OO-CH5_handouts.pdf - 1 Operationeel Onderzoek Chapter 5 Prof dr Lieselot Vanhaverbeke drs Quentin De Clerck L.Vanhaverbeke 2 The Theory of the Simplex

OO-CH5_handouts.pdf - 1 Operationeel Onderzoek Chapter 5...

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© 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
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© 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
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© 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
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© L. Vanhaverbeke
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