© L. Vanhaverbeke Operationeel Onderzoek Chapter 5 Prof. dr. Lieselot Vanhaverbeke drs. Quentin De Clerck 1 © L. Vanhaverbeke The Theory of the Simplex Method Chapter 5 2
© L. Vanhaverbeke 5.1 Foundations of the Simplex Method • Constraint boundary equation • Obtained by replacing the inequality sign in the constraint equation with an equals sign • Defines a hyperplane in n -dimensional space • Any point on the boundary of the feasible region lies on at least one of the hyperplanes • Corner-point feasible (CPF) solution in n -dimensional space • Feasible solution not on any line segment connecting two other feasible solutions 3 © L. Vanhaverbeke Foundations of the Simplex Method • For a linear programming problem with n decision variables: • Each CPF solution lies at the intersection of n constraint boundaries • This is the simultaneous solution of n constraint boundary equations • A system of n constraint boundary equations might have no solution • Or yield an infeasible solution 4
© L. Vanhaverbeke Foundations of the Simplex Method • Adjacent CPF solutions • Lie on a line segment forming an edge of the feasible region • Polyhedron planes form the boundary of the feasible region • Darker line segment illustrates the path of the simplex method • On a typical iteration 5 © L. Vanhaverbeke 6
© L. Vanhaverbeke
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