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Course
Year
: D0744 - Deterministic Optimization
: 2009
Linear Programming
Meeting 4
Linear Programming – Review
Solving Systems of Linear Equations:
• What is a basic solution?
• How did we obtain a basic solution?
• What is a basic feasible solution?
Relationship between graphical and algebraic
representation of the feasible region:
corner point
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basic solution
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• Fundamental insight – the optimal solution to a linear
program, if it exists, is also a basic feasible solution.
• Naïve approach – solve for all basic solutions and find
the feasible solution with the largest value (maximization
problem).
• What is the problem with this approach? – there are
n
n!
  
 m  m!(n  m)!
possible basic solutions, where m is the number of
constraints and n is the number of variables.
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Simplex Algorithm
Step 1
Step 2
Step 3
Step 4
Convert the LP to standard form.
Obtain a bfs (if possible) from the standard form.
Determine whether the current bfs is optimal.
If the current bfs is not optimal, then determine
which nonbasic basic variable should become a
basic variable and which basic variable should
become a nonbasic variable to find a new bfs with a
better objective function value. (pivot operation)
Step 5 Use EROs to find the new bfs with the better
objective function value. Go back to step 3.
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