Abstract
Efficient extreme points in decision space of multiple objective linear programming (MOLP) may not map to non dominated extreme points in objective space under the linear mapping, condition that efficient extreme points have a non dominated extreme is given, the important of this study is that the decision-Maker may depends on extreme points of the set of the objective space than that of the decision space since they have fewer extreme points.
Highlights
The multiple objectives linear programming (MOLP) problems arises when several linear objective functions has to be maximized on a convex polytope
More researches involve the objective space analysis of multiple objective linear programming has been studied by[7] relation between faces of the decision space and those of the objective space was investigated by[8], the reason for this investigation is that the objective space may have fewer dimension than those of the decision space under the linear mapping
Solving (MOLP) problem is to find the set of efficient solution E where E={x X | there is no x X such that C x ≤ C x }
Summary
The multiple objectives linear programming (MOLP) problems arises when several linear objective functions has to be maximized (or minimized) on a convex polytope. We say that y is non dominated point if y Y and there is no y Y such that y ≤ y .For (MOLP) problem defined by (1.1) if x is a basic feasible solution of A x = b, x ≥ 0 with corresponding basic decomposition. The canonical simplex tableau for x in multiple objective forms can be defined as: Notations and theory: Multiple objective linear programming (MOLP) problems arises when several linear objective functions has to be maximized (or minimized) on a convex polytope. Where A is an m x n matrix and b Rm. Solving (MOLP) problem is to find the set of efficient solution E where E={x X | there is no x X such that C x ≤ C x }
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