Modular Product Family Design

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Modular Product Family Design

• Dhananjay Trichinapally

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Categorization of Product Family Design

• Function Configuration (Architecture) Models
• Module Configuration Models
• Catalog problems
• New design problems
• Parametric problems

Rahul Rai, (2002) Module Based Product Family
Design An Agent-Based Optimization Method ,IJPR
2002.
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Research Questions???

• Development of a game theory framework to handle
  multi-objective nature of the product family
  design problem.
• How to determine the minimum number of module
  types and instances that can generate an entire
  family of products for all the market segments
  while maximizing the profit of a company.
• A Methodology for developing product platform.

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Overall Framework
Optimization Using Game Theory Approach
Model for platforming
Input
Stage 1
Stage 2
Stage 3
NonCooperative game theory Nash equilibrium
Post Optimal Analysis Stackable Game Theory
Catalog of modules
For the optimal Platform solution Generated
Cooperative game theory Pareto solution set
Post Optimal Analysis Stackable Game Theory
Hierarchal game theory Stackelberg game theory
(single leader/Nash followers)
Post Optimal Analysis Stackable Game Theory
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Game Theory

• Pareto Game ( cooperative game theory)
• Cooperative game theory assumes that each player
  is a member of a team willing to compromise his
  own objective to improve the solution as a whole.
  In the cooperative solution, the team would
  reallocate the resources with the intent that all
  the players should be as optimal as possible-in
  other words, a Pareto optimal solution.
• Nash game theory (Non cooperative game theory)
• Non-cooperative theory of game assumes that each
  player is looking out for his own interests. Each
  player select his share of resources only with
  the view of optimizing his own objective and does
  not care for other players. The players then
  bargain with each other, exchanging resources,
  until an equilibrium is reached. The resultant
  solution is referred to as a Nash equilibrium.
• Stackelberg game theory
• In Stackelbergs (Single leader/Nash
  followers) game theory considers a case when one
  player dominates another,i.e a player who holds
  the powerful position in is called the leader,
  and the other players who react (rationally) to
  the leaders decision (strategy) are called the
  followers.

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Data
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Approach

• Two step approach
• Developing a Pareto optimal solutions
• Post-optimal analysis

Stage 1
Stage 2
Total Design Solutions
Pareto-surface
Optimal solution
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Pareto Solution
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Game theory Cont
Stackelbergs Leader/follower Game theory
P1 Leader
D1
To Follow
Not to Follow
P2 Followers
D2
D2
Y
N
N
Y
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Flow Chart For The Two Step Approach
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Pareto Optimization

• Initialization
• Create design solutions from the inputs
• (modules and module characteristics)
• Satisfy
• Design constraints
• In an iterative approach, select solution x1 such
  that
• The solution is x1 strictly better than x2 in at
  least one objective
• i.e., fi(x1) ? fi(x2) for at least one i
  ?1,2,, M.
• 2. The solution x1 is no worse (say the operator
  ? denotes worse
• and ? denotes better) than x2 in all
  objectives
• i.e., fi(x1) ? fi(x2) ? i 1,2,, M
  objectives.
• Objectives
• minimize cost
• minimize weight
• maximize cubic feet area
• maximize capacity
• maximize horsepower

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Nash Game Theory

• Initialization
• Create design solutions from the inputs
• (modules and module characteristics)
• Satisfy
• Design constraints
• In an iterative approach, select solution f(x1N,
  x2N) such that
• Select design solution satisfying
• f(x1N, x2N)gt f(x1, x2N), for more then
  one i ?1,2,, M.
• Objectives
• minimize cost
• minimize weight
• maximize cubic feet area
• maximize capacity
• maximize horsepower
• Goal
• Develop a Nash solution representing a dominated
  surface

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Stackelberg Game Theory (Leader and Nash
followers)

• Initialization
• Create design solutions from the inputs
• (modules and module characteristics)
• Satisfy
• Design constraints
• Leader
• In an iterative approach, select solution x1 such
  that
• The solution is x1 as the maximum capacity
  objective.
• Objective
• maximize capacity
• Follower
• After satisfying the leaders objective, In an
  iterative approach,
• select solution f(x1N, x2N) such that
  
• Select design solution satisfying
• f(x1N, x2N)gt f(x1, x2N), for more then
  one i ?1,2,, M.
• Objectives
• minimize cost

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Results
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Results Contd
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STACKELBERG GAME THEORY
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Results
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Methodology for Platforms Development

• Monte Carlo Simulations of the Ising ModelThe
  Ising model is a simple model of magnetism. Ising
  model is used to measure physical properties of
  an n-dimensional lattice spin .Each spin has
  the value -1 or1 representing positive and
  negative charges respectively. The energy of this
  system is given by the Hamiltonian equation

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The Ising Model

• The Ising model is a simple model of magnetism.
  Ising model is used to measure physical
  properties of an n-dimensional lattice spin
  .Each spin has the value -1 or1 representing
  positive and negative charges respectively. The
  energy of this system is given by the Hamiltonian
  equation

where lti,jgt gives the nearest neighbors of i
The basic algorithm for this simulation is as
follows (1) Pick a random lattice location (2)
Calculate the change in the system energy is spin
is flipped (3) accept move with prob min(1,
)
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Ising Model Flow Chart
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Quality Loss Function

• Quadratic function of QLF

where, L(y)-Loss in dollars due to a deviation
away from the targeted
performance. y- measured response for
a product. m- target value of the
products response. k- is a constant
known as quality loss coefficient.
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Algorithm steps

• Establish an initial microstate a random initial
  configuration of spins.
• Make a random trial change in the microstate
  choose a spin at random and flip it, si gt - si.
• Compute E E trial E old, the change in
  the energy of the system due to the trial change.
  
• If E lt 0, accept the new microstate and go to
  step 8.
• If E gt 0, compute the Boltzmann weighting
  factor w exp-( E)/kT.
• Generate a random number r in the unit interval.
• If r lt w, accept the new microstate otherwise
  retain the previous microstate.
• Determine the value of the desired physical
  quantities.
• Repeat steps (2) through (8) to obtain a
  sufficient number of microstates.
• Periodically compute averages over microstates.

Steps 2 through 7 give the conditional
probability that the system is in microstate
sj given that it was in microstate si.
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Results
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References

• Baldwin Y. C. and K. B. Clark, 1997, Managing in
  an age of modularity, Harvard Business Review,
  Sep-Oct 1997, pp 84-93.
• Baldwin Y. C. and K. B. Clark, 1999, Design
  Rules The power of modularity, MIT press,
  Cambridge, MA.
• Fujita K., H. Sakaguchi. and S. Akagi, 1999,
  Product variety deployment and its optimization
  under modular architecture and module
  communalization, DETC99/DFM-8923, Las Vegas,
  Nevada.
• Fujita K. and H. Yoshida, 2001, Product variety
  optimization Simultaneous optimization of module
  combination and module attributes,
  DETC01/DAC-21058, Pittsburgh, Pennsylvania.
• Gonzalez-Zugasti J. and K. N.Otto, 1999,
  Assessing value for product platform design and
  selection, DETC99/DAC-8613, Las Vegas, Nevada.
• Gonzalez-Zugasti J. and K. N. Otto, 2000,
  Platform-based spacecraft design A formulation
  implementation procedure, IEEE Aerospace
  Conference, Big Sky, MT, March 18-24, 2000. Paper
  13.0401. IEEE Paper Number 0-7803-5846-5/00.

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Questions?