4120_lecture-10-F10

4120_lecture-10-F10 - Computational Methods for Management...

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Computational Methods for Management and Economics Carla Gomes Lecture 10 Reading: 4.1-4.3 of textbook
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Outline Simplex: algebraic procedure By hand Using IOR Java applet (CD textbook)
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Corner Point Solutions Corner-point feasible solution – special solution that plays a key role when the simplex method searches for an optimal solution. Relationship between optimal solutions and CPF solutions: Any LP with feasible solutions and bounded feasible region (1) the problem must possess CPF solutions and at least one optimal solution (2) the best CPF solution must be an optimal solution Ι f the problem has exactly one optimal solution it must be a CFP solution If the problem has multiple optimal solutions, at least two must be CPF solutions
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Geometric View Point of Simplex Method Iterative procedure involving the following steps: 1. Initialization – find initial CPF solution Whenever possible pick (0,0) as initial solution 1. Optimality test (check value of Z of adjacent CPF solutions) 1. Iteration – find a better CPF solution; go to 2. 1. Consider edges that emanate from current CPF solution and pick the one that increases Z at a faster rate 2. Stop at the first new constraint boundary
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Wyndor Glass   0 2 4 6 8 8 6 4 2 Production rate for windows Production rate for doors Feasible region (2, 6) Optimal solution 10 W D P = 3600 = 300D + 500W P = 3000 = 300D + 500W P = 1500 = 300D + 500W CPF Edge of Feasible region 0 1 Z=0 Z=30 Let D
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