Linear Cases, MC- and MC2-Simplex Methods
We shall discuss some interesting properties of N-points when X is a polyhedron and the constant dominated cone is also polyhedral in Section 8.1. A multiple-criteria (MC) simplex method is then described in Section 8.2 to facilitate the location of N-points. Identification of optimal weights for each nondominated extreme point is also discussed. In Section 8.3 we shall discuss a method to generate all N-points using known extreme N-points. As a natural extension of MC simplex methods, a multiple-criteria and multiple-constraint level (MC2) simplex method is then described in Section 8.4. Potential solutions and duality theory of MC- and MC2-simplex are then discussed. MC- and MC2-simplex methods have been extensively studied by Gal (see Ref. 155) in the context of sensitivity analysis of linear programming problems. Here we use them as tools for locating N-points as well as formulating solution concepts. Note that throughout this chapter we focus on constant dominated cone structures for N-points, unless otherwise specified.
KeywordsExtreme Point Potential Solution Optimal Weight Simplex Method Nondominated Solution
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