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4120_lecture9-F10

# 4120_lecture9-F10 - Computational Methods for Management...

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Unformatted text preview: Computational Methods for Management and Economics Carla Gomes Lecture 9 Reading: 3.6-3.8 of textbook Introduction to Simplex (Textbook – Hillier and Lieberman) LP Concepts • Corner point feasible solution (CPF solution) – intersection of n (or more; n - number of variables) constraint boundaries; • For any LP with n decision variables two CPF solutions are adjacent to each other if they share (n-1) constraint boundaries • Edge of feasible region – intersection of the (n-1) constraint boundaries shared by two adjacent CPF solutions • Optimality test – for any LP problem that possesses at least one optimal solution, if a CPF solution has no adjacent CPF solutions that are better (as measure by Z) then it must be an optimal solution Algebraic Model for Wyndor Glass Co. Let D = the number of doors to produce W = the number of windows to produce Maximize P = 3 D + 5 W subject to D ≤ 4 2 W ≤ 12 3 D + 2 W ≤ 18 and D ≥ 0, W ≥ 0. Wyndor Glass 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 3D feasible region Edge of feasible region between two CPFS’s the edge is the line that lies at the intersection of the common constraint boundaries of the two CPFS’s 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 Geometric View Point of Simplex Method...
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4120_lecture9-F10 - Computational Methods for Management...

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