Modeling in Optimization

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Modeling in Optimization
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Models
A model is a necessary ingredient to optimization.

• Questions
• What are models?
• What is modeling?
• What is a good model?

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Models in OR

• The essence of OR lies in the construction and
  use of models.
• A model is a simplified representation of
  something real.
• There are different types of models.

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EcoSystem Landscape Models
Surface Water Height Difference (m) Between
Release and Baseline due to Textile Mill in
Location 2
Suppose we placed Interfaces factory in this
ecosystem. What would happen?
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Facility Eco-Dash
Integrated Financial Environmental Performance
Monitoring
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Paint Line Model
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Gear Manufacturing
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Gears are part of this
How do you model this?
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Paper versus Plastic B2B Packaging
Conventional Packaging (cardboard)
From Shanghai, China
Regrind
New Packaging (plastic)
Transmission Part (aluminum)
Reprocessing into splash shields (parts)
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Rethinking Sourcing Options

• Packaging work led to rethinking of where to
  source from
• Environmental Sourcing Tool helps assessing
  emissions from
• Production in different localities with different
  electrical generation emissions.
• E.g., hydro vs coal
• Transport modes and distances

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Decision Support
A Goal Integration of data, models, knowledge
learning to support high impact decision-making
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The Modeling Process (in OR)
Formulation
Model
Real system
Deduction
Interpretation
Real conclusions
Model conclusions
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Formulation

• Formulation
• Often considered to be an art.
• Typical questions to answer in formulating a
  model
• What aspects of the real system should be
  included, which can be ignored?
• What assumptions can and should be made?

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Deduction

• Deduction
• Involves techniques that depend on the nature of
  the model.
• It may involve solving equations, running a
  computer program, expressing a sequence of
  logical statements whatever it takes to solve
  the problem of interest relative to the model.
• It should not be subject to differences of
  opinion, provided that the assumptions are
  clearly stated and identified.

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Interpretation

• Interpretation
• Again involves a large amount of human judgment.
• The model conclusions must be translated to the
  real world conclusions, in full cognizance of
  possible discrepancies between the model and its
  real-world referent.

Remember Ties between model and system are
often only at best ties of plausible association,
SO BE CAREFUL WITH THE CONCLUSIONS!!!!
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Validation  An Introduction

• The process of acquiring the conviction that a
  model actually works is commonly called
  validation.
• When people are persuaded or convinced that a
  model is useful in some basic context, they will
  speak of it as a valid model.
• However, the validity is often restricted to a
  certain context.
• Hence, it is vital to know the limitations of the
  model.
• Some people may never accept a model.

Validation is a considerably weaker term than
"proof"
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The Scientific Method (in natural science)
Inductive generalization
Hypothesis
Real system
Testing and revision
Verification
Application
Real conclusions
Theory
Models are invented Theories are discovered
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How about design?

• What is the difference between designing,
  modeling, and OR?

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Difference between OR and designing
build and test
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Modeling and Designing

• Designing is very open-ended
• This openness is very unique
• Openness is troublesome, but a fact of life.

• Ask yourself,
• how would you model the process of configuring a
  general arrangement of parts, and solve it as a
  mathematical optimization problem?
• You have to model and deal with geometrical
  forms, type of motions, force transmissions, etc.
• Combining all these issues in a single model is
  almost impossible

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Types of Design

• Three types of design are often considered (e.g.,
  Pahl and Beitz)
• Original Design an original solution principle
  is determined for a desired system and used to
  create the design of a product.
• Adaptive Design an existing design is adapted
  to different conditions or tasks thus, the
  solution principle remains the same but the
  product will be sufficiently different so that it
  can meet the changed tasks that have been
  specified.
• Variant Design the size and/or arrangement of
  parts or subsystems of the chosen system are
  varied. The desired tasks and solution principle
  are not changed.

Where do you think optimization is most used?
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Modeling and Optimization in Design

• Shape optimization is relatively frequently done.
• Configuration optimization is difficult.
• Invariably, you have to account for hierarchical
  interactions.
• Questions to be asked when modeling designs
• Does the problem contain identifiable components?
• How are the components linked?
• Can we identify component variables and system
  variables?
• Does the system interact with other systems at
  the same level and/or higher levels?

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Some Basic Principles of Modeling
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Principles of Modeling

• 1. Do not build a complicated model when a simple
  one will suffice.
• This can be contrary to traditional mathematics
  or when one wants to build a general, strong
  model. Typically, though, a useful model is a
  simple model.
• 2. Beware of molding the problem to fit the
  technique.
• This happens often if somebody is an "expert" in
  a specific solution technique. However,
  optimization is just one of many decision support
  techniques.

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Principles of Modeling

• 3. The deduction phase of modeling must be
  conducted rigorously.
• If you do this and the conclusions are
  inconsistent with reality, then the fault lies in
  the assumptions.
• Be extremely careful with computer programs
  which may contain hidden bugs.

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Principles of Modeling

• 4. Models should be validated prior to
  implementation.
• Some ways to do this
• retrospective testing against historical data
  (especially for forecasting models).
• If the model is supposed to represent a class of
  things, test it against members of a class which
  was not used in the modeling (e.g., as in
  regression analysis).
• systematically vary parameters in the model and
  real system (if possible) and see whether the
  changes in behavior match.
• construct artificial tests, e.g., enter extreme
  values and see what happens (zero is always an
  interesting number to try).

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Principles of Modeling

• 5. A model should never be taken too literally.
• This sounds obvious, but is often forgotten as
  the model grows and is supposed to be more
  accurate
• 6. A models should neither be pressed to do, nor
  criticized for failing to do, that for which it
  was never intended.
• Always remember and investigate the original
  context in which a model was made (e.g., a model
  for predicting the resistance of fishing vessels
  should not be used for aircraft carriers).

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Principles of Modeling

• 7. Beware of overselling a model.
• It is very tempting to state that your model can
  solve all problems in the world, but be truthful.
  Honesty goes a long way and keeps you out of
  lawsuits.
• 8. Some of the primary benefits of modeling are
  associated with the process of developing the
  model.
• The model itself never contains the full
  knowledge and understanding of the real system
  that the builder must acquire in order to
  successfully model it.

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Principles of Modeling

• 9. A model cannot be better than the information
  that goes into it.
• Garbage In, Garbage Out (GIGO) is very
  applicable to modeling.
• Also, models do not create information, but
  condense or convert information.
• In some cases, instead of exerting one's efforts
  on model construction, one would be better off
  just gathering more information about the real
  system.
• Be careful that you don't put in too much
  information.

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Principles of Modeling

• 10. Models cannot replace decision makers
• One of the most common misconceptions about the
  purpose of optimization and other OR models is
  that they are supposed to provide "optimal"
  solutions, free of human subjectivity and error.
• There are so many decisions and assumptions to
  be made in the modeling, that only in a
  restricted and tight context we can speak of
  optimal solutions.
• A human decision maker is always necessary,
  whether you like it or not.