WrapUp for Linear Programming

1
Wrap-Up for Linear Programming

• RPAD 504
• Data, Models,and Decisions I

2
How Does the Simplex Algorithm Guess the Optimum

• In our problem sets, we set up the problem and
  iteratively guessed (explored) for the optimum.
• How does the simplex algorithm do this?

3
How Does the Simplex Algorithm Guess the
Optimum (continued)

• Always guess at a corner point
• Solve N equations in NM unknowns
• Where N is the number of activity variables
• and M is the number of constraints
• Enter one slack or surplus variable for each
  constraint
• For Large Problems, there can be trillions of
  corner points

4
How Does the Simplex Algorithm Guess the
Optimum (continued)

• Always pick a corner point where the objective
  function is increasing (avoids wandering)
• Always pick a next corner point where objective
  function is increasing most rapidly (most
  efficient)
• Unique optimum assured by convex shape of
  constraint space and duality theorem (they got
  the Nobel Prize for figuring this out)

5
Optimization as a Conceptual Framework

• Ill let you define the objective if youll let
  me define the constraints Herbert Simon
• Even if you never compute an optimal solution,
  thinking about what optimal means in a formal
  sense can help you think about your
  organizations operations.

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Optimization as a Conceptual Framework (continued)

• Activity variables construct a vast space of all
  possible outputs that our organization might
  produce.
• Constraints carve out a feasible region in that
  space.
• Always strive toward the frontier (minimize slack
  and surplus)
• Clear objectives/objective functions (tradeoffs
  between activities) define the best outcome.