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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 Bina Nusantara University basic solution 3 • 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. Bina Nusantara University 4 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. Bina Nusantara University 5 Bina Nusantara University 6 Bina Nusantara University 7 Bina Nusantara University 8 Bina Nusantara University 9 Bina Nusantara University 10