassemblies found at the
assembly lines is stochastic.
– Production times for Stage One Process and Stage
Two Line are constant.
– Set up time, time between failures and time to repair
have triangular distributions.
– Runs: 10 day warm up and 20 day steady state.
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Two-Stage Pull Production contd
• Four independent runs of the models are
performed each time a solution is evaluated.
• Performance score is the average of the four
runs.
• SimRunner finds 110 kanban cards and f =
37.945 after 150 generations.
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